| Arkansas | K.CC.A.1 | Count to 100 by ones, fives, and tens. | Kindergarten |
| Arkansas | K.CC.A.2 | Count forward, by ones, from any given number up to 100. | Kindergarten |
| Arkansas | K.CC.A.3 | Read, write, and represent numerals from 0 to 20. | Kindergarten |
| Arkansas | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten |
| Arkansas | K.CC.B.5 | Count to answer how many; count up to 20 objects in an arrangement, count up to 10 objects in a scattered configuration, given a number from 1-20 count out that many objects. | Kindergarten |
| Arkansas | K.CC.C.6 | Identify whether the number of objects in one group from 0-10 is greater than (more, most), less than (less, fewer, least), or equal to (same as) the number of objects in another group of 0-10. | Kindergarten |
| Arkansas | K.CC.C.7 | Compare two numbers between 0 and 20 presented as written numerals. | Kindergarten |
| Arkansas | K.CC.C.8 | Quickly identify a number of items in a set from 0-10 without counting (e.g., dominoes, dot cubes, tally marks, ten-frames). | Kindergarten |
| Arkansas | K.G.A.1 | Describe the positions of objects in the environment and geometric shapes in space using names of shapes, and describe the relative positions of these objects. | Kindergarten |
| Arkansas | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Arkansas | K.G.A.3 | Identify shapes as two-dimensional or three-dimensional. | Kindergarten |
| Arkansas | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Arkansas | K.G.B.5 | Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Kindergarten |
| Arkansas | K.G.B.6 | Compose two-dimensional shapes to form larger two-dimensional shapes. | Kindergarten |
| Arkansas | K.MD.A.1 | Describe several measurable attributes of a single object, including but not limited to length, weight, height, and temperature . | Kindergarten |
| Arkansas | K.MD.A.2 | Describe the difference when comparing two objects (side-by-side) with a measurable attribute in common, to see which object has more of or less of the common attribute. | Kindergarten |
| Arkansas | K.MD.B.3 | Classify, sort, and count objects using both measureable and non-measureable attributes such as size, number, color, or shape. | Kindergarten |
| Arkansas | K.MD.C.4 | Understand concepts of time including morning, afternoon, evening, today, yesterday, tomorrow, day, week, month and year. Understand that clocks, both analog and digital, and calendars are tools thatmeasure time. | Kindergarten |
| Arkansas | K.MD.C.5 | Read time to the hour on digital and analog clocks. | Kindergarten |
| Arkansas | K.MD.C.6 | Identify pennies, nickels, and dimes, and know the vlaue of each. | Kindergarten |
| Arkansas | K.NBT.A.1 | Develop initial understanding of place value and the base-ten number system by showing equivalent forms of whole numbers from 11 to 19 as groups of tens and ones using objects and drawings. | Kindergarten |
| Arkansas | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Arkansas | K.OA.A.2 | Solve real-world problems that involve addition and subtraction within 10 (e.g., by using objects or drawings to represent the problem). | Kindergarten |
| Arkansas | K.OA.A.3 | Use objects or drawings to decompose (break apart) numbers less than or equal to 10 into pairs in more than one way, and record each decomposition (part) by a drawing or an equation. | Kindergarten |
| Arkansas | K.OA.A.4 | Find the number that makes 10 when added to the given number (e.g., by using objects or drawings) and record the answer with a drawing or equation. | Kindergarten |
| Arkansas | K.OA.A.5 | Fluently add and subtract within 10 by using various strategies and manipulatives. | Kindergarten |
| Arkansas | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Arkansas | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Arkansas | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Arkansas | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Arkansas | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Arkansas | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Arkansas | 1.MD.B.4 | Identify and know the value of a penny, nickel, dime and quarter. | Grade 1 |
| Arkansas | 1.MD.B.5 | Count collections of like coins (pennies, nickels, and dimes). | Grade 1 |
| Arkansas | 1.MD.C.6 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Arkansas | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Arkansas | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| Arkansas | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 |
| Arkansas | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Arkansas | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Arkansas | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Arkansas | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. | Grade 1 |
| Arkansas | 1.OA.A.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 . | Grade 1 |
| Arkansas | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 |
| Arkansas | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 |
| Arkansas | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Arkansas | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Arkansas | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| Arkansas | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 |
| Arkansas | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Arkansas | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Arkansas | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Arkansas | 2.G.A.4 | Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Arkansas | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Arkansas | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Arkansas | 2.MD.A.3 | Estimate lengths using units of inches, feet, centimeters, and meters. | Grade 2 |
| Arkansas | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Arkansas | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Arkansas | 2.MD.B.6 | Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram. | Grade 2 |
| Arkansas | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Arkansas | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Arkansas | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Arkansas | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Arkansas | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| Arkansas | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Arkansas | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Arkansas | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons. | Grade 2 |
| Arkansas | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Arkansas | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Arkansas | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Arkansas | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Arkansas | 2.NBT.B.9 | Explain why addition and subtraction strategies work, using place value and the properties of operations. | Grade 2 |
| Arkansas | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Arkansas | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Arkansas | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Arkansas | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Arkansas | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Arkansas | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Arkansas | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Arkansas | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Arkansas | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Arkansas | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Arkansas | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Arkansas | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Arkansas | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Arkansas | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Arkansas | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Arkansas | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Arkansas | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Arkansas | 3.NBT.A.4 | Understand that the four digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones. | Grade 3 |
| Arkansas | 3.NBT.A.5 | Read and write numbers to 10,000 using base-ten numerals, number names, and expanded form(s). | Grade 3 |
| Arkansas | 3.NBT.A.6 | Compare two four-digit numbers based on meanings of thousands, hundreds, tens, and ones digits using symbols (<, >, =) to record the results of comparisons. | Grade 3 |
| Arkansas | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| Arkansas | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 |
| Arkansas | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 3 |
| Arkansas | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. | Grade 3 |
| Arkansas | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. | Grade 3 |
| Arkansas | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Arkansas | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ? | Grade 3 |
| Arkansas | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 |
| Arkansas | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| Arkansas | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Arkansas | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Arkansas | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Arkansas | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Arkansas | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Arkansas | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Arkansas | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Arkansas | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Arkansas | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Arkansas | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Arkansas | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Arkansas | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Arkansas | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Arkansas | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 |
| Arkansas | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Arkansas | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Arkansas | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Arkansas | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Arkansas | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Arkansas | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Arkansas | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Arkansas | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 |
| Arkansas | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 |
| Arkansas | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| Arkansas | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 |
| Arkansas | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Arkansas | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Arkansas | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Arkansas | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Arkansas | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 — 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 |
| Arkansas | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| Arkansas | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Arkansas | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Arkansas | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Arkansas | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Arkansas | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Arkansas | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Arkansas | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Arkansas | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Arkansas | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Arkansas | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Arkansas | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Arkansas | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Arkansas | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Arkansas | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Arkansas | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Arkansas | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Arkansas | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Arkansas | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Arkansas | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| Arkansas | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Arkansas | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 |
| Arkansas | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| Arkansas | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Arkansas | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Arkansas | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Arkansas | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 |
| Arkansas | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Arkansas | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Arkansas | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Arkansas | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Arkansas | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Arkansas | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Arkansas | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| Arkansas | 6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Arkansas | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Arkansas | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 |
| Arkansas | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 |
| Arkansas | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Arkansas | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Arkansas | 6.NS.B.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. | Grade 6 |
| Arkansas | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Arkansas | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Arkansas | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Arkansas | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Arkansas | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Arkansas | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 |
| Arkansas | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 |
| Arkansas | 6.SP.A.1 | Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. | Grade 6 |
| Arkansas | 6.SP.A.2 | Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. | Grade 6 |
| Arkansas | 6.SP.A.3 | Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. | Grade 6 |
| Arkansas | 6.SP.B.4 | Display numerical data in plots on a number line, including dot plots, histograms, and box plots. | Grade 6 |
| Arkansas | 6.SP.B.5 | Summarize numerical data sets in relation to their context. | Grade 6 |
| Arkansas | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Arkansas | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Arkansas | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Arkansas | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Arkansas | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Arkansas | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Arkansas | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Arkansas | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Arkansas | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Arkansas | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Arkansas | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Arkansas | 7.NS.A.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 |
| Arkansas | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Arkansas | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 |
| Arkansas | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Arkansas | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Arkansas | 7.SP.A.1 | Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. | Grade 7 |
| Arkansas | 7.SP.A.2 | Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. | Grade 7 |
| Arkansas | 7.SP.B.3 | Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. | Grade 7 |
| Arkansas | 7.SP.B.4 | Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. | Grade 7 |
| Arkansas | 7.SP.C.5 | Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. | Grade 7 |
| Arkansas | 7.SP.C.6 | Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. | Grade 7 |
| Arkansas | 7.SP.C.7 | Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. | Grade 7 |
| Arkansas | 7.SP.C.8 | Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | Grade 7 |
| Arkansas | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Arkansas | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Arkansas | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 |
| Arkansas | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| Arkansas | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| Arkansas | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Arkansas | 8.EE.C.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 |
| Arkansas | 8.EE.C.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 |
| Arkansas | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Arkansas | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| Arkansas | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| Arkansas | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Arkansas | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Arkansas | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Arkansas | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Arkansas | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Arkansas | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Arkansas | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Arkansas | 8.G.B.6 | Explain a proof of the Pythagorean Theorem and its converse. | Grade 8 |
| Arkansas | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Arkansas | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Arkansas | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Arkansas | 8.NS.A.1 | Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. | Grade 8 |
| Arkansas | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Arkansas | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Arkansas | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Arkansas | 8.SP.A.3 | Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. | Grade 8 |
| Arkansas | 8.SP.A.4 | Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. | Grade 8 |
| Arkansas | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra |
| Arkansas | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra |
| Arkansas | A-REI.C.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | Algebra |
| Arkansas | A-REI.C.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3. | Algebra |
| Arkansas | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra |
| Arkansas | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra |
| Arkansas | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra |
| Arkansas | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| Arkansas | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra |
| Arkansas | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra |
| Arkansas | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra |
| Arkansas | S-ID.C.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | Algebra |
| Arizona | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra |
| Arizona | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra |
| Arizona | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra |
| Arizona | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra |
| Arizona | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra |
| Arizona | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| Arizona | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra |
| Arizona | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra |
| Arizona | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra |
| Arizona | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Arizona | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Arizona | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Arizona | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| Arizona | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 |
| Arizona | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Arizona | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Arizona | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Arizona | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 |
| Arizona | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 |
| Arizona | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Arizona | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Arizona | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| Arizona | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 |
| Arizona | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Arizona | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Arizona | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Arizona | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Arizona | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| Arizona | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Arizona | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Arizona | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons. | Grade 2 |
| Arizona | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Arizona | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Arizona | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Arizona | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Arizona | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Arizona | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Arizona | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Arizona | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Arizona | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ñhow many moreî and ñhow many lessî problems using information presented in scaled bar graphs. | Grade 3 |
| Arizona | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Arizona | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Arizona | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Arizona | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Arizona | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Arizona | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Arizona | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations. | Grade 3 |
| Arizona | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| Arizona | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 |
| Arizona | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 3 |
| Arizona | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 _ 7. | Grade 3 |
| Arizona | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56
8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56
8. | Grade 3 |
| Arizona | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Arizona | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 _ ? = 48, 5 = _
3, 6 _ 6 = ? | Grade 3 |
| Arizona | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 _ 4 = 24 is known, then 4 _ 6 = 24 is also known. (Commutative property of multiplication.) 3 _ 5 _ 2 can be found by 3 _ 5 = 15, then 15 _ 2 = 30, or by 5 _ 2 = 10, then 3 _ 10 = 30. (Associative property of multiplication.) Knowing that 8 _ 5 = 40 and 8 _ 2 = 16, one can find 8 _ 7 as 8 _ (5 + 2) = (8 _ 5) + (8 _ 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 |
| Arizona | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32
8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| Arizona | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40
5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Arizona | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Arizona | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Arizona | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Arizona | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Arizona | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Arizona | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| Arizona | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Arizona | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Arizona | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 |
| Arizona | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Arizona | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Arizona | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Arizona | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Arizona | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Arizona | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Arizona | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or | Grade 4 |
| Arizona | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 |
| Arizona | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 |
| Arizona | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| Arizona | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 |
| Arizona | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 4 |
| Arizona | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Arizona | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Arizona | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 |
| Arizona | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| Arizona | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Arizona | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Arizona | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Arizona | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Arizona | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Arizona | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Arizona | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Arizona | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Arizona | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Arizona | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Arizona | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Arizona | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Arizona | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| Arizona | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Arizona | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 |
| Arizona | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| Arizona | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Arizona | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Arizona | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 |
| Arizona | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Arizona | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Arizona | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Arizona | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Arizona | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| Arizona | 6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Arizona | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 |
| Arizona | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 |
| Arizona | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Arizona | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Arizona | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Arizona | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Arizona | 6.NS.C.7 | Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. | Grade 6 |
| Arizona | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Arizona | 6.NS.C.9 | Convert between expressions for positive rational numbers, including fractions, decimals, and percents. | Grade 6 |
| Arizona | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Arizona | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 |
| Arizona | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 |
| Arizona | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Arizona | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Arizona | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Arizona | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Arizona | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Arizona | 7.NS.A.1 | Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. | Grade 7 |
| Arizona | 7.NS.A.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 |
| Arizona | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Arizona | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 |
| Arizona | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Arizona | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Arizona | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 |
| Arizona | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| Arizona | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| Arizona | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Arizona | 8.EE.C.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 |
| Arizona | 8.EE.C.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 |
| Arizona | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Arizona | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| Arizona | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| Arizona | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Arizona | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Arizona | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| Arizona | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Arizona | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Arizona | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Arizona | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Arizona | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Arizona | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Arizona | K.CC.A.1 | Count to 100 by ones and by tens | Kindergarten |
| Arizona | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Arizona | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Arizona | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten |
| Arizona | K.CC.B.5 | Count to answer 'how many' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Arizona | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Arizona | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Arizona | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Arizona | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Arizona | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Arizona | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Arizona | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Arizona | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| California | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| California | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| California | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| California | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| California | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| California | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| California | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| California | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| California | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| California | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| California | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| California | K.G.5 | Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Kindergarten |
| California | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| California | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| California | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| California | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| California | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| California | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| California | K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| California | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| California | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| California | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| California | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| California | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| California | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| California | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| California | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| California | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| California | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| California | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| California | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 |
| California | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| California | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| California | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| California | 1.NBT.6 | Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| California | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| California | 1.OA.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| California | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| California | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| California | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| California | 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| California | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| California | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| California | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| California | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| California | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| California | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| California | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| California | 2.MD.3 | Estimate lengths using units of inches, feet, centimeters, and meters. | Grade 2 |
| California | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| California | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| California | 2.MD.6 | Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, . . . , and represent whole-number sums and differences within 100 on a number line diagram. | Grade 2 |
| California | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). | Grade 2 |
| California | 2.MD.8 | Solve word problems involving combinations of dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| California | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| California | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| California | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 |
| California | 2.NBT.2 | Count within 1000; skip-count by 2s, 5s, 10s, and 100s. | Grade 2 |
| California | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| California | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| California | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| California | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| California | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| California | 2.NBT.7.1 | Use estimation strategies to make reasonable estimates in problem solving. | Grade 2 |
| California | 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| California | 2.NBT.9 | Explain why addition and subtraction strategies work, using place value and the properties of operations. | Grade 2 |
| California | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| California | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| California | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| California | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| California | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| California | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| California | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| California | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| California | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| California | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| California | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| California | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| California | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| California | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| California | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| California | 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| California | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| California | 3.NF.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| California | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| California | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| California | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| California | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| California | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| California | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| California | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| California | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| California | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| California | 3.OA.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| California | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| California | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| California | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two-dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) | Grade 4 |
| California | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| California | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| California | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| California | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 |
| California | 4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| California | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| California | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| California | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| California | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| California | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| California | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| California | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| California | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| California | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| California | 4.NF.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| California | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| California | 4.NF.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| California | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| California | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| California | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| California | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model. | Grade 4 |
| California | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| California | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| California | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| California | 4.OA.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| California | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| California | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| California | 5.G.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| California | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| California | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| California | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. | Grade 5 |
| California | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| California | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| California | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| California | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| California | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| California | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| California | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| California | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| California | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| California | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| California | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| California | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| California | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| California | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| California | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| California | 5.NF.5 | Interpret multiplication as scaling (resizing), by: | Grade 5 |
| California | 5.NF.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| California | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| California | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| California | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| California | 5.OA.2.1 | Express a whole number in the range 2-50 as a product of its prime factors. | Grade 5 |
| California | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| California | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| California | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| California | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| California | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| California | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| California | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| California | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| California | 6.EE.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 < 𝘤 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form 𝘹 > 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| California | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| California | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| California | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| California | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| California | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| California | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| California | 6.RP.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| California | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| California | 6.SP.1 | Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. | Grade 6 |
| California | 6.SP.2 | Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. | Grade 6 |
| California | 6.SP.3 | Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. | Grade 6 |
| California | 6.SP.4 | Display numerical data in plots on a number line, including dot plots, histograms, and box plots. | Grade 6 |
| California | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| California | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| California | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| California | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| California | 6.NS.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. | Grade 6 |
| California | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| California | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| California | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| California | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| California | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| California | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| California | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| California | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| California | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| California | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| California | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| California | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| California | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| California | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| California | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| California | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| California | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| California | 7.SP.1 | Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. | Grade 7 |
| California | 7.SP.2 | Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. | Grade 7 |
| California | 7.SP.3 | Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. | Grade 7 |
| California | 7.SP.4 | Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. | Grade 7 |
| California | 7.SP.5 | Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. | Grade 7 |
| California | 7.SP.6 | Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. | Grade 7 |
| California | 7.SP.7 | Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. | Grade 7 |
| California | 7.SP.8 | Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | Grade 7 |
| California | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| California | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| California | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| California | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| California | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| California | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| California | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| California | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| California | 8.EE.6 | Use similar triangles to explain why the slope 𝘮 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| California | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| California | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| California | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| California | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| California | 8.F.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| California | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| California | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| California | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| California | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| California | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| California | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| California | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| California | 8.G.6 | Explain a proof of the Pythagorean Theorem and its converse. | Grade 8 |
| California | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| California | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| California | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| California | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| California | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| California | 8.SP.3 | Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. | Grade 8 |
| California | 8.SP.4 | Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. | Grade 8 |
| California | 8.NS.1 | Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. | Grade 8 |
| California | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Algebra I |
| California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra I |
| California | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra I |
| California | A-APR.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Algebra I |
| California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. | Algebra I |
| California | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra I |
| California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Algebra I |
| California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Algebra I |
| California | A-REI.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | Algebra I |
| California | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra I |
| California | A-REI.3.1 | Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. | Algebra I |
| California | A-REI.4 | Solve quadratic equations in one variable. | Algebra I |
| California | A-REI.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | Algebra I |
| California | A-REI.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | Algebra I |
| California | A-REI.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | Algebra I |
| California | A-REI.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | Algebra I |
| California | A-REI.11 | Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Algebra I |
| California | A-REI.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | Algebra I |
| California | F-IF.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹). | Algebra I |
| California | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra I |
| California | F-IF.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | Algebra I |
| California | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra I |
| California | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Algebra I |
| California | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Algebra I |
| California | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra I |
| California | F-IF.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Algebra I |
| California | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Algebra I |
| California | F-BF.1 | Write a function that describes a relationship between two quantities. | Algebra I |
| California | F-BF.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | Algebra I |
| California | F-BF.3 | Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Algebra I |
| California | F-BF.4 | Find inverse functions. | Algebra I |
| California | F-LE.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. | Algebra I |
| California | F-LE.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | Algebra I |
| California | F-LE.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | Algebra I |
| California | F-LE.5 | Interpret the parameters in a linear or exponential function in terms of a context. | Algebra I |
| California | F-LE.6 | Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. | Algebra I |
| California | N-RN.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | Algebra I |
| California | N-RN.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | Algebra I |
| California | N-RN.3 | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | Algebra I |
| California | N-Q.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | Algebra I |
| California | N-Q.2 | Define appropriate quantities for the purpose of descriptive modeling. | Algebra I |
| California | N-Q.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | Algebra I |
| California | S-ID.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | Algebra I |
| California | S-ID.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | Algebra I |
| California | S-ID.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | Algebra I |
| California | S-ID.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | Algebra I |
| California | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra I |
| California | S-ID.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | Algebra I |
| California | S-ID.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | Algebra I |
| California | S-ID.9 | Distinguish between correlation and causation. | Algebra I |
| California | G-CO.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | Geometry |
| California | G-CO.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | Geometry |
| California | G-CO.3 | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | Geometry |
| California | G-CO.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | Geometry |
| California | G-CO.5 | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | Geometry |
| California | G-CO.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | Geometry |
| California | G-CO.7 | Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | Geometry |
| California | G-CO.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | Geometry |
| California | G-CO.9 | Prove theorems about lines and angles. | Geometry |
| California | G-CO.10 | Prove theorems about triangles. | Geometry |
| California | G-CO.11 | Prove theorems about parallelograms. | Geometry |
| California | G-CO.12 | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). | Geometry |
| California | G-CO.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | Geometry |
| California | G-SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor: | Geometry |
| California | G-SRT.2 | Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | Geometry |
| California | G-SRT.3 | Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar. | Geometry |
| California | G-SRT.4 | Prove theorems about triangles. | Geometry |
| California | G-SRT.5 | Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | Geometry |
| California | G-SRT.6 | Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. | Geometry |
| California | G-SRT.7 | Explain and use the relationship between the sine and cosine of complementary angles. | Geometry |
| California | G-SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | Geometry |
| California | G-SRT.8.1 | Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90° and 45°, 45°, 90°). | Geometry |
| California | G-SRT.9 | Derive the formula 𝐴 = 1/2 𝘢𝘣 sin(𝐶) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | Geometry |
| California | G-SRT.10 | Prove the Laws of Sines and Cosines and use them to solve problems. | Geometry |
| California | G-SRT.11 | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | Geometry |
| California | G-C.1 | Prove that all circles are similar. | Geometry |
| California | G-C.2 | Identify and describe relationships among inscribed angles, radii, and chords. | Geometry |
| California | G-C.3 | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | Geometry |
| California | G-C.4 | Construct a tangent line from a point outside a given circle to the circle. | Geometry |
| California | G-C.5 | Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. | Geometry |
| California | G-GPE.1 | Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | Geometry |
| California | G-GPE.2 | Derive the equation of a parabola given a focus and directrix. | Geometry |
| California | G-GPE.4 | Use coordinates to prove simple geometric theorems algebraically. | Geometry |
| California | G-GPE.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | Geometry |
| California | G-GPE.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | Geometry |
| California | G-GPE.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. | Geometry |
| California | G-GMD.1 | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. | Geometry |
| California | G-GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | Geometry |
| California | G-GMD.4 | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | Geometry |
| California | G-GMD.5 | Know that the effect of a scale factor 𝑘 greater than zero on length, area, and volume is to multiply each by 𝑘, 𝑘², and 𝑘³, respectively; determine length, area and volume measures using scale factors. | Geometry |
| California | G-GMD.6 | Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems. | Geometry |
| California | G-MG.1 | Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | Geometry |
| California | G-MG.2 | Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). | Geometry |
| California | G-MG.3 | Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). | Geometry |
| California | S-CP.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). | Geometry |
| California | S-CP.2 | Understand that two events 𝘈 and 𝘉 are independent if the probability of 𝘈 and 𝘉 occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | Geometry |
| California | S-CP.3 | Understand the conditional probability of 𝘈 given 𝘉 as 𝘗(𝘈 and 𝘉)/𝘗(𝘉), and interpret independence of 𝘈 and 𝘉 as saying that the conditional probability of 𝘈 given 𝘉 is the same as the probability of 𝘈, and the conditional probability of 𝘉 given 𝘈 is the same as the probability of 𝘉. | Geometry |
| California | S-CP.4 | Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | Geometry |
| California | S-CP.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | Geometry |
| California | S-CP.6 | Find the conditional probability of 𝘈 given 𝘉 as the fraction of 𝘉’s outcomes that also belong to 𝘈, and interpret the answer in terms of the model. | Geometry |
| California | S-CP.7 | Apply the Addition Rule, 𝘗(𝘈 or 𝘉) = 𝘗(𝘈) + 𝘗(𝘉) – 𝘗(𝘈 and 𝘉), and interpret the answer in terms of the model. | Geometry |
| California | S-CP.8 | Apply the general Multiplication Rule in a uniform probability model, 𝘗(𝘈 and 𝘉) = 𝘗(𝘈)𝘗(𝘉|𝘈) = 𝘗(𝘉)𝘗(𝘈|𝘉), and interpret the answer in terms of the model. | Geometry |
| California | S-CP.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. | Geometry |
| California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Geometry |
| California | S-MD.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Geometry |
| California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Algebra II |
| California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra II |
| California | A-SSE.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | Algebra II |
| California | A-APR.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Algebra II |
| California | A-APR.2 | Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹). | Algebra II |
| California | A-APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra II |
| California | A-APR.4 | Prove polynomial identities and use them to describe numerical relationships. | Algebra II |
| California | A-APR.5 | Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle. | Algebra II |
| California | A-APR.6 | Rewrite simple rational expressions in different forms; write 𝘢(𝘹)/𝘣(𝘹) in the form 𝘲(𝘹) + 𝘳(𝘹)/𝘣(𝘹), where 𝘢(𝘹), 𝘣(𝘹), 𝘲(𝘹), and 𝘳(𝘹) are polynomials with the degree of 𝘳(𝘹) less than the degree of 𝘣(𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system. | Algebra II |
| California | A-APR.7 | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. | Algebra II |
| California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. | Algebra II |
| California | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra II |
| California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Algebra II |
| California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Algebra II |
| California | A-REI.2 | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | Algebra II |
| California | A-REI.3.1 | Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. | Algebra II |
| California | A-REI.11 | Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Algebra II |
| California | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra II |
| California | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Algebra II |
| California | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Algebra II |
| California | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra II |
| California | F-IF.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Algebra II |
| California | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Algebra II |
| California | F-BF.1 | Write a function that describes a relationship between two quantities. | Algebra II |
| California | F-BF.3 | Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Algebra II |
| California | F-BF.4 | Find inverse functions. | Algebra II |
| California | F-LE.4 | For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology. | Algebra II |
| California | F-LE.4.1 | Prove simple laws of logarithms. | Algebra II |
| California | F-LE.4.2 | Use the definition of logarithms to translate between logarithms in any base. | Algebra II |
| California | F-LE.4.3 | Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. | Algebra II |
| California | F-TF.1 | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | Algebra II |
| California | F-TF.2 | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | Algebra II |
| California | F-TF.2.1 | Graph all 6 basic trigonometric functions. | Algebra II |
| California | F-TF.5 | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | Algebra II |
| California | F-TF.8 | Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. | Algebra II |
| California | G-GPE.3.1 | Given a quadratic equation of the form ax² + by2 + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation. | Algebra II |
| California | N-CN.1 | Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real. | Algebra II |
| California | N-CN.2 | Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | Algebra II |
| California | N-CN.7 | Solve quadratic equations with real coefficients that have complex solutions. | Algebra II |
| California | N-CN.8 | Extend polynomial identities to the complex numbers. | Algebra II |
| California | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | Algebra II |
| California | S-ID.4 | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | Algebra II |
| California | S-IC.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | Algebra II |
| California | S-IC.2 | Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | Algebra II |
| California | S-IC.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | Algebra II |
| California | S-IC.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | Algebra II |
| California | S-IC.5 | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | Algebra II |
| California | S-IC.6 | Evaluate reports based on data. | Algebra II |
| California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Algebra II |
| California | S-MD.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Algebra II |
| California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Mathematics I |
| California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. | Mathematics I |
| California | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Mathematics I |
| California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Mathematics I |
| California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Mathematics I |
| California | A-REI.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | Mathematics I |
| California | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Mathematics I |
| California | A-REI.3.1 | Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. | Mathematics I |
| California | A-REI.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | Mathematics I |
| California | A-REI.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | Mathematics I |
| California | A-REI.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | Mathematics I |
| California | A-REI.11 | Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Mathematics I |
| California | A-REI.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | Mathematics I |
| California | F-IF.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹). | Mathematics I |
| California | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Mathematics I |
| California | F-IF.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | Mathematics I |
| California | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Mathematics I |
| California | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Mathematics I |
| California | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Mathematics I |
| California | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Mathematics I |
| California | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Mathematics I |
| California | F-BF.1 | Write a function that describes a relationship between two quantities. | Mathematics I |
| California | F-BF.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | Mathematics I |
| California | F-BF.3 | Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Mathematics I |
| California | F-LE.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. | Mathematics I |
| California | F-LE.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | Mathematics I |
| California | F-LE.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | Mathematics I |
| California | F-LE.5 | Interpret the parameters in a linear or exponential function in terms of a context. | Mathematics I |
| California | G-CO.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | Mathematics I |
| California | G-CO.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | Mathematics I |
| California | G-CO.3 | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | Mathematics I |
| California | G-CO.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | Mathematics I |
| California | G-CO.5 | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | Mathematics I |
| California | G-CO.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | Mathematics I |
| California | G-CO.7 | Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | Mathematics I |
| California | G-CO.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | Mathematics I |
| California | G-CO.12 | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). | Mathematics I |
| California | G-CO.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | Mathematics I |
| California | G-GPE.4 | Use coordinates to prove simple geometric theorems algebraically. | Mathematics I |
| California | G-GPE.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | Mathematics I |
| California | G-GPE.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. | Mathematics I |
| California | N-Q.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | Mathematics I |
| California | N-Q.2 | Define appropriate quantities for the purpose of descriptive modeling. | Mathematics I |
| California | N-Q.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | Mathematics I |
| California | S-ID.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | Mathematics I |
| California | S-ID.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | Mathematics I |
| California | S-ID.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | Mathematics I |
| California | S-ID.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | Mathematics I |
| California | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Mathematics I |
| California | S-ID.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | Mathematics I |
| California | S-ID.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | Mathematics I |
| California | S-ID.9 | Distinguish between correlation and causation. | Mathematics I |
| California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Mathematics II |
| California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Mathematics II |
| California | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Mathematics II |
| California | A-APR.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Mathematics II |
| California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. | Mathematics II |
| California | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Mathematics II |
| California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Mathematics II |
| California | A-REI.4 | Solve quadratic equations in one variable. | Mathematics II |
| California | A-REI.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | Mathematics II |
| California | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Mathematics II |
| California | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Mathematics II |
| California | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Mathematics II |
| California | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Mathematics II |
| California | F-IF.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Mathematics II |
| California | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Mathematics II |
| California | F-BF.1 | Write a function that describes a relationship between two quantities. | Mathematics II |
| California | F-BF.3 | Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Mathematics II |
| California | F-BF.4 | Find inverse functions. | Mathematics II |
| California | F-LE.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | Mathematics II |
| California | F-LE.6 | Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. | Mathematics II |
| California | F-TF.8 | Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. | Mathematics II |
| California | G-CO.9 | Prove theorems about lines and angles. | Mathematics II |
| California | G-CO.10 | Prove theorems about triangles. | Mathematics II |
| California | G-CO.11 | Prove theorems about parallelograms. | Mathematics II |
| California | G-SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor: | Mathematics II |
| California | G-SRT.2 | Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | Mathematics II |
| California | G-SRT.3 | Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar. | Mathematics II |
| California | G-SRT.4 | Prove theorems about triangles. | Mathematics II |
| California | G-SRT.5 | Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | Mathematics II |
| California | G-SRT.6 | Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. | Mathematics II |
| California | G-SRT.7 | Explain and use the relationship between the sine and cosine of complementary angles. | Mathematics II |
| California | G-SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | Mathematics II |
| California | G-SRT.8.1 | Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90° and 45°, 45°, 90°). | Mathematics II |
| California | G-C.1 | Prove that all circles are similar. | Mathematics II |
| California | G-C.2 | Identify and describe relationships among inscribed angles, radii, and chords. | Mathematics II |
| California | G-C.3 | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | Mathematics II |
| California | G-C.4 | Construct a tangent line from a point outside a given circle to the circle. | Mathematics II |
| California | G-C.5 | Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. | Mathematics II |
| California | G-GPE.1 | Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | Mathematics II |
| California | G-GPE.2 | Derive the equation of a parabola given a focus and directrix. | Mathematics II |
| California | G-GPE.4 | Use coordinates to prove simple geometric theorems algebraically. | Mathematics II |
| California | G-GPE.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | Mathematics II |
| California | G-GMD.1 | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. | Mathematics II |
| California | G-GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | Mathematics II |
| California | G-GMD.5 | Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k², and k³, respectively; determine length, area and volume measures using scale factors. | Mathematics II |
| California | G-GMD.6 | Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems. | Mathematics II |
| California | N-RN.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | Mathematics II |
| California | N-RN.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | Mathematics II |
| California | N-RN.3 | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | Mathematics II |
| California | N-CN.1 | Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real. | Mathematics II |
| California | N-CN.2 | Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | Mathematics II |
| California | N-CN.7 | Solve quadratic equations with real coefficients that have complex solutions. | Mathematics II |
| California | N-CN.8 | Extend polynomial identities to the complex numbers. | Mathematics II |
| California | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | Mathematics II |
| California | S-CP.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). | Mathematics II |
| California | S-CP.2 | Understand that two events 𝘈 and 𝘉 are independent if the probability of 𝘈 and 𝘉 occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | Mathematics II |
| California | S-CP.3 | Understand the conditional probability of 𝘈 given 𝘉 as 𝘗(𝘈 and 𝘉)/𝘗(𝘉), and interpret independence of 𝘈 and 𝘉 as saying that the conditional probability of 𝘈 given 𝘉 is the same as the probability of 𝘈, and the conditional probability of 𝘉 given 𝘈 is the same as the probability of 𝘉. | Mathematics II |
| California | S-CP.4 | Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | Mathematics II |
| California | S-CP.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | Mathematics II |
| California | S-CP.6 | Find the conditional probability of 𝘈 given 𝘉 as the fraction of 𝘉’s outcomes that also belong to 𝘈, and interpret the answer in terms of the model. | Mathematics II |
| California | S-CP.7 | Apply the Addition Rule, 𝘗(𝘈 or 𝘉) = 𝘗(𝘈) + 𝘗(𝘉) – 𝘗(𝘈 and 𝘉), and interpret the answer in terms of the model. | Mathematics II |
| California | S-CP.8 | Apply the general Multiplication Rule in a uniform probability model, 𝘗(𝘈 and 𝘉) = 𝘗(𝘈)𝘗(𝘉|𝘈) = 𝘗(𝘉)𝘗(𝘈|𝘉), and interpret the answer in terms of the model. | Mathematics II |
| California | S-CP.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. | Mathematics II |
| California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Mathematics II |
| California | S-MD.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Mathematics II |
| California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Mathematics III |
| California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Mathematics III |
| California | A-SSE.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | Mathematics III |
| California | A-APR.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Mathematics III |
| California | A-APR.2 | Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹). | Mathematics III |
| California | A-APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Mathematics III |
| California | A-APR.4 | Prove polynomial identities and use them to describe numerical relationships. | Mathematics III |
| California | A-APR.5 | Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle. | Mathematics III |
| California | A-APR.6 | Rewrite simple rational expressions in different forms; write 𝘢(𝘹)/𝘣(𝘹) in the form 𝘲(𝘹) + 𝘳(𝘹)/𝘣(𝘹), where 𝘢(𝘹), 𝘣(𝘹), 𝘲(𝘹), and 𝘳(𝘹) are polynomials with the degree of 𝘳(𝘹) less than the degree of 𝘣(𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system. | Mathematics III |
| California | A-APR.7 | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. | Mathematics III |
| California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. | Mathematics III |
| California | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Mathematics III |
| California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Mathematics III |
| California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Mathematics III |
| California | A-REI.2 | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | Mathematics III |
| California | A-REI.11 | Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Mathematics III |
| California | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Mathematics III |
| California | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Mathematics III |
| California | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Mathematics III |
| California | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Mathematics III |
| California | F-IF.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Mathematics III |
| California | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Mathematics III |
| California | F-BF.1 | Write a function that describes a relationship between two quantities. | Mathematics III |
| California | F-BF.3 | Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Mathematics III |
| California | F-BF.4 | Find inverse functions. | Mathematics III |
| California | F-LE.4 | For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology. | Mathematics III |
| California | F-LE.4.1 | Prove simple laws of logarithms. | Mathematics III |
| California | F-LE.4.2 | Use the definition of logarithms to translate between logarithms in any base. | Mathematics III |
| California | F-LE.4.3 | Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. | Mathematics III |
| California | F-TF.1 | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | Mathematics III |
| California | F-TF.2 | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | Mathematics III |
| California | F-TF.2.1 | Graph all 6 basic trigonometric functions. | Mathematics III |
| California | F-TF.5 | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | Mathematics III |
| California | G-SRT.9 | Derive the formula 𝐴 = 1/2 𝘢𝘣 sin(𝐶) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | Mathematics III |
| California | G-SRT.10 | Prove the Laws of Sines and Cosines and use them to solve problems. | Mathematics III |
| California | G-SRT.11 | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | Mathematics III |
| California | G-GPE.3.1 | Given a quadratic equation of the form ax² + by² + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation | Mathematics III |
| California | G-GMD.4 | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | Mathematics III |
| California | G-MG.1 | Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | Mathematics III |
| California | G-MG.2 | Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). | Mathematics III |
| California | G-MG.3 | Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). | Mathematics III |
| California | N-CN.8 | Extend polynomial identities to the complex numbers. | Mathematics III |
| California | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | Mathematics III |
| California | S-ID.4 | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | Mathematics III |
| California | S-IC.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | Mathematics III |
| California | S-IC.2 | Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | Mathematics III |
| California | S-IC.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | Mathematics III |
| California | S-IC.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | Mathematics III |
| California | S-IC.5 | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | Mathematics III |
| California | S-IC.6 | Evaluate reports based on data. | Mathematics III |
| California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Mathematics III |
| California | S-MD.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Mathematics III |
| California | N-Q.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | High School - Number and Quantity |
| California | N-Q.2 | Define appropriate quantities for the purpose of descriptive modeling. | High School - Number and Quantity |
| California | N-Q.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | High School - Number and Quantity |
| California | N-CN.1 | Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real. | High School - Number and Quantity |
| California | N-CN.2 | Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | High School - Number and Quantity |
| California | N-CN.3 | Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. | High School - Number and Quantity |
| California | N-CN.4 | Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. | High School - Number and Quantity |
| California | N-CN.5 | Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. | High School - Number and Quantity |
| California | N-CN.6 | Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. | High School - Number and Quantity |
| California | N-CN.7 | Solve quadratic equations with real coefficients that have complex solutions. | High School - Number and Quantity |
| California | N-CN.8 | Extend polynomial identities to the complex numbers. | High School - Number and Quantity |
| California | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | High School - Number and Quantity |
| California | N-RN.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | High School - Number and Quantity |
| California | N-RN.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | High School - Number and Quantity |
| California | N-RN.3 | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | High School - Number and Quantity |
| California | N-VM.1 | Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., 𝙫, |𝙫|, ||𝙫||, 𝙫). | High School - Number and Quantity |
| California | N-VM.2 | Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. | High School - Number and Quantity |
| California | N-VM.3 | Solve problems involving velocity and other quantities that can be represented by vectors. | High School - Number and Quantity |
| California | N-VM.4 | Add and subtract vectors. | High School - Number and Quantity |
| California | N-VM.5 | Multiply a vector by a scalar. | High School - Number and Quantity |
| California | N-VM.6 | Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. | High School - Number and Quantity |
| California | N-VM.7 | Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | High School - Number and Quantity |
| California | N-VM.8 | Add, subtract, and multiply matrices of appropriate dimensions. | High School - Number and Quantity |
| California | N-VM.9 | Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. | High School - Number and Quantity |
| California | N-VM.10 | Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. | High School - Number and Quantity |
| California | N-VM.11 | Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. | High School - Number and Quantity |
| California | N-VM.12 | Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. | High School - Number and Quantity |
| California | A-APR.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | High School - Algebra |
| California | A-APR.2 | Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹). | High School - Algebra |
| California | A-APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School - Algebra |
| California | A-APR.4 | Prove polynomial identities and use them to describe numerical relationships. | High School - Algebra |
| California | A-APR.5 | Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle. | High School - Algebra |
| California | A-APR.6 | Rewrite simple rational expressions in different forms; write 𝘢(𝘹)/𝘣(𝘹) in the form 𝘲(𝘹) + 𝘳(𝘹)/𝘣(𝘹), where 𝘢(𝘹), 𝘣(𝘹), 𝘲(𝘹), and 𝘳(𝘹) are polynomials with the degree of 𝘳(𝘹) less than the degree of 𝘣(𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system. | High School - Algebra |
| California | A-APR.7 | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. | High School - Algebra |
| California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. | High School - Algebra |
| California | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School - Algebra |
| California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School - Algebra |
| California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | High School - Algebra |
| California | A-REI.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | High School - Algebra |
| California | A-REI.2 | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | High School - Algebra |
| California | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School - Algebra |
| California | A-REI.3.1 | Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. | High School - Algebra |
| California | A-REI.4 | Solve quadratic equations in one variable. | High School - Algebra |
| California | A-REI.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | High School - Algebra |
| California | A-REI.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | High School - Algebra |
| California | A-REI.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | High School - Algebra |
| California | A-REI.8 | Represent a system of linear equations as a single matrix equation in a vector variable. | High School - Algebra |
| California | A-REI.9 | Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). | High School - Algebra |
| California | A-REI.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | High School - Algebra |
| California | A-REI.11 | Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | High School - Algebra |
| California | A-REI.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | High School - Algebra |
| California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | High School - Algebra |
| California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School - Algebra |
| California | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School - Algebra |
| California | A-SSE.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | High School - Algebra |
| California | F-BF.1 | Write a function that describes a relationship between two quantities. | High School - Functions |
| California | F-BF.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | High School - Functions |
| California | F-BF.3 | Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | High School - Functions |
| California | F-BF.4 | Find inverse functions. | High School - Functions |
| California | F-BF.5 | Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. | High School - Functions |
| California | F-IF.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹). | High School - Functions |
| California | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School - Functions |
| California | F-IF.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | High School - Functions |
| California | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School - Functions |
| California | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | High School - Functions |
| California | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | High School - Functions |
| California | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School - Functions |
| California | F-IF.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | High School - Functions |
| California | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | High School - Functions |
| California | F-IF.10 | Demonstrate an understanding of functions and equations defined parametrically and graph them. | High School - Functions |
| California | F-IF.11 | Graph polar coordinates and curves. Convert between polar and rectangular coordinate systems. | High School - Functions |
| California | F-LE.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. | High School - Functions |
| California | F-LE.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | High School - Functions |
| California | F-LE.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | High School - Functions |
| California | F-LE.4 | For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology. | High School - Functions |
| California | F-LE.4.1 | Prove simple laws of logarithms. | High School - Functions |
| California | F-LE.4.2 | Use the definition of logarithms to translate between logarithms in any base. | High School - Functions |
| California | F-LE.4.3 | Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. | High School - Functions |
| California | F-LE.5 | Interpret the parameters in a linear or exponential function in terms of a context. | High School - Functions |
| California | F-LE.6 | Apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. | High School - Functions |
| California | F-TF.1 | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | High School - Functions |
| California | F-TF.2 | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | High School - Functions |
| California | F-TF.2.1 | Graph all 6 basic trigonometric functions. | High School - Functions |
| California | F-TF.3 | Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–𝘹, π+𝘹, and 2π–𝘹 in terms of their values for 𝘹, where 𝘹 is any real number. | High School - Functions |
| California | F-TF.4 | Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. | High School - Functions |
| California | F-TF.5 | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | High School - Functions |
| California | F-TF.6 | Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. | High School - Functions |
| California | F-TF.7 | Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. | High School - Functions |
| California | F-TF.8 | Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. | High School - Functions |
| California | F-TF.9 | Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. | High School - Functions |
| California | F-TF.10 | Prove the half angle and double angle identities for sine and cosine and use them to solve problems. | High School - Functions |
| California | G-C.1 | Prove that all circles are similar. | High School - Geometry |
| California | G-C.2 | Identify and describe relationships among inscribed angles, radii, and chords. | High School - Geometry |
| California | G-C.3 | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | High School - Geometry |
| California | G-C.4 | Construct a tangent line from a point outside a given circle to the circle. | High School - Geometry |
| California | G-C.5 | Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. | High School - Geometry |
| California | G-CO.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | High School - Geometry |
| California | G-CO.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | High School - Geometry |
| California | G-CO.3 | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | High School - Geometry |
| California | G-CO.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | High School - Geometry |
| California | G-CO.5 | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | High School - Geometry |
| California | G-CO.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | High School - Geometry |
| California | G-CO.7 | Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | High School - Geometry |
| California | G-CO.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | High School - Geometry |
| California | G-CO.9 | Prove theorems about lines and angles. | High School - Geometry |
| California | G-CO.10 | Prove theorems about triangles. | High School - Geometry |
| California | G-CO.11 | Prove theorems about parallelograms. | High School - Geometry |
| California | G-CO.12 | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). | High School - Geometry |
| California | G-CO.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | High School - Geometry |
| California | G-GPE.1 | Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | High School - Geometry |
| California | G-GPE.2 | Derive the equation of a parabola given a focus and directrix. | High School - Geometry |
| California | G-GPE.3 | Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. | High School - Geometry |
| California | G-GPE.3.1 | Given a quadratic equation of the form ax² + by² + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation. | High School - Geometry |
| California | G-GPE.4 | Use coordinates to prove simple geometric theorems algebraically. | High School - Geometry |
| California | G-GPE.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | High School - Geometry |
| California | G-GPE.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | High School - Geometry |
| California | G-GPE.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. | High School - Geometry |
| California | G-GMD.1 | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. | High School - Geometry |
| California | G-GMD.2 | Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. | High School - Geometry |
| California | G-GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | High School - Geometry |
| California | G-GMD.4 | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | High School - Geometry |
| California | G-GMD.5 | Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k², and k³, respectively; determine length, area and volume measures using scale factors. | High School - Geometry |
| California | G-GMD.6 | Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems. | High School - Geometry |
| California | G-MG.1 | Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | High School - Geometry |
| California | G-MG.2 | Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). | High School - Geometry |
| California | G-MG.3 | Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). | High School - Geometry |
| California | G-SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor: | High School - Geometry |
| California | G-SRT.2 | Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | High School - Geometry |
| California | G-SRT.3 | Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. | High School - Geometry |
| California | G-SRT.4 | Prove theorems about triangles. | High School - Geometry |
| California | G-SRT.5 | Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | High School - Geometry |
| California | G-SRT.6 | Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. | High School - Geometry |
| California | G-SRT.7 | Explain and use the relationship between the sine and cosine of complementary angles. | High School - Geometry |
| California | G-SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | High School - Geometry |
| California | G-SRT.8.1 | Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90° and 45°, 45°, 90°). | High School - Geometry |
| California | G-SRT.9 | Derive the formula 𝐴 = 1/2 𝘢𝘣 sin(𝐶) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | High School - Geometry |
| California | G-SRT.10 | Prove the Laws of Sines and Cosines and use them to solve problems. | High School - Geometry |
| California | G-SRT.11 | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | High School - Geometry |
| California | S-CP.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). | High School - Statistics and Probability |
| California | S-CP.2 | Understand that two events 𝘈 and 𝘉 are independent if the probability of 𝘈 and 𝘉 occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | High School - Statistics and Probability |
| California | S-CP.3 | Understand the conditional probability of 𝘈 given 𝘉 as 𝘗(𝘈 and 𝘉)/𝘗(𝘉), and interpret independence of 𝘈 and 𝘉 as saying that the conditional probability of 𝘈 given 𝘉 is the same as the probability of 𝘈, and the conditional probability of 𝘉 given 𝘈 is the same as the probability of 𝘉. | High School - Statistics and Probability |
| California | S-CP.4 | Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | High School - Statistics and Probability |
| California | S-CP.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | High School - Statistics and Probability |
| California | S-CP.6 | Find the conditional probability of 𝘈 given 𝘉 as the fraction of 𝘉’s outcomes that also belong to 𝘈, and interpret the answer in terms of the model. | High School - Statistics and Probability |
| California | S-CP.7 | Apply the Addition Rule, 𝘗(𝘈 or 𝘉) = 𝘗(𝘈) + 𝘗(𝘉) – 𝘗(𝘈 and 𝘉), and interpret the answer in terms of the model. | High School - Statistics and Probability |
| California | S-CP.8 | Apply the general Multiplication Rule in a uniform probability model, 𝘗(𝘈 and 𝘉) = 𝘗(𝘈)𝘗(𝘉|𝘈) = 𝘗(𝘉)𝘗(𝘈|𝘉), and interpret the answer in terms of the model. | High School - Statistics and Probability |
| California | S-CP.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. | High School - Statistics and Probability |
| California | S-ID.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | High School - Statistics and Probability |
| California | S-ID.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | High School - Statistics and Probability |
| California | S-ID.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | High School - Statistics and Probability |
| California | S-ID.4 | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | High School - Statistics and Probability |
| California | S-ID.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | High School - Statistics and Probability |
| California | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School - Statistics and Probability |
| California | S-ID.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | High School - Statistics and Probability |
| California | S-ID.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | High School - Statistics and Probability |
| California | S-ID.9 | Distinguish between correlation and causation. | High School - Statistics and Probability |
| California | S-IC.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | High School - Statistics and Probability |
| California | S-IC.2 | Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | High School - Statistics and Probability |
| California | S-IC.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | High School - Statistics and Probability |
| California | S-IC.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | High School - Statistics and Probability |
| California | S-IC.5 | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | High School - Statistics and Probability |
| California | S-IC.6 | Evaluate reports based on data. | High School - Statistics and Probability |
| California | S-MD.1 | Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. | High School - Statistics and Probability |
| California | S-MD.2 | Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. | High School - Statistics and Probability |
| California | S-MD.3 | Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. | High School - Statistics and Probability |
| California | S-MD.4 | Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. | High School - Statistics and Probability |
| California | S-MD.5 | Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. | High School - Statistics and Probability |
| California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | High School - Statistics and Probability |
| California | S-MD.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | High School - Statistics and Probability |
| CCSSM | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra |
| CCSSM | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra |
| CCSSM | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra |
| CCSSM | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra |
| CCSSM | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra |
| CCSSM | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| CCSSM | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra |
| CCSSM | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra |
| CCSSM | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra |
| CCSSM | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| CCSSM | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| CCSSM | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| CCSSM | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| CCSSM | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 |
| CCSSM | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| CCSSM | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| CCSSM | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| CCSSM | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 |
| CCSSM | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 |
| CCSSM | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| CCSSM | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| CCSSM | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| CCSSM | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 |
| CCSSM | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| CCSSM | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| CCSSM | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| CCSSM | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| CCSSM | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| CCSSM | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| CCSSM | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| CCSSM | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons. | Grade 2 |
| CCSSM | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| CCSSM | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| CCSSM | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| CCSSM | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| CCSSM | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| CCSSM | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| CCSSM | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| CCSSM | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| CCSSM | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ñhow many moreî and ñhow many lessî problems using information presented in scaled bar graphs. | Grade 3 |
| CCSSM | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| CCSSM | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| CCSSM | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| CCSSM | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| CCSSM | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| CCSSM | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| CCSSM | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations. | Grade 3 |
| CCSSM | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| CCSSM | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 |
| CCSSM | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 3 |
| CCSSM | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 _ 7. | Grade 3 |
| CCSSM | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56
8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56
8. | Grade 3 |
| CCSSM | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| CCSSM | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 _ ? = 48, 5 = _
3, 6 _ 6 = ? | Grade 3 |
| CCSSM | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 _ 4 = 24 is known, then 4 _ 6 = 24 is also known. (Commutative property of multiplication.) 3 _ 5 _ 2 can be found by 3 _ 5 = 15, then 15 _ 2 = 30, or by 5 _ 2 = 10, then 3 _ 10 = 30. (Associative property of multiplication.) Knowing that 8 _ 5 = 40 and 8 _ 2 = 16, one can find 8 _ 7 as 8 _ (5 + 2) = (8 _ 5) + (8 _ 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 |
| CCSSM | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32
8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| CCSSM | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40
5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| CCSSM | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| CCSSM | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| CCSSM | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| CCSSM | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| CCSSM | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| CCSSM | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| CCSSM | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| CCSSM | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| CCSSM | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 |
| CCSSM | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| CCSSM | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| CCSSM | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| CCSSM | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| CCSSM | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| CCSSM | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| CCSSM | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or | Grade 4 |
| CCSSM | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 |
| CCSSM | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 |
| CCSSM | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| CCSSM | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 |
| CCSSM | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 4 |
| CCSSM | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| CCSSM | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| CCSSM | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 |
| CCSSM | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| CCSSM | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| CCSSM | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| CCSSM | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| CCSSM | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| CCSSM | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| CCSSM | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| CCSSM | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| CCSSM | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| CCSSM | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| CCSSM | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| CCSSM | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| CCSSM | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| CCSSM | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| CCSSM | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| CCSSM | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 |
| CCSSM | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| CCSSM | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| CCSSM | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| CCSSM | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 |
| CCSSM | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| CCSSM | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| CCSSM | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| CCSSM | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| CCSSM | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| CCSSM | 6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| CCSSM | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 |
| CCSSM | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 |
| CCSSM | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| CCSSM | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| CCSSM | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| CCSSM | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| CCSSM | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| CCSSM | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| CCSSM | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| CCSSM | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 |
| CCSSM | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 |
| CCSSM | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| CCSSM | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| CCSSM | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| CCSSM | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| CCSSM | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| CCSSM | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| CCSSM | 7.NS.A.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 |
| CCSSM | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| CCSSM | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 |
| CCSSM | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| CCSSM | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| CCSSM | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 |
| CCSSM | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| CCSSM | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| CCSSM | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| CCSSM | 8.EE.C.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 |
| CCSSM | 8.EE.C.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 |
| CCSSM | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| CCSSM | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| CCSSM | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| CCSSM | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| CCSSM | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| CCSSM | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| CCSSM | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| CCSSM | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| CCSSM | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| CCSSM | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| CCSSM | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| CCSSM | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| CCSSM | K.CC.A.1 | Count to 100 by ones and by tens | Kindergarten |
| CCSSM | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| CCSSM | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| CCSSM | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten |
| CCSSM | K.CC.B.5 | Count to answer 'how many' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| CCSSM | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| CCSSM | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| CCSSM | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| CCSSM | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| CCSSM | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| CCSSM | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| CCSSM | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| CCSSM | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Florida | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra |
| Florida | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra |
| Florida | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra |
| Florida | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra |
| Florida | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra |
| Florida | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| Florida | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra |
| Florida | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra |
| Florida | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra |
| Florida | 1.MD.2.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Florida | 1.MD.3.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Florida | 1.NBT.1.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Florida | 1.NBT.2.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). Decompose two-digit numbers in multiple ways (e.g., 64 can be decomposed into 6 tens and 4 ones or into 5 tens and 14 ones). | Grade 1 |
| Florida | 1.NBT.2.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Florida | 1.NBT.3.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Florida | 1.NBT.3.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Florida | 1.NBT.3.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Florida | 1.OA.2.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 |
| Florida | 1.OA.2.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. | Grade 1 |
| Florida | 1.OA.3.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Florida | 1.OA.3.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Florida | 1.OA.4.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| Florida | 1.OA.4.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 |
| Florida | 2.G.1.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Florida | 2.MD.3.7 | Tell and write time from analog and digital clocks to the nearest five minutes. | Grade 2 |
| Florida | 2.MD.4.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Florida | 2.MD.4.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Florida | 2.NBT.1.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| Florida | 2.NBT.1.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Florida | 2.NBT.1.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Florida | 2.NBT.1.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Florida | 2.NBT.2.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Florida | 2.NBT.2.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Florida | 2.NBT.2.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Florida | 2.NBT.2.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Florida | 2.OA.1.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Florida | 2.OA.1.a | Determine the unknown whole number in an equation relating four or more whole numbers. For example, determine the unknown number that makes the equation true in the equations 37 + 10 + 10 = _ + 18, ? - 6 = 13 - 4, and 15 - 9 = 6 + _. | Grade 2 |
| Florida | 2.OA.2.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Florida | 3.G.1.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Florida | 3.MD.1.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Florida | 3.MD.2.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ñhow many moreî and ñhow many lessî problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. | Grade 3 |
| Florida | 3.MD.2.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Florida | 3.MD.3.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. A square with side length 1 unit, called 'a unit square,' is said to have 'one square unit' of area, and can be used to measure area. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. | Grade 3 |
| Florida | 3.MD.3.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Florida | 3.MD.3.7 | Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths. Use area models to represent the distributive property in mathematical reasoning. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. | Grade 3 |
| Florida | 3.NBT.1.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Florida | 3.NBT.1.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Florida | 3.NBT.1.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations. | Grade 3 |
| Florida | 3.NF.1.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| Florida | 3.NF.1.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 |
| Florida | 3.NF.1.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 3 |
| Florida | 3.OA.1.1 | Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 _ 7. | Grade 3 |
| Florida | 3.OA.1.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56
8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56
8. | Grade 3 |
| Florida | 3.OA.1.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Florida | 3.OA.1.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 _ ? = 48, 5 = _
3, 6 _ 6 = ? | Grade 3 |
| Florida | 3.OA.2.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 _ 4 = 24 is known, then 4 _ 6 = 24 is also known. (Commutative property of multiplication.) 3 _ 5 _ 2 can be found by 3 _ 5 = 15, then 15 _ 2 = 30, or by 5 _ 2 = 10, then 3 _ 10 = 30. (Associative property of multiplication.) Knowing that 8 _ 5 = 40 and 8 _ 2 = 16, one can find 8 _ 7 as 8 _ (5 + 2) = (8 _ 5) + (8 _ 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 |
| Florida | 3.OA.2.6 | Understand division as an unknown-factor problem. For example, find 32
8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| Florida | 3.OA.3.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40
5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Florida | 4.G.1.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Florida | 4.G.1.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Florida | 4.MD.1.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... | Grade 4 |
| Florida | 4.MD.1.2 | Use the four operations to solve word problems involving distances, intervals of time, and money, including problems involving simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models. (Computational fluency with fractions and decimals is not the goal for students at this grade level.) | Grade 4 |
| Florida | 4.MD.2.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. | Grade 4 |
| Florida | 4.MD.3.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where two rays intersect the circle. An angle that turns through 1/360 of a circle is called a 'one-degree angle,' and can be used to measure angles. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. | Grade 4 |
| Florida | 4.MD.3.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Florida | 4.MD.3.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Florida | 4.NBT.1.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 |
| Florida | 4.NBT.1.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Florida | 4.NBT.1.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Florida | 4.NBT.2.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Florida | 4.NBT.2.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Florida | 4.NBT.2.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Florida | 4.NF.1.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Florida | 4.NF.1.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or | Grade 4 |
| Florida | 4.NF.2.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 |
| Florida | 4.NF.2.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 |
| Florida | 4.NF.3.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| Florida | 4.NF.3.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 |
| Florida | 4.NF.3.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 4 |
| Florida | 4.OA.1.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Florida | 4.OA.1.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Florida | 4.OA.2.4 | Investigate factors and multiples. Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 |
| Florida | 4.OA.3.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| Florida | 5.G.1.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Florida | 5.G.1.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Florida | 5.G.2.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. | Grade 5 |
| Florida | 5.G.2.4 | Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. | Grade 5 |
| Florida | 5.MD.2.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid in each beaker would contain if the total amount in all the beakers were redistributed equally. | Grade 5 |
| Florida | 5.NBT.1.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Florida | 5.NBT.1.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Florida | 5.NBT.1.3 | Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 5 |
| Florida | 5.NBT.1.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Florida | 5.NBT.2.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Florida | 5.NBT.2.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Florida | 5.NBT.2.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Florida | 5.NF.2.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| Florida | 5.NF.2.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Florida | 5.NF.2.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence to the effect of multiplying a/b by 1. | Grade 5 |
| Florida | 5.NF.2.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Florida | 5.NF.2.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. | Grade 5 |
| Florida | 5.OA.1.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Florida | 5.OA.2.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 |
| Florida | 6.EE.1.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Florida | 6.EE.1.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Florida | 6.EE.1.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Florida | 6.EE.2.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Florida | 6.EE.2.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| Florida | 6.EE.2.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Florida | 6.G.1.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 |
| Florida | 6.NS.1.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 |
| Florida | 6.NS.2.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Florida | 6.NS.2.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Florida | 6.NS.3.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Florida | 6.NS.3.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Florida | 6.NS.3.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Florida | 6.NS.3.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Florida | 6.RP.1.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Florida | 6.RP.1.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 |
| Florida | 6.RP.1.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 |
| Florida | 7.EE.1.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Florida | 7.EE.2.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Florida | 7.G.1.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Florida | 7.G.1.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Florida | 7.G.2.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Florida | 7.NS.1.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Florida | 7.NS.1.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 |
| Florida | 7.NS.1.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Florida | 7.RP.1.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 |
| Florida | 7.RP.1.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Florida | 7.RP.1.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Florida | 8.EE.1.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 |
| Florida | 8.EE.1.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| Florida | 8.EE.2.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| Florida | 8.EE.2.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Florida | 8.EE.3.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 |
| Florida | 8.EE.3.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 |
| Florida | 8.F.1.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Florida | 8.F.1.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| Florida | 8.F.1.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| Florida | 8.F.2.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Florida | 8.F.2.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Florida | 8.G.1.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Florida | 8.G.1.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Florida | 8.G.1.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Florida | 8.G.2.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Florida | 8.G.2.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Florida | 8.SP.1.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Florida | 8.SP.1.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Florida | K.CC.1.1 | Count to 100 by ones and by tens. | Kindergarten |
| Florida | K.CC.1.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Florida | K.CC.1.3 | Read and write numerals from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Florida | K.CC.2.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten |
| Florida | K.CC.2.5 | Count to answer 'how many' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Florida | K.CC.3.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Florida | K.CC.3.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Florida | K.NBT.1.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Florida | K.OA.1.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Florida | K.OA.1.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem (Students are not required to independently read the word problems.) | Kindergarten |
| Florida | K.OA.1.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Florida | K.OA.1.5 | Fluently add and subtract within 5. | Kindergarten |
| Florida | K.OA.1.a | Use addition and subtraction within 10 to solve word problems involving both addends unknown, e.g., by using objects, drawings, and equations with symbols for the unknown numbers to represent the problem. (Students are not required to independently read the word problems.) | Kindergarten |
| Georgia | A.APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra |
| Georgia | A.CED.A.2 | Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra |
| Georgia | A.SSE.A.2 | Use the structure of an expression to rewrite it in different equivalent forms. | Algebra |
| Georgia | A.SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra |
| Georgia | F.BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra |
| Georgia | F.IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| Georgia | F.IF.B.4 | Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | Algebra |
| Georgia | F.IF.C.7 | Graph functions expressed algebraically and show key features of the graph both by hand and by using technology. | Algebra |
| Georgia | S.ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra |
| Georgia | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Georgia | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Georgia | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Georgia | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Georgia | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 |
| Georgia | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Georgia | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Georgia | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Georgia | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Georgia | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 |
| Georgia | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Georgia | 1.OA.C.6 | Add and subtract within 20. | Grade 1 |
| Georgia | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Georgia | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Georgia | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Georgia | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Georgia | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Georgia | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Georgia | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. | Grade 2 |
| Georgia | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Georgia | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Georgia | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, < symbols to record the results of comparisons. | Grade 2 |
| Georgia | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Georgia | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Georgia | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. | Grade 2 |
| Georgia | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Georgia | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem. Problems include contexts that involve adding to, taking from, putting together/taking apart (part/part/whole) and comparing with unknowns in all positions. | Grade 2 |
| Georgia | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Georgia | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Georgia | 3.MD.A.1 | Tell and write time to the nearest minute and measure elapsed time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram, drawing a pictorial representation on a clock face, etc. | Grade 3 |
| Georgia | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ñhow many moreî and ñhow many lessî problems using information presented in scaled bar graphs. | Grade 3 |
| Georgia | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Georgia | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Georgia | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Georgia | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Georgia | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Georgia | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Georgia | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations. | Grade 3 |
| Georgia | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| Georgia | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Georgia | 3.NF.A.3 | Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size. | Grade 3 |
| Georgia | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Georgia | 3.OA.A.2 | Interpret whole number quotients of whole numbers, e.g., interpret 56
8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?). | Grade 3 |
| Georgia | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Georgia | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. | Grade 3 |
| Georgia | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Georgia | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Georgia | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40
5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Georgia | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Georgia | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Georgia | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. | Grade 4 |
| Georgia | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Georgia | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Georgia | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Georgia | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Georgia | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol or letter for the unknown angle measure. | Grade 4 |
| Georgia | 4.MD.C.8 | Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. | Grade 4 |
| Georgia | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Georgia | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Georgia | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Georgia | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Georgia | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Georgia | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Georgia | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b). | Grade 4 |
| Georgia | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or | Grade 4 |
| Georgia | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. | Grade 4 |
| Georgia | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number e.g., by using a visual such as a number line or area model. | Grade 4 |
| Georgia | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Georgia | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Georgia | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 4 |
| Georgia | 4.OA.A.1 | Understand that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity. | Grade 4 |
| Georgia | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison. Use drawings and equations with a symbol or letter for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Georgia | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 |
| Georgia | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the pattern will continue to develop in this way. | Grade 4 |
| Georgia | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Georgia | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Georgia | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Georgia | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Georgia | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Georgia | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Georgia | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Georgia | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Georgia | 5.NBT.A.4 | Use place value understanding to round decimals up to the hundredths place. | Grade 5 |
| Georgia | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm (or other strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor. | Grade 5 |
| Georgia | 5.NBT.B.6 | Fluently divide up to 4-digit dividends and 2-digit divisors by using at least one of the following methods: strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations or concrete models (e.g., rectangular arrays, area models). | Grade 5 |
| Georgia | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Georgia | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Georgia | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Georgia | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Georgia | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| Georgia | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Georgia | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Georgia | 5.OA.B.3 | Generate two numerical patterns using a given rule. Identify apparent relationships between corresponding terms by completing a function table or input/output table. Using the terms created, form and graph ordered pairs on a coordinate plane. | Grade 5 |
| Georgia | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Georgia | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Georgia | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Georgia | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Georgia | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| Georgia | 6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Georgia | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Georgia | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, including reasoning strategies such as using visual fraction models and equations to represent the problem. | Grade 6 |
| Georgia | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Georgia | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Georgia | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Georgia | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Georgia | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Georgia | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Georgia | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Georgia | 6.RP.A.2 | Understand the concept of a unit rate a / b associated with a ratio a:b with b ? 0 (b not equal to zero), and use rate language in the context of a ratio relationship. | Grade 6 |
| Georgia | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems utilizing strategies such as tables of equivalent ratios, tape diagrams (bar models), double number line diagrams, and/or equations. | Grade 6 |
| Georgia | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Georgia | 7.EE.B.3 | Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Georgia | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Georgia | 7.G.A.2 | Explore various geometric shapes with given conditions. Focus on creating triangles from three measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Georgia | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Georgia | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Georgia | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Georgia | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Georgia | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Georgia | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Georgia | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Georgia | 8.EE.A.3 | Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Georgia | 8.EE.A.4 | Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Understand scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g. use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g. calculators). | Grade 8 |
| Georgia | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Georgia | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Georgia | 8.EE.C.7 | Give examples of linear equations in one variable. | Grade 8 |
| Georgia | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations (systems of linear equations). | Grade 8 |
| Georgia | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Georgia | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Georgia | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Georgia | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Georgia | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Georgia | 8.G.A.1 | Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines. | Grade 8 |
| Georgia | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Georgia | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Georgia | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Georgia | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Georgia | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Georgia | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Georgia | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Georgia | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Georgia | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Georgia | K.CC.B.4 | Understand the relationship between numbers and quantities. | Kindergarten |
| Georgia | K.CC.B.5 | Count to answer ïhow many?î questions. | Kindergarten |
| Georgia | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Georgia | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Georgia | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, four, five, six , seven, eight, or nine ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8). | Kindergarten |
| Georgia | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Georgia | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Georgia | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation. | Kindergarten |
| Georgia | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Georgia | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Illinois | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Illinois | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Illinois | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Illinois | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Illinois | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Illinois | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Illinois | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Illinois | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Illinois | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Illinois | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Illinois | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Illinois | K.G.B.5 | Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Kindergarten |
| Illinois | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Illinois | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Illinois | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Illinois | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Illinois | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Illinois | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Illinois | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Illinois | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Illinois | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Illinois | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Illinois | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Illinois | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Illinois | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Illinois | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Illinois | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Illinois | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Illinois | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Illinois | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Illinois | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 |
| Illinois | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Illinois | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Illinois | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Illinois | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Illinois | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Illinois | 1.OA.A.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Illinois | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Illinois | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Illinois | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Illinois | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Illinois | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Illinois | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Illinois | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Illinois | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Illinois | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Illinois | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Illinois | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Illinois | 2.MD.A.3 | Estimate lengths using units of inches, feet, centimeters, and meters. | Grade 2 |
| Illinois | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Illinois | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Illinois | 2.MD.B.6 | Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram. | Grade 2 |
| Illinois | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Illinois | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Illinois | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Illinois | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Illinois | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 |
| Illinois | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Illinois | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Illinois | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Illinois | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Illinois | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Illinois | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Illinois | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Illinois | 2.NBT.B.9 | Explain why addition and subtraction strategies work, using place value and the properties of operations. | Grade 2 |
| Illinois | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Illinois | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Illinois | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Illinois | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Illinois | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Illinois | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Illinois | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Illinois | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Illinois | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Illinois | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Illinois | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Illinois | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Illinois | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Illinois | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Illinois | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Illinois | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Illinois | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Illinois | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Illinois | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Illinois | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Illinois | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Illinois | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Illinois | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Illinois | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Illinois | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Illinois | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Illinois | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Illinois | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Illinois | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Illinois | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Illinois | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Illinois | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Illinois | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Illinois | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Illinois | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Illinois | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Illinois | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| Illinois | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Illinois | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Illinois | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Illinois | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Illinois | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Illinois | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Illinois | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Illinois | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Illinois | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Illinois | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Illinois | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Illinois | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Illinois | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Illinois | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Illinois | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Illinois | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Illinois | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Illinois | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Illinois | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Illinois | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Illinois | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Illinois | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Illinois | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Illinois | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Illinois | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Illinois | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Illinois | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Illinois | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Illinois | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Illinois | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Illinois | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Illinois | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Illinois | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Illinois | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Illinois | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Illinois | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Illinois | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Illinois | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Illinois | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Illinois | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Illinois | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by: | Grade 5 |
| Illinois | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Illinois | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Illinois | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Illinois | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Illinois | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Illinois | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Illinois | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Illinois | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Illinois | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Illinois | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Illinois | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Illinois | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Illinois | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 < 𝘤 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form 𝘹 > 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Illinois | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Illinois | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Illinois | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Illinois | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Illinois | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Illinois | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Illinois | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Illinois | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Illinois | 6.SP.A.1 | Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. | Grade 6 |
| Illinois | 6.SP.A.2 | Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. | Grade 6 |
| Illinois | 6.SP.A.3 | Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. | Grade 6 |
| Illinois | 6.SP.B.4 | Display numerical data in plots on a number line, including dot plots, histograms, and box plots. | Grade 6 |
| Illinois | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Illinois | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Illinois | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Illinois | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Illinois | 6.NS.B.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. | Grade 6 |
| Illinois | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Illinois | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Illinois | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Illinois | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Illinois | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Illinois | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Illinois | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Illinois | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Illinois | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Illinois | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Illinois | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Illinois | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Illinois | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Illinois | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Illinois | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Illinois | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Illinois | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Illinois | 7.SP.A.1 | Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. | Grade 7 |
| Illinois | 7.SP.A.2 | Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. | Grade 7 |
| Illinois | 7.SP.B.3 | Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. | Grade 7 |
| Illinois | 7.SP.B.4 | Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. | Grade 7 |
| Illinois | 7.SP.C.5 | Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. | Grade 7 |
| Illinois | 7.SP.C.6 | Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. | Grade 7 |
| Illinois | 7.SP.C.7 | Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. | Grade 7 |
| Illinois | 7.SP.C.8 | Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | Grade 7 |
| Illinois | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Illinois | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Illinois | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Illinois | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Illinois | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Illinois | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Illinois | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Illinois | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Illinois | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Illinois | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Illinois | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Illinois | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Illinois | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Illinois | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Illinois | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Illinois | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Illinois | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| Illinois | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Illinois | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Illinois | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Illinois | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Illinois | 8.G.B.6 | Explain a proof of the Pythagorean Theorem and its converse. | Grade 8 |
| Illinois | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Illinois | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Illinois | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Illinois | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Illinois | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Illinois | 8.SP.A.3 | Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. | Grade 8 |
| Illinois | 8.SP.A.4 | Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. | Grade 8 |
| Illinois | 8.NS.A.1 | Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. | Grade 8 |
| Illinois | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Illinois | HSN-Q.A.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | High School - Number and Quantity |
| Illinois | HSN-Q.A.2 | Define appropriate quantities for the purpose of descriptive modeling. | High School - Number and Quantity |
| Illinois | HSN-Q.A.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | High School - Number and Quantity |
| Illinois | HSN-CN.A.1 | Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real. | High School - Number and Quantity |
| Illinois | HSN-CN.A.2 | Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | High School - Number and Quantity |
| Illinois | HSN-CN.A.3 | Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. | High School - Number and Quantity |
| Illinois | HSN-CN.B.4 | Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. | High School - Number and Quantity |
| Illinois | HSN-CN.B.5 | Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. | High School - Number and Quantity |
| Illinois | HSN-CN.B.6 | Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. | High School - Number and Quantity |
| Illinois | HSN-CN.C.7 | Solve quadratic equations with real coefficients that have complex solutions. | High School - Number and Quantity |
| Illinois | HSN-CN.C.8 | Extend polynomial identities to the complex numbers. | High School - Number and Quantity |
| Illinois | HSN-CN.C.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | High School - Number and Quantity |
| Illinois | HSN-RN.A.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | High School - Number and Quantity |
| Illinois | HSN-RN.A.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | High School - Number and Quantity |
| Illinois | HSN-RN.B.3 | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | High School - Number and Quantity |
| Illinois | HSN-VM.A.1 | Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., 𝙫, |𝙫|, ||𝙫||, 𝘷). | High School - Number and Quantity |
| Illinois | HSN-VM.A.2 | Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. | High School - Number and Quantity |
| Illinois | HSN-VM.A.3 | Solve problems involving velocity and other quantities that can be represented by vectors. | High School - Number and Quantity |
| Illinois | HSN-VM.B.4 | Add and subtract vectors. | High School - Number and Quantity |
| Illinois | HSN-VM.B.5 | Multiply a vector by a scalar. | High School - Number and Quantity |
| Illinois | HSN-VM.C.6 | Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. | High School - Number and Quantity |
| Illinois | HSN-VM.C.7 | Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | High School - Number and Quantity |
| Illinois | HSN-VM.C.8 | Add, subtract, and multiply matrices of appropriate dimensions. | High School - Number and Quantity |
| Illinois | HSN-VM.C.9 | Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. | High School - Number and Quantity |
| Illinois | HSN-VM.C.10 | Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. | High School - Number and Quantity |
| Illinois | HSN-VM.C.11 | Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. | High School - Number and Quantity |
| Illinois | HSN-VM.C.12 | Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. | High School - Number and Quantity |
| Illinois | HSA-APR.A.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | High School - Algebra |
| Illinois | HSA-APR.B.2 | Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹). | High School - Algebra |
| Illinois | HSA-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School - Algebra |
| Illinois | HSA-APR.C.4 | Prove polynomial identities and use them to describe numerical relationships. | High School - Algebra |
| Illinois | HSA-APR.C.5 | Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle. | High School - Algebra |
| Illinois | HSA-APR.D.6 | Rewrite simple rational expressions in different forms; write 𝘢(𝘹)/𝘣(𝘹) in the form 𝘲(𝘹) + 𝘳(𝘹)/𝘣(𝘹), where 𝘢(𝘹), 𝘣(𝘹), 𝘲(𝘹), and 𝘳(𝘹) are polynomials with the degree of 𝘳(𝘹) less than the degree of 𝘣(𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system. | High School - Algebra |
| Illinois | HSA-APR.D.7 | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. | High School - Algebra |
| Illinois | HSA-CED.A.1 | Create equations and inequalities in one variable and use them to solve problems. | High School - Algebra |
| Illinois | HSA-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School - Algebra |
| Illinois | HSA-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School - Algebra |
| Illinois | HSA-CED.A.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | High School - Algebra |
| Illinois | HSA-REI.A.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | High School - Algebra |
| Illinois | HSA-REI.A.2 | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | High School - Algebra |
| Illinois | HSA-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School - Algebra |
| Illinois | HSA-REI.B.4 | Solve quadratic equations in one variable. | High School - Algebra |
| Illinois | HSA-REI.C.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | High School - Algebra |
| Illinois | HSA-REI.C.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | High School - Algebra |
| Illinois | HSA-REI.C.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | High School - Algebra |
| Illinois | HSA-REI.C.8 | Represent a system of linear equations as a single matrix equation in a vector variable. | High School - Algebra |
| Illinois | HSA-REI.C.9 | Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). | High School - Algebra |
| Illinois | HSA-REI.D.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | High School - Algebra |
| Illinois | HSA-REI.D.11 | Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | High School - Algebra |
| Illinois | HSA-REI.D.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | High School - Algebra |
| Illinois | HSA-SSE.A.1 | Interpret expressions that represent a quantity in terms of its context. | High School - Algebra |
| Illinois | HSA-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School - Algebra |
| Illinois | HSA-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School - Algebra |
| Illinois | HSA-SSE.B.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | High School - Algebra |
| Illinois | HSF-BF.A.1 | Write a function that describes a relationship between two quantities. | High School - Functions |
| Illinois | HSF-BF.A.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | High School - Functions |
| Illinois | HSF-BF.B.3 | Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | High School - Functions |
| Illinois | HSF-BF.B.4 | Find inverse functions. | High School - Functions |
| Illinois | HSF-BF.B.5 | Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. | High School - Functions |
| Illinois | HSF-IF.A.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹). | High School - Functions |
| Illinois | HSF-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School - Functions |
| Illinois | HSF-IF.A.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | High School - Functions |
| Illinois | HSF-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School - Functions |
| Illinois | HSF-IF.B.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | High School - Functions |
| Illinois | HSF-IF.B.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | High School - Functions |
| Illinois | HSF-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School - Functions |
| Illinois | HSF-IF.C.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | High School - Functions |
| Illinois | HSF-IF.C.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | High School - Functions |
| Illinois | HSF-LE.A.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. | High School - Functions |
| Illinois | HSF-LE.A.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | High School - Functions |
| Illinois | HSF-LE.A.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | High School - Functions |
| Illinois | HSF-LE.A.4 | For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology. | High School - Functions |
| Illinois | HSF-LE.B.5 | Interpret the parameters in a linear or exponential function in terms of a context. | High School - Functions |
| Illinois | HSF-TF.A.1 | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | High School - Functions |
| Illinois | HSF-TF.A.2 | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | High School - Functions |
| Illinois | HSF-TF.A.3 | Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–𝘹, π+𝘹, and 2π–𝘹 in terms of their values for 𝘹, where 𝘹 is any real number. | High School - Functions |
| Illinois | HSF-TF.A.4 | Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. | High School - Functions |
| Illinois | HSF-TF.B.5 | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | High School - Functions |
| Illinois | HSF-TF.B.6 | Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. | High School - Functions |
| Illinois | HSF-TF.B.7 | Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. | High School - Functions |
| Illinois | HSF-TF.C.8 | Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. | High School - Functions |
| Illinois | HSF-TF.C.9 | Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. | High School - Functions |
| Illinois | HSG-C.A.1 | Prove that all circles are similar. | High School - Geometry |
| Illinois | HSG-C.A.2 | Identify and describe relationships among inscribed angles, radii, and chords. | High School - Geometry |
| Illinois | HSG-C.A.3 | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | High School - Geometry |
| Illinois | HSG-C.A.4 | Construct a tangent line from a point outside a given circle to the circle. | High School - Geometry |
| Illinois | HSG-C.B.5 | Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. | High School - Geometry |
| Illinois | HSG-CO.A.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | High School - Geometry |
| Illinois | HSG-CO.A.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | High School - Geometry |
| Illinois | HSG-CO.A.3 | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | High School - Geometry |
| Illinois | HSG-CO.A.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | High School - Geometry |
| Illinois | HSG-CO.A.5 | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | High School - Geometry |
| Illinois | HSG-CO.B.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | High School - Geometry |
| Illinois | HSG-CO.B.7 | Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | High School - Geometry |
| Illinois | HSG-CO.B.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | High School - Geometry |
| Illinois | HSG-CO.C.9 | Prove theorems about lines and angles. | High School - Geometry |
| Illinois | HSG-CO.C.10 | Prove theorems about triangles. | High School - Geometry |
| Illinois | HSG-CO.C.11 | Prove theorems about parallelograms. | High School - Geometry |
| Illinois | HSG-CO.D.12 | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). | High School - Geometry |
| Illinois | HSG-CO.D.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | High School - Geometry |
| Illinois | HSG-GPE.A.1 | Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | High School - Geometry |
| Illinois | HSG-GPE.A.2 | Derive the equation of a parabola given a focus and directrix. | High School - Geometry |
| Illinois | HSG-GPE.A.3 | Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. | High School - Geometry |
| Illinois | HSG-GPE.B.4 | Use coordinates to prove simple geometric theorems algebraically. | High School - Geometry |
| Illinois | HSG-GPE.B.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | High School - Geometry |
| Illinois | HSG-GPE.B.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | High School - Geometry |
| Illinois | HSG-GPE.B.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. | High School - Geometry |
| Illinois | HSG-GMD.A.1 | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. | High School - Geometry |
| Illinois | HSG-GMD.A.2 | Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. | High School - Geometry |
| Illinois | HSG-GMD.A.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | High School - Geometry |
| Illinois | HSG-GMD.B.4 | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | High School - Geometry |
| Illinois | HSG-MG.A.1 | Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | High School - Geometry |
| Illinois | HSG-MG.A.2 | Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). | High School - Geometry |
| Illinois | HSG-MG.A.3 | Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). | High School - Geometry |
| Illinois | HSG-SRT.A.1 | Verify experimentally the properties of dilations given by a center and a scale factor: | High School - Geometry |
| Illinois | HSG-SRT.A.2 | Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | High School - Geometry |
| Illinois | HSG-SRT.A.3 | Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. | High School - Geometry |
| Illinois | HSG-SRT.B.4 | Prove theorems about triangles. | High School - Geometry |
| Illinois | HSG-SRT.B.5 | Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | High School - Geometry |
| Illinois | HSG-SRT.C.6 | Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. | High School - Geometry |
| Illinois | HSG-SRT.C.7 | Explain and use the relationship between the sine and cosine of complementary angles. | High School - Geometry |
| Illinois | HSG-SRT.C.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | High School - Geometry |
| Illinois | HSG-SRT.D.9 | Derive the formula 𝐴 = 1/2 𝘢𝘣 sin(𝐶) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | High School - Geometry |
| Illinois | HSG-SRT.D.10 | Prove the Laws of Sines and Cosines and use them to solve problems. | High School - Geometry |
| Illinois | HSG-SRT.D.11 | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | High School - Geometry |
| Illinois | HSS-CP.A.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). | High School - Statistics and Probability |
| Illinois | HSS-CP.A.2 | Understand that two events 𝘈 and 𝘉 are independent if the probability of 𝘈 and 𝘉 occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | High School - Statistics and Probability |
| Illinois | HSS-CP.A.3 | Understand the conditional probability of 𝘈 given 𝘉 as 𝘗(𝘈 and 𝘉)/𝘗(𝘉), and interpret independence of 𝘈 and 𝘉 as saying that the conditional probability of 𝘈 given 𝘉 is the same as the probability of 𝘈, and the conditional probability of 𝘉 given 𝘈 is the same as the probability of 𝘉. | High School - Statistics and Probability |
| Illinois | HSS-CP.A.4 | Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | High School - Statistics and Probability |
| Illinois | HSS-CP.A.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | High School - Statistics and Probability |
| Illinois | HSS-CP.B.6 | Find the conditional probability of 𝘈 given 𝘉 as the fraction of 𝘉’s outcomes that also belong to 𝘈, and interpret the answer in terms of the model. | High School - Statistics and Probability |
| Illinois | HSS-CP.B.7 | Apply the Addition Rule, 𝘗(𝘈 or 𝘉) = 𝘗(𝘈) + 𝘗(𝘉) – 𝘗(𝘈 and 𝘉), and interpret the answer in terms of the model. | High School - Statistics and Probability |
| Illinois | HSS-CP.B.8 | Apply the general Multiplication Rule in a uniform probability model, 𝘗(𝘈 and 𝘉) = 𝘗(𝘈)𝘗(𝘉|𝘈) = 𝘗(𝘉)𝘗(𝘈|𝘉), and interpret the answer in terms of the model. | High School - Statistics and Probability |
| Illinois | HSS-CP.B.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. | High School - Statistics and Probability |
| Illinois | HSS-ID.A.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | High School - Statistics and Probability |
| Illinois | HSS-ID.A.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | High School - Statistics and Probability |
| Illinois | HSS-ID.A.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | High School - Statistics and Probability |
| Illinois | HSS-ID.A.4 | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | High School - Statistics and Probability |
| Illinois | HSS-ID.B.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | High School - Statistics and Probability |
| Illinois | HSS-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School - Statistics and Probability |
| Illinois | HSS-ID.C.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | High School - Statistics and Probability |
| Illinois | HSS-ID.C.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | High School - Statistics and Probability |
| Illinois | HSS-ID.C.9 | Distinguish between correlation and causation. | High School - Statistics and Probability |
| Illinois | HSS-IC.A.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | High School - Statistics and Probability |
| Illinois | HSS-IC.A.2 | Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | High School - Statistics and Probability |
| Illinois | HSS-IC.B.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | High School - Statistics and Probability |
| Illinois | HSS-IC.B.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | High School - Statistics and Probability |
| Illinois | HSS-IC.B.5 | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | High School - Statistics and Probability |
| Illinois | HSS-IC.B.6 | Evaluate reports based on data. | High School - Statistics and Probability |
| Illinois | HSS-MD.A.1 | Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. | High School - Statistics and Probability |
| Illinois | HSS-MD.A.2 | Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. | High School - Statistics and Probability |
| Illinois | HSS-MD.A.3 | Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. | High School - Statistics and Probability |
| Illinois | HSS-MD.A.4 | Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. | High School - Statistics and Probability |
| Illinois | HSS-MD.B.5 | Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. | High School - Statistics and Probability |
| Illinois | HSS-MD.B.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | High School - Statistics and Probability |
| Illinois | HSS-MD.B.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | High School - Statistics and Probability |
| Indiana | AI.DS.2 | Graph bivariate data on a scatter plot and describe the relationship between the variables. | Algebra |
| Indiana | AI.DS.3 | Use technology to find a linear function that models a relationship for a bivariate data set to make predictions; interpret the slope and y-intercept, and compute (using technology) and interpret the correlation coefficient. | Algebra |
| Indiana | AI.F.2 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. Identify independent and dependent variables and make predictions about the relationship. | Algebra |
| Indiana | AI.F.4 | Understand and interpret statements that use function notation in terms of a context; relate the domain of the function to its graph and to the quantitative relationship it describes. | Algebra |
| Indiana | AI.QE.3 | Graph exponential and quadratic equations in two variables with and without technology. | Algebra |
| Indiana | AI.QE.5 | Represent real-world problems using quadratic equations in one or two variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. | Algebra |
| Indiana | AI.QE.7 | Describe the relationships among the solutions of a quadratic equation, the zeros of the function, the x-intercepts of the graph, and the factors of the expression. | Algebra |
| Indiana | AI.RNE.6 | Factor common terms from polynomials and factor polynomials completely. Factor the difference of two squares, perfect square trinomials, and other quadratic expressions. | Algebra |
| Indiana | AI.SEI.3 | Write a system of two linear equations in two variables that represents a real-world problem and solve the problem with and without technology. Interpret the solution and determine whether the solution is reasonable. | Algebra |
| Indiana | AII.CNE.4 | Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). | Algebra II |
| Indiana | AII.DSP.2 | Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. | Algebra II |
| Indiana | AII.EL.2 | Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, and asymptotic and end behavior. | Algebra II |
| Indiana | AII.EL.4 | Use the properties of exponents to transform expressions for exponential functions (e.g., the express ion 1.15^t can be rewritten as (1.15^1/12)^12t ? 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%) | Algebra II |
| Indiana | AII.EL.7 | Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. | Algebra II |
| Indiana | AII.F.2 | Understand composition of functions and combine functions by composition. | Algebra II |
| Indiana | AII.PR.2 | Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. | Algebra II |
| Indiana | AII.Q.2 | Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeros, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. | Algebra II |
| Indiana | 1.CA.1 | Demonstrate fluency with addition facts and the corresponding subtraction facts within 20. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Understand the role of 0 in addition and subtraction. | Grade 1 |
| Indiana | 1.CA.5 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; describe the strategy and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and that sometimes it is necessary to compose a ten. | Grade 1 |
| Indiana | 1.CA.6 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false (e.g., Which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2). | Grade 1 |
| Indiana | 1.DA.1 | Organize and interpret data with up to three choices (What is your favorite fruit? apples, bananas, oranges); ask and answer questions about the total number of data points, how many in each choice, and how many more or less in one choice compared to another. | Grade 1 |
| Indiana | 1.M.2 | Tell and write time to the nearest half-hour and relate time to events (before/after, shorter/longer) using analog clocks. Understand how to read hours and minutes using digital clocks. | Grade 1 |
| Indiana | 1.NS.1 | Count to at least 120 by ones, fives, and tens from any given number. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Indiana | 1.NS.2 | Understand that 10 can be thought of as a group of ten ones - called a "ten." Understand that the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Understand that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| Indiana | 1.NS.4 | Use place value understanding to compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Indiana | 1.NS.5 | Find mentally 10 more or 10 less than a given two-digit the number without having to count, and explain the thinking process used to get the answer. | Grade 1 |
| Indiana | 2.CA.1 | Add and subtract fluently within 100. | Grade 2 |
| Indiana | 2.CA.2 | Solve real-world problems involving addition and subtraction within 100 in situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all parts of the addition or subtraction problem (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Use estimation to decide whether answers are reasonable in addition problems. | Grade 2 |
| Indiana | 2.DA.1 | Draw a picture graph (with single-unit scale) and a bar graph (with single-unit scale) to represent a data set with up to four choices (What is your favorite color? red, blue, yellow, green). Solve simple put-together, take-apart, and compare problems using information presented in the graphs. | Grade 2 |
| Indiana | 2.G.1 | Identify, describe, and classify two- and three-dimensional shapes (triangle, square, rectangle, cube, right rectangular prism) according to the number and shape of faces and the number of sides and/or vertices. Draw two-dimensional shapes. | Grade 2 |
| Indiana | 2.G.2 | Create squares, rectangles, triangles, cubes, and right rectangular prisms using appropriate materials. | Grade 2 |
| Indiana | 2.M.2 | Estimate and measure the length of an object by selecting and using appropriate tools, such as rulers, yardsticks, meter sticks, and measuring tapes to the nearest inch, foot, yard, centimeter and meter. | Grade 2 |
| Indiana | 2.M.5 | Tell and write time to the nearest five minutes from analog clocks, using a.m. and p.m. Solve real-world problems involving addition and subtraction of time intervals on the hour or half hour. | Grade 2 |
| Indiana | 2.NS.1 | Count by ones, twos, fives, tens, and hundreds up to at least 1,000 from any given number. | Grade 2 |
| Indiana | 2.NS.2 | Read and write whole numbers up to 1,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000. | Grade 2 |
| Indiana | 2.NS.6 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (e.g., 706 equals 7 hundreds, 0 tens, and 6 ones). Understand that 100 can be thought of as a group of ten tens - called a "hundred." Understand that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| Indiana | 2.NS.7 | Use place value understanding to compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Indiana | 3.AT.1 | Solve real-world problems involving addition and subtraction of whole numbers within 1000 (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 3 |
| Indiana | 3.AT.2 | Solve real-world problems involving whole number multiplication and division within 100 in situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 3 |
| Indiana | 3.AT.4 | Interpret a multiplication equation as equal groups (e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each). Represent verbal statements of equal groups as multiplication equations. | Grade 3 |
| Indiana | 3.AT.5 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Indiana | 3.C.1 | Add and subtract whole numbers fluently within 1000. | Grade 3 |
| Indiana | 3.C.3 | Represent the concept of division of whole numbers with the following models: partitioning, sharing, and an inverse of multiplication. Understand the properties of 0 and 1 in division. | Grade 3 |
| Indiana | 3.C.4 | Interpret whole-number quotients of whole numbers (e.g., interpret 56 divided by 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each). | Grade 3 |
| Indiana | 3.C.5 | Multiply and divide within 100 using strategies, such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 divided by 5 = 8), or properties of operations. | Grade 3 |
| Indiana | 3.DA.1 | Create scaled picture graphs, scaled bar graphs, and frequency tables to represent a data set-including data collected through observations, surveys, and experiments-with several categories. Solve one- and two-step 'how many more' and 'how many less' problems regarding the data and make predictions based on the data. | Grade 3 |
| Indiana | 3.DA.2 | Generate measurement data by measuring lengths with rulers to the nearest quarter of an inch. Display the data by making a line plot, where the horizontal scale is marked off in appropriate units, such as whole numbers, halves, or quarters. | Grade 3 |
| Indiana | 3.G.2 | Understand that shapes (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize and draw rhombuses, rectangles, and squares as examples of quadrilaterals. Recognize and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Indiana | 3.M.3 | Tell and write time to the nearest minute from analog clocks, using a.m. and p.m., and measure time intervals in minutes. Solve real-world problems involving addition and subtraction of time intervals in minutes. | Grade 3 |
| Indiana | 3.M.5 | Find the area of a rectangle with whole-number side lengths by modeling with unit squares, and show that the area is the same as would be found by multiplying the side lengths. Identify and draw rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Indiana | 3.M.6 | Multiply side lengths to find areas of rectangles with whole-number side lengths to solve real-world problems and other mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. | Grade 3 |
| Indiana | 3.NS.3 | Understand a fraction, 1/b, as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction, a/b, as the quantity formed by a parts of size 1/b. | Grade 3 |
| Indiana | 3.NS.4 | Represent a fraction, 1/b, on a number line by defining the interval from 0 to 1 as the whole, and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. | Grade 3 |
| Indiana | 3.NS.5 | Represent a fraction, a/b, on a number line by marking off lengths 1/b from 0. Recognize that the resulting interval has size a/b, and that its endpoint locates the number a/b on the number line. | Grade 3 |
| Indiana | 3.NS.6 | Understand two fractions as equivalent (equal) if they are the same size, based on the same whole or the same point on a number line. | Grade 3 |
| Indiana | 3.NS.7 | Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model). | Grade 3 |
| Indiana | 3.NS.8 | Compare two fractions with the same numerator or the same denominator by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or | Grade 3 |
| Indiana | 3.NS.9 | Use place value understanding to round 2- and 3-digit whole numbers to the nearest 10 or 100. | Grade 3 |
| Indiana | 4.AT.3 | Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Indiana | 4.AT.4 | Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Indiana | 4.AT.5 | Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). | Grade 4 |
| Indiana | 4.AT.6 | Understand that an equation, such as y = 3x + 5, is a rule to describe a relationship between two variables and can be used to find a second number when a first number is given. Generate a number pattern that follows a given rule. | Grade 4 |
| Indiana | 4.C.1 | Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. | Grade 4 |
| Indiana | 4.C.2 | Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. | Grade 4 |
| Indiana | 4.C.3 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. | Grade 4 |
| Indiana | 4.C.5 | Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. | Grade 4 |
| Indiana | 4.C.6 | Add and subtract mixed numbers with common denominators (e.g. by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction). | Grade 4 |
| Indiana | 4.DA.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in line plots. | Grade 4 |
| Indiana | 4.G.4 | Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. | Grade 4 |
| Indiana | 4.G.5 | Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). | Grade 4 |
| Indiana | 4.M.2 | Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit within a single system of measurement. Record measurement equivalents in a two-column table. | Grade 4 |
| Indiana | 4.M.3 | Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. | Grade 4 |
| Indiana | 4.M.4 | Apply the area and perimeter formulas for rectangles to solve real-world problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems. | Grade 4 |
| Indiana | 4.M.5 | Understand that an angle is measured with reference to a circle, with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. Understand an angle that turns through 1/360 of a circle is called a "one-degree angle", and can be used to measure other angles. Understand an angle that turns through n one-degree angles is said to have an angle measure of n degrees. | Grade 4 |
| Indiana | 4.M.6 | Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure. | Grade 4 |
| Indiana | 4.NS.1 | Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. | Grade 4 |
| Indiana | 4.NS.2 | Compare two whole numbers up to 1,000,000 using >, =, and < symbols. | Grade 4 |
| Indiana | 4.NS.3 | Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. | Grade 4 |
| Indiana | 4.NS.4 | Explain why a fraction, a/b, is equivalent to a fraction, (n x a)/(n x b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use the principle to recognize and generate equivalent fractions. | Grade 4 |
| Indiana | 4.NS.5 | Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or | Grade 4 |
| Indiana | 4.NS.6 | Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). | Grade 4 |
| Indiana | 4.NS.7 | Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or | Grade 4 |
| Indiana | 4.NS.8 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. | Grade 4 |
| Indiana | 4.NS.9 | Use place value understanding to round multi-digit whole numbers to any given place value. | Grade 4 |
| Indiana | 5.AT.3 | Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem). | Grade 5 |
| Indiana | 5.AT.4 | Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions (e.g., by using visual fraction models and equations to represent the problem). | Grade 5 |
| Indiana | 5.AT.6 | Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Indiana | 5.AT.7 | Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Indiana | 5.C.1 | Multiply multi-digit whole numbers fluently using a standard algorithmic approach. | Grade 5 |
| Indiana | 5.C.2 | Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used. | Grade 5 |
| Indiana | 5.C.3 | Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 |
| Indiana | 5.C.5 | Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number. | Grade 5 |
| Indiana | 5.C.6 | Explain why multiplying a positive number by a fraction greater than 1 results in a product greater than the given number. Explain why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence, a/b = (n x a)/(n x b), to the effect of multiplying a/b by 1. | Grade 5 |
| Indiana | 5.C.7 | Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction. | Grade 5 |
| Indiana | 5.C.8 | Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. | Grade 5 |
| Indiana | 5.G.2 | Identify and classify polygons including quadrilaterals, pentagons, hexagons, and triangles (equilateral, isosceles, scalene, right, acute and obtuse) based on angle measures and sides. Classify polygons in a hierarchy based on properties. | Grade 5 |
| Indiana | 5.M.2 | Find the area of a rectangle with fractional side lengths by modeling with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. | Grade 5 |
| Indiana | 5.NS.1 | Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols. | Grade 5 |
| Indiana | 5.NS.2 | Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by whole numbers. | Grade 5 |
| Indiana | 5.NS.3 | Recognize the relationship that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right, and inversely, a digit in one place represents 1/10 of what it represents in the place to its left. | Grade 5 |
| Indiana | 5.NS.4 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Indiana | 5.NS.5 | Use place value understanding to round decimal numbers up to thousandths to any given place value. | Grade 5 |
| Indiana | 5.NS.6 | Understand, interpret, and model percents as part of a hundred (e.g. by using pictures, diagrams, and other visual models). | Grade 5 |
| Indiana | 6.AF.1 | Evaluate expressions for specific values of their variables, including expressions with whole-number exponents and those that arise from formulas used in real-world problems. | Grade 6 |
| Indiana | 6.AF.2 | Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them. | Grade 6 |
| Indiana | 6.AF.3 | Define and use multiple variables when writing expressions to represent real-world and other mathematical problems, and evaluate them for given values. | Grade 6 |
| Indiana | 6.AF.4 | Understand that solving an equation or inequality is the process of answering the following question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Indiana | 6.AF.5 | Solve equations of the form x + p = q, x ? p = q, px = q, and x/p = q fluently for cases in which p, q and x are all nonnegative rational numbers. Represent real world problems using equations of these forms and solve such problems. | Grade 6 |
| Indiana | 6.AF.6 | Write an inequality of the form x > c, x ? c, x < c, or x ? c, where c is a rational number, to represent a constraint or condition in a real-world or other mathematical problem. Recognize inequalities have infinitely many solutions and represent solutions on a number line diagram. | Grade 6 |
| Indiana | 6.AF.7 | Understand that signs of numbers in ordered pairs indicate the quadrant containing the point; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Graph points with rational number coordinates on a coordinate plane. | Grade 6 |
| Indiana | 6.AF.8 | Solve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane. Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Indiana | 6.AF.9 | Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. | Grade 6 |
| Indiana | 6.C.1 | Divide multi-digit whole numbers fluently using a standard algorithmic approach. | Grade 6 |
| Indiana | 6.C.2 | Compute with positive fractions and positive decimals fluently using a standard algorithmic approach. | Grade 6 |
| Indiana | 6.C.4 | Compute quotients of positive fractions and solve real-world problems involving division of fractions by fractions. Use a visual fraction model and/or equation to represent these calculations. | Grade 6 |
| Indiana | 6.C.6 | Apply the order of operations and properties of operations (identity, inverse, commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property) to evaluate numerical expressions with nonnegative rational numbers, including those using grouping symbols, such as parentheses, and involving whole number exponents. Justify each step in the process. | Grade 6 |
| Indiana | 6.GM.1 | Convert between measurement systems (English to metric and metric to English) given conversion factors, and use these conversions in solving real-world problems. | Grade 6 |
| Indiana | 6.GM.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate; apply these techniques to solve real-world and other mathematical problems. | Grade 6 |
| Indiana | 6.NS.1 | Understand that positive and negative numbers are used to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). Use positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Indiana | 6.NS.10 | Use reasoning involving rates and ratios to model real-world and other mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). | Grade 6 |
| Indiana | 6.NS.2 | Understand the integer number system. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself (e.g., -(-3) = 3), and that 0 is its own opposite. | Grade 6 |
| Indiana | 6.NS.3 | Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts. | Grade 6 |
| Indiana | 6.NS.4 | Understand that the absolute value of a number is the distance from zero on a number line. Find the absolute value of real numbers and know that the distance between two numbers on the number line is the absolute value of their difference. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. | Grade 6 |
| Indiana | 6.NS.8 | Interpret, model, and use ratios to show the relative sizes of two quantities. Describe how a ratio shows the relationship between two quantities. Use the following notations: a/b, a to b, a:b. | Grade 6 |
| Indiana | 6.NS.9 | Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship. | Grade 6 |
| Indiana | 7.AF.1 | Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions, including situations that involve factoring (e.g., given 2x - 10, create an equivalent expression 2(x - 5)). Justify each step in the process. | Grade 7 |
| Indiana | 7.AF.6 | Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin). | Grade 7 |
| Indiana | 7.AF.7 | Identify the unit rate or constant of proportionality in tables, graphs, equations, and verbal descriptions of proportional relationships. | Grade 7 |
| Indiana | 7.AF.8 | Explain what the coordinates of a point on the graph of a proportional relationship mean in terms of the situation, with special attention to the points (0,0) and (1,r), where r is the unit rate. | Grade 7 |
| Indiana | 7.AF.9 | Identify real-world and other mathematical situations that involve proportional relationships. Write equations and draw graphs to represent proportional relationships and recognize that these situations are described by a linear function in the form y = mx, where the unit rate, m, is the slope of the line. | Grade 7 |
| Indiana | 7.C.1 | Understand p + q as the number located a distance |q| from p, in the positive or negative direction, depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. | Grade 7 |
| Indiana | 7.C.2 | Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. | Grade 7 |
| Indiana | 7.C.3 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. | Grade 7 |
| Indiana | 7.C.4 | Understand that integers can be divided, provided that the divisor is not zero, and that every quotient of integers (with non-zero divisor) is a rational number. Understand that if p and q are integers, then -(p/q) = (-p)/q = p/(-q). | Grade 7 |
| Indiana | 7.C.5 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Indiana | 7.C.6 | Use proportional relationships to solve ratio and percent problems with multiple operations, such as the following: simple interest, tax, markups, markdowns, gratuities, commissions, fees, conversions within and across measurement systems, percent increase and decrease, and percent error. | Grade 7 |
| Indiana | 7.C.7 | Compute with rational numbers fluently using a standard algorithmic approach. | Grade 7 |
| Indiana | 7.C.8 | Solve real-world problems with rational numbers by using one or two operations. | Grade 7 |
| Indiana | 7.GM.1 | Draw triangles (freehand, with ruler and protractor, and using technology) with given conditions from three measures of angles or sides, and notice when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Indiana | 7.GM.3 | Solve real-world and other mathematical problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Create a scale drawing by using proportional reasoning. | Grade 7 |
| Indiana | 7.GM.4 | Solve real-world and other mathematical problems that involve vertical, adjacent, complementary, and supplementary angles. | Grade 7 |
| Indiana | 8.AF.1 | Solve linear equations with rational number coefficients fluently, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Represent real-world problems using linear equations and inequalities in one variable and solve such problems. | Grade 8 |
| Indiana | 8.AF.2 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by transforming a given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 |
| Indiana | 8.AF.3 | Understand that a function assigns to each x-value (independent variable) exactly one y-value (dependent variable), and that the graph of a function is the set of ordered pairs (x,y). | Grade 8 |
| Indiana | 8.AF.4 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. | Grade 8 |
| Indiana | 8.AF.5 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Describe similarities and differences between linear and nonlinear functions from tables, graphs, verbal descriptions, and equations. | Grade 8 |
| Indiana | 8.AF.6 | Construct a function to model a linear relationship between two quantities given a verbal description, table of values, or graph. Recognize in y = mx + b that m is the slope (rate of change) and b is the y-intercept of the graph, and describe the meaning of each in the context of a problem. | Grade 8 |
| Indiana | 8.AF.7 | Compare properties of two linear functions given in different forms, such as a table of values, equation, verbal description, and graph (e.g., compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed). | Grade 8 |
| Indiana | 8.AF.8 | Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs because points of intersection satisfy both equations simultaneously. Approximate the solution of a system of equations by graphing and interpreting the reasonableness of the approximation. | Grade 8 |
| Indiana | 8.C.2 | Solve real-world and other mathematical problems involving numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology, such as a scientific calculator, graphing calculator, or excel spreadsheet. | Grade 8 |
| Indiana | 8.DSP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantitative variables. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Indiana | 8.DSP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and describe the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Indiana | 8.GM.3 | Verify experimentally the properties of rotations, reflections, and translations, including: lines are mapped to lines, and line segments to line segments of the same length; angles are mapped to angles of the same measure; and parallel lines are mapped to parallel lines. | Grade 8 |
| Indiana | 8.GM.4 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. Describe a sequence that exhibits the congruence between two given congruent figures. | Grade 8 |
| Indiana | 8.GM.5 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. Describe a sequence that exhibits the similarity between two given similar figures. | Grade 8 |
| Indiana | 8.GM.8 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and other mathematical problems in two dimensions. | Grade 8 |
| Indiana | 8.GM.9 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. | Grade 8 |
| Indiana | 8.NS.1 | Give examples of rational and irrational numbers and explain the difference between them. Understand that every number has a decimal expansion; for rational numbers, show that the decimal expansion terminates or repeats, and convert a decimal expansion that repeats into a rational number. | Grade 8 |
| Indiana | K.CA.1 | Use objects, drawings, mental images, sounds, etc., to represent addition and subtraction within 10. | Kindergarten |
| Indiana | K.CA.2 | Solve real-world problems that involve addition and subtraction within 10 (e.g., by using objects or drawings to represent the problem). | Kindergarten |
| Indiana | K.CA.3 | Use objects, drawings, etc., to decompose numbers less than or equal to 10 into pairs in more than one way, and record each decomposition with a drawing or an equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Indiana | K.CA.4 | Find the number that makes 10 when added to the given number for any number from 1 to 9 (e.g., by using objects or drawings), and record the answer with a drawing or an equation. | Kindergarten |
| Indiana | K.NS.1 | Count to at least 100 by ones and tens and count on by one from any number. | Kindergarten |
| Indiana | K.NS.2 | Write whole numbers from 0 to 20 and recognize number words from 0 to 10. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Indiana | K.NS.4 | Say the number names in standard order when counting objects, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said describes the number of objects counted and that the number of objects is the same regardless of their arrangement or the order in which they were counted. | Kindergarten |
| Indiana | K.NS.5 | Count up to 20 objects arranged in a line, a rectangular array, or a circle. Count up to 10 objects in a scattered configuration. Count out the number of objects, given a number from 1 to 20. | Kindergarten |
| Indiana | K.NS.7 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (e.g., by using matching and counting strategies). | Kindergarten |
| Indiana | K.NS.8 | Compare the values of two numbers from 1 to 20 presented as written numerals. | Kindergarten |
| Indiana | PC.EL.3 | Graph and solve real-world and other mathematical problems that can be modeled using exponential and logarithmic equations and inequalities; interpret the solution and determine whether it is reasonable. | Pre-Calculus |
| Indiana | PC.F.1 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | Pre-Calculus |
| Indiana | PC.F.8 | Define arithmetic and geometric sequences recursively. Use a variety of recursion equations to describe a function. Model and solve word problems involving applications of sequences and series, interpret the solutions and determine whether the solutions are reasonable. | Pre-Calculus |
| Indiana | PC.QPR.2 | Graph rational functions with and without technology. Identify and describe features such as intercepts, domain and range, and asymptotic and end behavior. | Pre-Calculus |
| Indiana | PS.DA.11 | Find linear models by using median fit and least squares regression methods to make predictions. Decide which among several linear models gives a better fit. Interpret the slope and intercept in terms of the original context. Informally assess the fit of a function by plotting and analyzing residuals. | Probability and Statistics |
| Indiana | TR.PF.2 | Graph trigonometric functions with and without technology. Use the graphs to model and analyze periodic phenomena, stating amplitude, period, frequency, phase shift, and midline (vertical shift). | Trigonometry |
| .Kansas | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra |
| .Kansas | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra |
| .Kansas | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra |
| .Kansas | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra |
| .Kansas | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra |
| .Kansas | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| .Kansas | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra |
| .Kansas | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra |
| .Kansas | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra |
| .Kansas | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| .Kansas | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| .Kansas | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| .Kansas | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| .Kansas | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 |
| .Kansas | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| .Kansas | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| .Kansas | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| .Kansas | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 |
| .Kansas | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 |
| .Kansas | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| .Kansas | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| .Kansas | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| .Kansas | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 |
| .Kansas | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| .Kansas | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| .Kansas | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| .Kansas | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| .Kansas | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| .Kansas | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| .Kansas | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| .Kansas | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons. | Grade 2 |
| .Kansas | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| .Kansas | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| .Kansas | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| .Kansas | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| .Kansas | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| .Kansas | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| .Kansas | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| .Kansas | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| .Kansas | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ñhow many moreî and ñhow many lessî problems using information presented in scaled bar graphs. | Grade 3 |
| .Kansas | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| .Kansas | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| .Kansas | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| .Kansas | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| .Kansas | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| .Kansas | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| .Kansas | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations. | Grade 3 |
| .Kansas | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| .Kansas | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 |
| .Kansas | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 3 |
| .Kansas | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 _ 7. | Grade 3 |
| .Kansas | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56
8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56
8. | Grade 3 |
| .Kansas | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| .Kansas | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 _ ? = 48, 5 = _
3, 6 _ 6 = ? | Grade 3 |
| .Kansas | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 _ 4 = 24 is known, then 4 _ 6 = 24 is also known. (Commutative property of multiplication.) 3 _ 5 _ 2 can be found by 3 _ 5 = 15, then 15 _ 2 = 30, or by 5 _ 2 = 10, then 3 _ 10 = 30. (Associative property of multiplication.) Knowing that 8 _ 5 = 40 and 8 _ 2 = 16, one can find 8 _ 7 as 8 _ (5 + 2) = (8 _ 5) + (8 _ 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 |
| .Kansas | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32
8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| .Kansas | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40
5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| .Kansas | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| .Kansas | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| .Kansas | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| .Kansas | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| .Kansas | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| .Kansas | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| .Kansas | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| .Kansas | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| .Kansas | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 |
| .Kansas | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| .Kansas | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| .Kansas | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| .Kansas | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| .Kansas | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| .Kansas | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| .Kansas | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or | Grade 4 |
| .Kansas | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 |
| .Kansas | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 |
| .Kansas | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| .Kansas | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 |
| .Kansas | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 4 |
| .Kansas | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| .Kansas | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| .Kansas | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 |
| .Kansas | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| .Kansas | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| .Kansas | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| .Kansas | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| .Kansas | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| .Kansas | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| .Kansas | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| .Kansas | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| .Kansas | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| .Kansas | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| .Kansas | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| .Kansas | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| .Kansas | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| .Kansas | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| .Kansas | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| .Kansas | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 |
| .Kansas | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| .Kansas | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| .Kansas | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| .Kansas | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 |
| .Kansas | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| .Kansas | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| .Kansas | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| .Kansas | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| .Kansas | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| .Kansas | 6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| .Kansas | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 |
| .Kansas | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 |
| .Kansas | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| .Kansas | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| .Kansas | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| .Kansas | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| .Kansas | 6.NS.C.7 | Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. | Grade 6 |
| .Kansas | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| .Kansas | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| .Kansas | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 |
| .Kansas | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 |
| .Kansas | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| .Kansas | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| .Kansas | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| .Kansas | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| .Kansas | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| .Kansas | 7.NS.A.1 | Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. | Grade 7 |
| .Kansas | 7.NS.A.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 |
| .Kansas | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| .Kansas | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 |
| .Kansas | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| .Kansas | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| .Kansas | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 |
| .Kansas | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| .Kansas | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| .Kansas | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| .Kansas | 8.EE.C.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 |
| .Kansas | 8.EE.C.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 |
| .Kansas | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| .Kansas | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| .Kansas | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| .Kansas | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| .Kansas | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| .Kansas | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| .Kansas | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| .Kansas | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| .Kansas | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| .Kansas | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| .Kansas | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| .Kansas | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| .Kansas | K.CC.A.1 | Count to 100 by ones and by tens | Kindergarten |
| .Kansas | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| .Kansas | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| .Kansas | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten |
| .Kansas | K.CC.B.5 | Count to answer 'how many' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| .Kansas | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| .Kansas | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| .Kansas | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| .Kansas | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| .Kansas | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| .Kansas | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| .Kansas | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| .Kansas | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Knotion | 1.MYD.B.3 | Dicen y escriben la hora en medias horas utilizando relojes anàlogos y digitales. | Grade 1 |
| Knotion | 1.MYD.C.4 | Organizan, representan e interpretan datos que tienen hasta tres categorÕas; preguntan y responden a preguntas sobre la cantidad total de datos, cuàntos hay en cada categorÕa, y si hay una cantidad mayor o menor entre las categorÕas. | Grade 1 |
| Knotion | 1.OYPA.B.3 | Aplican las propiedades de las operaciones como estrategias para sumar y restar. 3 Ejemplos: Si saben que 8 + 3 = 11, entonces, saben tambi_n que 3 + 8 = 11 (Propiedad conmutativa de la suma). Para sumar 2 + 6 + 4, los Ïltimos dos nÏmeros se pueden sumar para obtener el nÏmero 10, por lo tanto 2 + 6 + 4 = 2 + 10 = 12 (Propiedad asociativa de la suma). | Grade 1 |
| Knotion | 1.OYPA.B.4 | Comprenden la resta como un problema de un sumando desconocido. | Grade 1 |
| Knotion | 1.OYPA.C.5 | Relacionan el conteo con la suma y la resta (por ejemplo, al contar de 2 en 2 para sumar 2). | Grade 1 |
| Knotion | 1.OYPA.C.6 | Suman y restan hasta el nÏmero 20, demostrando fluidez al sumar y al restar hasta 10. Utilizan estrategias tales como el contar hacia adelante; el formar diez; el descomponer un nÏmero para obtener el diez ; el utilizar la relaciÑn entre la suma y la resta ; y el crear sumas equivalentes pero màs sencillas o conocidas. | Grade 1 |
| Knotion | 1.OYPA.D.7 | Entienden el significado del signo igual, y determinan si las ecuaciones de suma y resta son verdaderas o falsas. Por ejemplo, ËCuàles de las siguientes ecuaciones son verdaderas y cuàles son falsas? 6 = 6, 7 = 8 -1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| Knotion | 1.OYPA.D.8 | Determinan el nÏmero entero desconocido en una ecuaciÑn de suma o resta que relaciona tres nÏmeros enteros. Por ejemplo, determinan el nÏmero desconocido que hace que la ecuaciÑn sea verdadera en cada una de las siguientes ecuaciones. | Grade 1 |
| Knotion | 1.SND.A.1 | Cuentan hasta 120, comenzando con cualquier nÏmero menor que 120. Dentro de este rango, leen y escriben numerales que representan una cantidad de objetos con un numeral escrito. | Grade 1 |
| Knotion | 1.SND.B.2 | Entienden que los dos dÕgitos de un nÏmero de dos dÕgitos representan cantidades de decenas y unidades. Entienden lo siguiente como casos especiales: 10 puede considerarse como un conjunto de 10 unidades llamado una decena. Los nÏmeros entre 11 y 19 se componen por una decena y una, dos, tres, cuatro, cinco, seis, siete, ocho o nueve unidades. Los nÏmeros 10, 20, 30, 40, 50, 60, 70, 80 y 90 se referieren a una, dos, tres, cuatro, cinco, seis, siete, ocho o nueve decenas (y 0 unidades). | Grade 1 |
| Knotion | 1.SND.B.3 | Comparan dos nÏmeros de dos dÕgitos basàndose en el significado de los dÕgitos en las unidades y decenas, anotando los resultados de las comparaciones con el uso de los sÕmbolos >, =, y <. | Grade 1 |
| Knotion | 1.SND.C.4 | Suman hasta el 100, incluyendo el sumar un nÏmero de dos dÕgitos y un nÏmero de un dÕgito, asÕ como el sumar un nÏmero de dos dÕgitos y un mÏltiplo de 10, utilizan modelos concretos o dibujos y estrategias basadas en el valor de posiciÑn, las propiedades de las operaciones, y/o la relaciÑn entre la suma y la resta; relacionan la estrategia con un m_todo escrito, y explican el razonamiento aplicado. Entienden que al sumar nÏmeros de dos dÕgitos, se suman decenas con decenas, unidades con unidades; y a veces es necesario el componer una decena. | Grade 1 |
| Knotion | 1.SND.C.5 | Dado un nÏmero de dos dÕgitos, hallan mentalmente 10 màs o 10 menos que un nÏmero, sin la necesidad de contar; explican el razonamiento que utilizaron. | Grade 1 |
| Knotion | 1.SND.C.6 | Restan mÏltiplos de 10 en el rango de 10 a 90 a partir de mÏltiplos de 10 en el rango de 10 a 90 (con diferencias positivas o de cero), utilizando ejemplos concretos o dibujos, y estrategias basadas en el valor de posiciÑn, las propiedades de operaciones, y/o la relaciÑn entre la suma y la resta; relacionan la estrategia con un m_todo escrito y explican el razonamiento utilizado. | Grade 1 |
| Knotion | 2.GE.A.1 | Reconocen y dibujan figuras que tengan atributos especÕficos, tales como un nÏmero dado de àngulos o un nÏmero dados de lados iguales. Identifican triàngulos, cuadrilàteros, pentàgonos, hexàgonos, y cubos. | Grade 2 |
| Knotion | 2.MYD.C.7 | Dicen y escriben la hora utilizando relojes anàlogos y digitales a los cinco minutos màs cercanos, usando a.m. y p.m. | Grade 2 |
| Knotion | 2.MYD.D.10 | Dibijan una pictografÕa y una gràfica de barras (con escala unitaria) para representar un grupo de datos de hasta cuatro categorÕas. Resuelven problemas simples para unir, separar, y comparar usando la informaciÑn representada en la gràfica de barras. | Grade 2 |
| Knotion | 2.MYD.D.9 | Generan datos de mediciÑn al medir las longitudes de varios objetos hasta la unidad entera màs cercana, o al tomar las medidas del mismo objeto varias veces. Muestran las medidas por medio de un diagrama de puntos, en la cual la escala horizontal està marcada por unidades con nÏmeros enteros. | Grade 2 |
| Knotion | 2.OYPA.A.1 | Usan la suma y la resta hasta el nÏmero 100 para resolver problemas verbales de uno y dos pasos relacionados a situaciones en las cuales tienen que sumar, restar, unir, separar, y comparar, con valores desconocidos en todas las posiciones, por ejemplo, al representar el problema a trav_s del uso de dibujos y ecuaciones con un sÕmbolo para el nÏmero desconocido. | Grade 2 |
| Knotion | 2.OYPA.B.2 | Suman y restan con fluidez hasta el nÏmero 20 usando estrategias mentales. 2 Al final del segundo grado, saben de memoria todas las sumas de dos nÏmeros de un solo dÕgito. | Grade 2 |
| Knotion | 2.SND.A.1 | Comprenden que los tres dÕgitos de un nÏmero de tres dÕgitos representan cantidades de centenas, decenas y unidades; por ejemplo, 706 es igual a 7 centenas, 0 decenas y 6 unidades. Comprenden los siguientes casos especiales: 100 puede considerarse como un conjunto de diez decenas llamado centena. Los nÏmeros 100, 200, 300, 400, 500, 600, 700, 800, 900 se refieren a una, dos, tres, cuatro, cinco, seis, siete, ocho o nueve centenas (y 0 decenas y 0 unidades). | Grade 2 |
| Knotion | 2.SND.A.2 | Cuentan hasta 1000; cuentan de 2 en 2, de 5 en 5, de 10 en 10, y de 100 en 100. | Grade 2 |
| Knotion | 2.SND.A.3 | Leen y escriben nÏmeros hasta 1000 usando numerales en base diez, los nombres de los nÏmeros, y en forma desarrollada. | Grade 2 |
| Knotion | 2.SND.A.4 | Comparan dos nÏmeros de tres dÕgitos basàndose en el significado de los dÕgitos de las centenas, decenas y las unidades usando los sÕmbolos >, =, < para anotar los resultados de las comparaciones. | Grade 2 |
| Knotion | 2.SND.B.5 | Suman y restan hasta 100 con fluidez usando estrategias basadas en el valor de posicion, las propiedades de las operaciones, y/o la relaciÑn entre la suma y la resta. | Grade 2 |
| Knotion | 2.SND.B.6 | Suman hasta cuatro nÏmeros de dos dÕgitos usando estrategias basadas en el valor decposiciona y las propiedades de las operaciones. | Grade 2 |
| Knotion | 2.SND.B.7 | Suman y restan hasta 1000, usando modelos concretos o dibujos y estrategias basadas en el valor de posiciÑn, las propiedades de las operaciones, y/o la relaciÑn entre la suma y la resta; relacionan la estrategia con un m_todo escrito. Comprenden que al sumar o restar nÏmeros de tres dÕgitos, se suman o restan centenas y centenas, decenas y decenas, unidades y unidades; y a veces es necesario componer y descomponer las decenas o las centenas. | Grade 2 |
| Knotion | 2.SND.B.8 | Suman mentalmente 10 Ñ 100 a un nÏmero dado del 100 a 900, y restan mentalmente 10 Ñ 100 de un nÏmero dado entre 100 a 900. | Grade 2 |
| Knotion | 3.FRA.A.1 | Comprenden una fracciÑn 1/b como la cantidad formada por 1 parte cuando un entero se separa entre b partes iguales; comprenden una fracciÑn a/b como la cantidad formada por partes a de tamaÐo 1/b. | Grade 3 |
| Knotion | 3.FRA.A.2 | Entienden una fracciÑn como un nÏmero en una recta num_rica; representan fracciones en un diagrama de recta num_rica. a. Representan una fracciÑn 1/b en una recta num_rica al definir el intervalo del 0 al 1 como el entero y marcàndolo en b partes iguales. Reconocen que cada parte tiene un tamaÐo 1/b y que el punto final de la parte basada en 0 sirve para localizar el nÏmero 1/b en la recta num_rica. b. Representan una fracciÑn a/b en una recta num_rica al marcar la longitud a en el espacio 1/b a partir del 0. Reconocen que el intervalo resultante tiene un tamaÐo a/b y que su punto final localiza el nÏmero a /b sobre la recta num_rica. | Grade 3 |
| Knotion | 3.FRA.A.3 | Explican la equivalencia de las fracciones en casos especiales, y comparan las fracciones al razonar sobre su tamaÐo. a. Reconocen a dos fracciones como equivalentes (iguales) si tienen el mismo tamaÐo, o el mismo punto en una recta num_rica. b. Reconocen y generan fracciones equivalentes simples, por ejemplo, 1/2 = 2/4; 4/6 = 2/3. Explican porqu_ las fracciones son equivalentes, por ejemplo, al utilizar un modelo visual de fracciones. c. Expresan nÏmeros enteros como fracciones, y reconocen fracciones que son equivalentes a nÏmeros enteros. Ejemplos: Expresan 3 en la forma 3 = 3/1; reconocen que 6/1 = 6; localizan 4/4 y 1 en el mismo punto de una recta num_rica. d. Comparan dos fracciones con el mismo numerador o el mismo denominador al razonar sobre su tamaÐo. Reconocen que las comparaciones son vàlidas solamente cuando las dos fracciones hacen referencia al mismo entero. Anotan los resultados de las comparaciones con los sÕmbolos >, = o | Grade 3 |
| Knotion | 3.GE.A.1 | Comprenden que las figuras geom_tricas en diferentes categorÕas (por ejemplo, rombos, rectàngulos y otros) pueden compartir atributos (por ejemplo, tener cuatro lados), y que los atributos compartidos pueden definir una categorÕa màs amplia (por ejemplo, cuadrilàteros). Reconocen los rombos, los rectàngulos, y los cuadrados como ejemplos de cuadrilàteros, y dibujan ejemplos de cuadrilàteros que no pertenecen a ninguna de estas sub-categorÕas. | Grade 3 |
| Knotion | 3.MYD.A.1 | Dicen y escriben la hora al minuto màs cercano y miden intervalos de tiempo en minutos. Resuelven problemas verbales de suma y resta sobre intervalos de tiempo en minutos, por ejemplo, al representar el problema en un diagrama de una recta num_rica. | Grade 3 |
| Knotion | 3.MYD.B.3 | Trazan una pictografÕa a escala y una gràfica de barra a escala para representar datos con varias categorÕas. Resuelven problemas de uno y dos pasos sobre cuàntos màs y cuàntos menos utilizando la informaciÑn presentada en gràficas de barra a escala. Por ejemplo, al dibujar una gràfica de barras en la cual cada cuadrado pudiera representar 5 mascotas. | Grade 3 |
| Knotion | 3.MYD.B.4 | Generan datos de mediciÑn al medir longitudes usando reglas marcadas con media pulgada y cuartos de pulgada. Muestran los datos trazando una lÕnea, cuya escala horizontal queda marcada con las unidades apropiadas- nÏmeros enteros, mitades, o cuartos. | Grade 3 |
| Knotion | 3.MYD.C.5 | Reconocen el àrea como un atributo de las figuras planas, y comprenden los conceptos de mediciÑn del àrea. a. Un cuadrado cuyos lados miden 1 unidad, se dice que tiene una unidad cuadrada de àrea y puede utilizarse para medir el àrea. b. Una figura plana que se puede cubrir sin espacios ni superposiciones por n unidades cuadradas se dice tener un àrea de n unidades cuadradas. | Grade 3 |
| Knotion | 3.MYD.C.6 | Miden àreas al contar unidades cuadradas (centÕmetros cuadrados, metros cuadrados, pulgadas cuadradas, pies cuadrados y unidades improvisadas). | Grade 3 |
| Knotion | 3.MYD.C.7 | Relacionan el àrea con las operaciones de multiplicaciÑn y suma. | Grade 3 |
| Knotion | 3.OYPA.A.1 | Interpretan productos de nÏmeros enteros, por ejemplo, interpretan 5 x 7 como la cantidad total de objetos en 5 grupos de 7 objetos cada uno. Por ejemplo, al describir un contexto en el que una cantidad total de objetos pueda expresarse como 5 x 7. | Grade 3 |
| Knotion | 3.OYPA.A.2 | Interpretan los cocientes de nÏmeros enteros, por ejemplo, al interpretar 56 8 como la cantidad de objetos en cada parte cuando se reparten 56 objetos entre 8 partes iguales, o como una cantidad de partes cuando se reparten 56 objetos en grupos iguales de 8 objetos cada uno. Por ejemplo, al describir un contexto en el cual una cantidad de partes o una cantidad de grupos se puede expresar como 56 8. | Grade 3 |
| Knotion | 3.OYPA.A.3 | Utilizan operaciones de multiplicaciÑn y divisiÑn hasta el nÏmero 100 para resolver problemas verbales en situaciones relacionados con grupos iguales, matrices, y cantidades de mediciÑn, por ejemplo, al usar dibujos y ecuaciones con un sÕmbolo para el nÏmero desconocido al representar el problema. | Grade 3 |
| Knotion | 3.OYPA.A.4 | Determinan el nÏmero entero desconocido en una ecuaciÑn de multiplicaciÑn o divisiÑn relacionada con tres nÏmeros enteros. Por ejemplo, al determinar el nÏmero desconocido que hace que la ecuaciÑn sea verdadera en cada una de las siguientes ecuaciones: 8 _ ? = 48, 5 = ? - 3, 6 _ 6 = ? | Grade 3 |
| Knotion | 3.OYPA.B.5 | Aplican propiedades de operaciones como estrategias para multiplicar y dividir. Ejemplos: Si se sabe que 6 x 4 = 24, entonces tambi_n se sabe que 4 x 6 = 24 (Propiedad conmutativa de la multiplicaciÑn). Se puede hallar 3 x 5 x 2 con 3 x 5 = 15, y luego 15 x 2 = 30, o con 5 x 2 = 10, y luego 3 x 10 = 30 (Propiedad asociativa de la multiplicaciÑn). Al saber que 8 x 5 = 40 y que 8 x 2 = 16, se puede hallar que 8 x 7 es como 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Propiedad distributiva). | Grade 3 |
| Knotion | 3.OYPA.B.6 | Entender la divisiÑn como un problema de factor desconocido. Por ejemplo, el hallar 32 8 al determinar el nÏmero que al multiplicarse por 8 da 32. | Grade 3 |
| Knotion | 3.OYPA.C.7 | Multiplican y dividen hasta el nÏmero 100 con facilidad, a trav_s del uso de estrategias como la relaciÑn entre la multiplicaciÑn y la divisiÑn (por ejemplo, al saber que 8 x 5 = 40, se sabe que 40 5 = 8), o las propiedades de las operaciones. Al final del Tercer grado, saben de memoria todos los productos de dos nÏmeros de un sÑlo dÕgito. | Grade 3 |
| Knotion | 3.SND.A.1 | Utilizan el entendimiento del valor posicional para redondear los nÏmeros enteros hasta la decena (10) o centena (100) màs prÑxima. | Grade 3 |
| Knotion | 3.SND.A.2 | Suman y restan con facilidad hasta el nÏmero 1000 usando estrategias y algoritmos basados en el valor posicional, las propiedades de las operaciones, y/o la relaciÑn entre la suma y la resta. | Grade 3 |
| Knotion | 3.SND.A.3 | Multiplican nÏmeros enteros de un sÑlo dÕgito por mÏltiplos de 10 en el rango del 10 a 90 (por ejemplo, 9 x 80, 5 x 60) usando estrategias basadas en el valor posicional y en las propiedades de las operaciones. | Grade 3 |
| Knotion | 4.FRA.A.1 | Explican por qu_ la fracciÑn a/b es equivalente a la fracciÑn (n _ a)/(n _ b) al utilizar modelos visuales de fracciones, poniendo atenciÑn a como el nÏmero y el tamaÐo de las partes difiere aÏn cuando ambas fracciones son del mismo tamaÐo. Utilizan este principio para reconocer y generar fracciones equivalentes. | Grade 4 |
| Knotion | 4.FRA.A.2 | Comparan dos fracciones con numeradores distintos y denominadores distintos, por ejemplo, al crear denominadores o numeradores comunes, o al comparar una fracciÑn de referencia como 1/2. Reconocen que las comparaciones son vàlidas solamente cuando las dos fracciones se refieren al mismo entero. Anotan los resultados de las comparaciones con los sÕmbolos >, = Ñ | Grade 4 |
| Knotion | 4.FRA.B.3 | Entienden la fracciÑn a/b cuando a > 1 como una suma de fracciones 1/b. a. Entienden la suma y la resta de fracciones como la uniÑn y la separaciÑn de partes que se refieren a un mismo entero. b. Descomponen de varias maneras una fracciÑn en una suma de fracciones con el mismo denominador, anotando cada descomposiciÑn con una ecuaciÑn. Justifican las descomposiciones, por ejemplo, utilizando un modelo visual de fracciones. Ejemplos: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8; 21/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Suman y restan nÏmeros mixtos con el mismo denominador, por ejemplo, al reemplazar cada nÏmero mixto por una fracciÑn equivalente, y/o al utilizar las propiedades de las operaciones y la relaciÑn entre la suma y la resta. d. Resuelven problemas verbales sobre sumas y restas de fracciones relacionados a un mismo entero y con el mismo denominador, por ejemplo, utilizando modelos visuales de fracciones y ecuaciones para representar el problema. | Grade 4 |
| Knotion | 4.FRA.B.4 | Aplican y amplÕan los conocimientos previos sobrela multiplicaciÑn para multiplicar una fracciÑn por un nÏmero entero. a. Entienden que una fracciÑn a/b es un mÏltiplo de 1/b. Por ejemplo, utilizan un modelo visual de fracciones para representar 5/4 como el producto 5 _ (1/4), anotando la conclusiÑn mediante la ecuaciÑn 5/4 = 5 _ (1/4). b.Entienden que un mÏltiplo de a/b es un mÏltiplo de 1/b, y utilizan este entendimiento para multiplicar una fracciÑn por un nÏmero entero. Por ejemplo, utilizan un modelo visual de fracciones para expresar 3 _ (2/5) como 6 _ (1/5), reconociendo el producto como 6/5. (En general, n _ (a/b) = (n _ a)/b). c. Resuelven problemas verbales relacionados a la multiplicaciÑn de una fracciÑn por un nÏmero entero, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, si cada persona en una fiesta come 3/8 de una libra de carne, y hay 5 personas en la fiesta, Ëcuàntas libras de carne se necesitaran? ËEntre qu_ nÏmeros enteros està tu respuesta? | Grade 4 |
| Knotion | 4.FRA.C.5 | Expresan una fracciÑn con denominador 10 como una fracciÑn equivalente con denominador 1000, y utilizan esta t_cnica para sumar dos fracciones condenominadores respectivos de 10 y 1000. Por ejemplo, expresan 3/10 como 30/100 y suman 3/10 + 4/100 = 34/100. | Grade 4 |
| Knotion | 4.FRA.C.6 | Utilizan la notaciÑn decimal para las fracciones con denominadores de 10 Ñ 100. Por ejemplo, al escribir 0.62 como 62/100; al describir una longitud como 0.62 metros; al localizar 0.62 en una recta num_rica. | Grade 4 |
| Knotion | 4.FRA.C.7 | Comparan dos decimales hasta las cent_simas al razonar sobre su tamaÐo. Reconocen que las comparaciones son vàlidas solamente cuando ambos decimales se refieren al mismo entero. Anotan los resultados de las comparaciones con los sÕmbolos >, = Ñ | Grade 4 |
| Knotion | 4.GE.A.1 | Dibujan puntos, rectas, segmentos de rectas, semirrectas, àngulos (rectos, agudos, obtusos), y rectas perpendiculares y paralelas. Identifican estos elementos en las figuras bidimensionales. | Grade 4 |
| Knotion | 4.GE.A.2 | Clasifican las figuras bidimensionales basàndoseen la presencia o ausencia de rectas paralelas o perpendiculares, o en la presencia o ausencia deàngulos de un tamaÐo especificado. Reconocen que los triàngulos rectos forman una categorÕa en sÕ, e identifican triàngulos rectos. | Grade 4 |
| Knotion | 4.MYD.A.1 | Reconocen los tamaÐos relativos de las unidadesde mediciÑn dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de mediciÑn, expresan las medidas en una unidad màs grande en t_rminos de una unidad màs pequeÐa. Anotan las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saben que 1 pie es 12 veces màs largo que 1 pulgada. Expresan la longitud de una culebra de 4 pies como 48 pulgadas. Generan una tabla de conversiÑn para pies y pulgadas con una lista de pares de nÏmeros (1, 12), (2, 24), (3, 36), ... | Grade 4 |
| Knotion | 4.MYD.A.2 | Utilizan las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volÏmenes lÕquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o decimales, y problemas que requieren expresar las medidas dadas en una unidad màs grande en t_rminos de una unidad màs pequeÐa. Representan cantidades medidas utilizando diagramas tales como rectas num_ricas con escalas de mediciÑn. | Grade 4 |
| Knotion | 4.MYD.B.4 | Hacen un diagrama de puntos para representar un conjunto de datos de medidas en fracciones de una unidad (1/2, 1/4, 1/8). Resuelven problemas sobre sumas y restas de fracciones utilizando la informaciÑn presentada en los diagramas de puntos. Por ejemplo, al utilizar un diagrama de puntos, hallan e interpretan la diferencia de longitud entre los ejemplares màs largos y màs cortos en una colecciÑn de insectos. | Grade 4 |
| Knotion | 4.MYD.C.5 | Reconocen que los àngulos son elementos geom_tricos formados cuando dos semirrectas comparten un extremo comÏn, y entienden los conceptos de la mediciÑn de àngulos. a. Un àngulo se mide con respecto a un cÕrculo, con su centro en el extremo comÏn de las semirrectas, tomando en cuenta la fracciÑn del arco circular entre los puntos donde ambas semirrectas intersecan el cÕrculo. Un àngulo que pasa por 1/360 de un cÕrculo se llama àngulo de un gradoy se puede utilizar para medir àngulos. b. Un àngulo que pasa por n àngulos de un grado tiene una medida angular de n grados. | Grade 4 |
| Knotion | 4.MYD.C.6 | Miden àngulos en grados de nÏmeros enteros utilizando un transportador. Dibujan àngulos con medidas dadas. | Grade 4 |
| Knotion | 4.MYD.C.7 | Reconocen la medida de un àngulo como una suma. Cuando un àngulo se descompone en partes que no se superponen, la medida del àngulo entero es la suma de las medidas de los àngulos de las partes. Resuelven problemas de suma y resta para encontrar àngulos desconocidos en problemas del mundo real y en problemas matemàticos, por ejemplo, al usar una ecuaciÑn con un sÕmbolo para la medida desconocida del àngulo. | Grade 4 |
| Knotion | 4.OYPA.A.1 | Interpretan una ecuaciÑn de multiplicaciÑn como una comparaciÑn, por ejemplo, 35 = 5x7 como un enunciado de que 35 es 5 veces 7, y 7 veces 5. Representan enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicaciÑn. | Grade 4 |
| Knotion | 4.OYPA.A.2 | Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un sÕmbolo para el nÏmero desconocido, distinguen una comparaciÑn multiplicativa de una comparaciÑn de suma. | Grade 4 |
| Knotion | 4.OYPA.B.4 | Hallan todos los pares de factores de nÏmeros enteros dentro del rango 1-100. Reconocen que un nÏmero entero es un mÏltiplo de cada uno de sus factores. Determinan si cierto nÏmero entero dentro del rango 1-100 es un mÏltiplo de cierto nÏmero de un solo dÕgito. Determinan si un nÏmero entero dentro del rango 1-100 es primo o compuesto. | Grade 4 |
| Knotion | 4.OYPA.C.5 | Generan un patrÑn de nÏmeros o figuras que sigue una regla dada. Identifican las caracterÕsticas aparentes del patrÑn que no eran explÕcitas en la regla misma. Por ejemplo, dada la regla Ðadir 3 y con el nÏmero 1 para comenzar, generan t_rminos en la secuencia resultante y observan que los t_rminos parecen alternarse entre nÏmeros impares y pares. Explican informalmente porqu_ los nÏmeros continuaràn alternàndose de esta manera. | Grade 4 |
| Knotion | 4.SND.A.1 | Reconocen que en un nÏmero entero de dÕgitos mÏltiples, un dÕgito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocen que 700 70 = 10 al aplicar conceptos de valor de posiciÑn y de divisiÑn. | Grade 4 |
| Knotion | 4.SND.A.2 | Leen y escriben nÏmeros enteros con dÕgitos mÏltiples usando numerales en base diez, los nombres de los nÏmeros, y sus formas desarrolladas. Comparan dos nÏmeros de dÕgitos mÏltiples basàndose en el valor de los dÕgitos en cada lugar, utilizando los sÕmbolos >, = y < para anotar los resultados de las comparaciones. | Grade 4 |
| Knotion | 4.SND.A.3 | Utilizan la comprensiÑn del valor de posiciÑn para redondear nÏmeros enteros con dÕgitos mÏltiples a cualquier lugar. | Grade 4 |
| Knotion | 4.SND.B.4 | Suman y restan con fluidez los nÏmeros enteros con dÕgitos mÏltiples utilizando el algoritmo convencional. | Grade 4 |
| Knotion | 4.SND.B.5 | Multiplican un nÏmero entero de hasta cuatro dÕgitos por un nÏmero entero de un dÕgito, y multiplican dos nÏmeros de dos dÕgitos, utilizando estrategias basadas en el valor de posiciÑn y las propiedades de operaciones. Ilustran y explican el càlculo utilizando ecuaciones, matrices rectangulares, y/o modelos de àrea. | Grade 4 |
| Knotion | 4.SND.B.6 | Hallan cocientes y residuos de nÏmeros enteros, a partir de divisiones con dividendos de hasta cuatrodÕgitos y divisores de un dÕgito, utilizando estrategias basadas en el valor de posiciÑn, las propiedades de las operaciones y/o la relaciÑn entre la multiplicaciÑn y la divisiÑn. Ilustran y explican el càlculo utilizando ecuaciones, matrices rectangulares, y/o modelos de àrea. | Grade 4 |
| Knotion | 5.FRA.B.3 | Interpretan una fracciÑn como la divisiÑn del numerador por el denominador (a/b = ab). Resuelven problemas verbales relacionados a la divisiÑn de nÏmeros enteros que resulten en fracciones o nÏmeros mixtos por ejemplo, emplean modelos visuales de fracciones o ecuaciones para representar el problema. Por ejemplo, al interpretar 3/4 como el resultado de la divisiÑn de 3 entre 4, notando que 3/4 multiplicados por 4 es igual a 3, y que cuando se comparten igualmente 3 enteros entre 4 personas, cada persona termina con una parte de _ de tamaÐo. Si 9 personas quieren compartir, por igual y en base al peso, un saco de arroz de 50 libras, Ëcuàntas libras de arroz debe recibir cada persona? ËEntre qu_ nÏmeros enteros se encuentra la respuesta? | Grade 5 |
| Knotion | 5.FRA.B.4 | Aplican y extienden conocimientos previos sobre la multiplicaciÑn para multiplicar una fracciÑn o un nÏmero entero por una fracciÑn. a. Interpretan el producto (a/b) _ q como tantas partes a de la reparticiÑn de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a _ q b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) _ 4 = 8/3, y crear un contexto para esta ecuaciÑn. Hacen lo mismo con (2/3) _ (4/5) = 8/15. (En general, (a /b) _ (c /d) = ac/bd). b. Hallan el àrea de un rectàngulo cuyos lados se miden en unidades fraccionarias, cubri_ndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demuestran que el àrea serÕa la misma que se hallarÕa si se multiplicaran las longitudes de los lados. Multiplican los nÏmeros fraccionarios de las longitudes de los lados para hallar el àrea de rectàngulos, y representar los productos de las fracciones como àreas rectangulares. | Grade 5 |
| Knotion | 5.FRA.B.5 | Interpretan la multiplicaciÑn como el poner a escala (cambiar el tamaÐo de) al: a. Comparan el tamaÐo de un producto al tamaÐo de un factor en base al tamaÐo del otro factor, sin efectuar la multiplicaciÑn indicada. b. Explican por qu_ al multiplicar un determinado nÏmero por una fracciÑn mayor que 1 se obtiene un producto mayor que el nÏmero dado (reconocen la multiplicaciÑn de nÏmeros enteros mayores que 1 como un caso comÏn); explican por qu_ la multiplicaciÑn de determinado nÏmero por una fracciÑn menor que 1 resulta en un producto menor que el nÏmero dado; y relacionan el principio de las fracciones equivalentes a/b = (n x a) / (n x b) con el fin de multiplicar a/ b por 1. | Grade 5 |
| Knotion | 5.FRA.B.6 | Resuelven problemas del mundo real relacionados a la multiplicaciÑn de fracciones y nÏmeros mixtos, por ejemplo, al usar modelos visuales de fracciones o ecuaciones para representar el problema. | Grade 5 |
| Knotion | 5.FRA.B.7 | Aplican y extienden conocimientos previos sobre la divisiÑn para dividir fracciones unitarias entre nÏmeros enteros y nÏmeros enteros entre fracciones unitarias. a. Interpretan la divisiÑn de una fracciÑn unitaria entre un nÏmero entero distinto al cero, y calculan sus cocientes. Por ejemplo, crean el contexto de un cuento para (1/3) 4, y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relaciÑn entre la multiplicaciÑn y la divisiÑn para explicar que (1/3) 4 = 1/12 porque (1/12) _ 4 = 1/3. b. Interpretan la divisiÑn de un nÏmero entero entre una fracciÑn unitaria y calculan sus cocientes. Por ejemplo, crean en el contexto de un cuento 4 (1/5), y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relaciÑn entre la multiplicaciÑn y la divisiÑn para explicar que 4 (1/5) =20 porque 20 _(1/5)= 4. c. Resuelven problemas del mundo real relacionados a la divisiÑn de fracciones unitarias entre nÏmeros enteros distintos al cero y la divisiÑn de nÏmeros enteros entre fracciones unitarias, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, Ëcuànto chocolate tendrà cada persona si 3 personas comparten _ libra de chocolate en partes iguales?ËCuàntas porciones de 1/3 de taza hay en 2 tazas de pasas? | Grade 5 |
| Knotion | 5.GE.A.1 | Utilizan un par de rectas num_ricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersecciÑn de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de nÏmeros ordenados, llamados coordenadas. Entienden que el primer nÏmero indica la distancia que se recorre desde el origen en direcciÑn sobre un eje, y el segundo nÏmero indica la distancia que se recorre sobre el segundo eje, siguiendo la convenciÑn de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). | Grade 5 |
| Knotion | 5.GE.A.2 | Representan problemas matemàticos y del mundo real al representar gràficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas segÏn el contexto. | Grade 5 |
| Knotion | 5.GE.B.3 | Entienden que los atributos que pertenecen a una categorÕa de figuras bidimensionales tambi_n pertenecen a todas las subcategorÕas de dicha categorÕa. Por ejemplo, todos los rectàngulos tienen cuatro àngulos rectos y los cuadrados son rectàngulos; por lo tanto, todos los cuadrados tienen cuatro àngulos rectos. | Grade 5 |
| Knotion | 5.GE.B.4 | Clasifican las figuras bidimensionales dentro de una jerarquÕa, segÏn sus propiedades. | Grade 5 |
| Knotion | 5.MYD.B.2 | Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). EfectÏan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la informaciÑn presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de lÕquido en vasos id_nticos de laboratorio, hallan la cantidad de lÕquido que cada vaso contiene si la cantidad total en todos los vasos fuera redistribuida igualmente. | Grade 5 |
| Knotion | 5.OYPA.A.1 | Incorpora sÕmbolos de agrupaciÑn como par_ntesis, corchetes y llaves, para separar operaciones dentro de una expresiÑn y denotar jerarquÕa de resoluciÑn. | Grade 5 |
| Knotion | 5.OYPA.B.3 | Generan dos patrones num_ricos utilizando dos reglas dadas. Identifican la relaciÑn aparente entre t_rminos correspondientes. Forman pares ordenados que consisten de los t_rminos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla Sumar 3 y el nÏmero inicial 0, y dada la regla Sumar 6 y el nÏmero inicial 0, generan los t_rminos en cada secuencia y observan que cada t_rmino de una secuencia, es el doble que el t_rmino correspondiente en la otra secuencia. Explican informalmente por qu_ esto es asÕ. | Grade 5 |
| Knotion | 5.SND.A.1 | Reconocen que en un nÏmero de varios dÕgitos, cualquier dÕgito en determinado lugar representa 10 veces lo que representa el mismo dÕgito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. | Grade 5 |
| Knotion | 5.SND.A.2 | Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un nÏmero por una potencia de 10, y explican los patrones en la posiciÑn del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan nÏmero enteros como exponentes para denotar la potencia de 10. | Grade 5 |
| Knotion | 5.SND.A.3 | Leen, escriben, y comparan decimales hasta las mil_simas. | Grade 5 |
| Knotion | 5.SND.A.4 | Utilizan el entendimiento del valor de posiciÑn para redondear decimales a cualquier lugar. | Grade 5 |
| Knotion | 5.SND.B.5 | Multiplican nÏmeros enteros de varios dÕgitos con fluidez, utilizando el algoritmo convencional. | Grade 5 |
| Knotion | 5.SND.B.6 | Encuentran nÏmeros enteros como cocientes de nÏmeros enteros con dividendos de hasta cuatro dÕgitos y divisores de dos dÕgitos, utilizando estrategias basadas en el valor de posiciÑn, las propiedades de las operaciones, y/o la relaciÑn entre la multiplicaciÑn y la divisiÑn. Ilustran y explican el càlculo utilizando ecuaciones, matrices rectangulares y modelos de àrea. | Grade 5 |
| Knotion | 6.EXEC.A.1 | Escriben y evalÏan expresiones num_ricas relacionadas a los exponentes de nÏmeros enteros. | Grade 6 |
| Knotion | 6.EXEC.A.2 | Escriben, leen y evalÏan expresiones en las cuales las letras representan nÏmeros. | Grade 6 |
| Knotion | 6.EXEC.A.3 | Aplican las propiedades de las operaciones para generar expresiones equivalentes. Por ejemplo, al aplicar la propiedad distributiva a la expresiÑn 3(2 + x) para obtener la expresiÑn equivalente 6 + 3x; al aplicar la propiedad distributiva a la expresiÑn 24 + 18y para obtener la expresiÑn equivalente 6(4x + 3y); al aplicar las propiedades de las operaciones a y + y + y para obtener la expresiÑn equivalente 3y. | Grade 6 |
| Knotion | 6.EXEC.B.5 | Entienden el resolver una ecuaciÑn o una desigualdad como un proceso en el cual se contesta una pregunta: Ëqu_ valores de un conjunto especificado, si es que los hay, hacen que la ecuaciÑn o la desigualdad sea verdadera? Utilizan la sustituciÑn para determinar si un nÏmero dado en un conjunto especificado hace que una ecuaciÑn o desigualdad sea verdadera. | Grade 6 |
| Knotion | 6.EXEC.B.7 | Resuelven problemas matemàticos o del mundo real al escribir y resolver ecuaciones de la forma x + p = q ademàs px = q en casos en los que p, q ademàs de x son todos nÏmeros racionales no negativos. | Grade 6 |
| Knotion | 6.EXEC.B.8 | Escriben una desigualdad de la forma x > c Ñ x < c para representar una restricciÑn o condiciÑn en un problema matemàtico o del mundo real. Reconocen que las desigualdades de la forma x > c Ñ x < c tienen un nÏmero infinito de soluciones; representan las soluciones de dichas desigualdades sobre una recta num_rica. | Grade 6 |
| Knotion | 6.GE.A.3 | Dibujan polÕgonos en un plano de coordenadas dadas las coordenadas para los v_rtices; utilizan coordenadas para hallar la longitud de un lado que conecta dos puntos cuya primera o segunda coordenada es la misma. Aplican estas t_cnicas al contexto de la resoluciÑn de problemas matemàticos y del mundo real. | Grade 6 |
| Knotion | 6.RAZ.A.1 | Relaciona la nociÑn de razÑn con proporciÑn. | Grade 6 |
| Knotion | 6.RAZ.A.2 | Entienden el concepto de una tasa por unidad a/b asociada con una razÑn a:b para b ? 0, y utilizan el lenguaje de las tasas en el contexto de una relaciÑn de razones. Por ejemplo, Esta receta tiene una razÑn de 3 tazas de harina por 4 tazas de azÏcar, asi que hay 3/4 de taza de harina por cada taza de azÏcar. Pagamos $75 por 15 hamburguesas, lo cual es una tasa de $5 por hamburguesa. | Grade 6 |
| Knotion | 6.RAZ.A.3 | Utilizan el razonamiento sobre las razones y tasas para resolver problemas matemàticos y del mundo real, por ejemplo, al razonar sobre tablas de razones equivalentes, diagramas de cintas, diagramas de rectas num_ricas dobles, o ecuaciones. | Grade 6 |
| Knotion | 6.SN.A.1 | Interpretan y calculan cocientes de fracciones, y resuelven problemas verbales relacionados a la divisiÑn de fracciones entre fracciones. | Grade 6 |
| Knotion | 6.SN.B.2 | Dividen con facilidad nÏmeros de mÏltiples dÕgito utilizando el algoritmo convencional. | Grade 6 |
| Knotion | 6.SN.B.3 | Suman, restan, multiplican y dividen decimales demÏltiples dÕgitos utilizando el algoritmo convencional para cada operaciÑn, con facilidad. | Grade 6 |
| Knotion | 6.SN.C.5 | Entienden que los nÏmeros positivos y negativos se usan juntos para describir cantidades que tienen valores o sentidos opuestos (por ejemplo, la temperatura sobre/bajo cero, la elevaciÑn sobre/bajo el nivel del mar, los cr_ditos/d_bitos, la carga el_ctrica positiva/negativa); utilizan nÏmeros positivos y negativos para representar cantidades en contextos del mundo real, explicando el significado del 0 en cada situaciÑn. | Grade 6 |
| Knotion | 6.SN.C.6 | Entienden un nÏmero racional como un punto en una recta num_rica. Extienden el conocimiento adquirido en los grados anteriores sobre las rectas num_ricas y los ejes de coordenadas para representar puntos de nÏmeros negativos en la recta y en el plano de coordenadas. | Grade 6 |
| Knotion | 6.SN.C.7 | Interpretan los enunciados de desigualdad como enunciados sobre la posiciÑn relativa de dos nÏmeros en una recta num_rica. Por ejemplo, al interpretar ?3 > ?7 como un enunciado de que ?3 està situado a la derecha de ?7 en una recta num_rica orientada de izquierda a derecha. | Grade 6 |
| Knotion | 6.SN.C.8 | Resuelven problemas matemàticos y del mundo real al marcar puntos en los cuatro cuadrantes de un plano de coordenadas. Incluyen el uso de coordenadas y el valor absoluto para hallar las distancias entre puntos que tienen la misma primera o segunda coordenada. | Grade 6 |
| Knotion | 7.EXEC.A.1 | Aplican las propiedades de operaciones como estrategias para sumar, restar, factorizar y expander expresiones lineales con coeficientes racionales. | Grade 7 |
| Knotion | 7.EXEC.A.3 | Resuelven problemas matemàticos de varios pasos relacionados con el mundo real, en los que se exponen nÏmeros racionales positivos y negativos de cualquier tipo (nÏmeros enteros, fracciones y decimales), al utilizar herramientas estrat_gicamente. Aplican las propiedades de operaciones con el fin de calcular nÏmeros en cualquier forma; convierten nÏmeros en cualquiera de sus formas segÏn sea lo apropiado; y evaluan la racionalidad de las respuestas utilizando càlculos mentales y estrategias de estimaciÑn. Por ejemplo, si una mujer que gana $25 / hora obtiene un aumento del 10%, ganarà 1/10 de su salario adicional por hora, o $2.50, lo que significa un salario nuevo de $27.50. Si se desea colocar un toallero de 93/4 pulgadas de largo en el centro de una puerta que tiene un ancho de 271/2 pulgadas, se deberà colocar la barra como a 9 pulgadas de distancia de cada borde; este estimado se puede usar para revisar el càlculo exacto. | Grade 7 |
| Knotion | 7.GE.A.1 | Resuelven problemas relacionados con dibujos aescala de figuras geom_tricas, incluyendo longitudes y àreas reales calculadas a partir de un dibujo a escala y reproducen un dibujo a escala en una escala diferente. | Grade 7 |
| Knotion | 7.GE.A.2 | Dibujan (a pulso, con regla y un transportador, y con recursos tecnolÑgicos) figuras geom_tricas con ciertas condiciones dadas. Se concentran en la construcciÑn de triàngulos a partir de tres medidas de àngulos o lados, notan cuando las condiciones determinan un sÑlo triàngulo, màs de un triàngulo o que no hay un triàngulo. | Grade 7 |
| Knotion | 7.GE.B.5 | Utilizan las propiedades de àngulos suplementarios, complementarios, verticales y adyacentes en problemas de pasos mÏltiples para escribir y resolver ecuaciones simples para un àngulo desconocido en una figura. | Grade 7 |
| Knotion | 7.RAZ.A.1 | Calculan razones unitarias relacionadas con proporciones de fracciones, incluyendo relaciones de longitud, àreas y otras cantidades medidas en unidades similares o diferentes. Por ejemplo, si una persona camina 1/2 milla en 1/4 de hora, calculan la tasa de unidad como la fracciÑn completa de 1/2 1/4 millas por hora, que equivale a 2 millas por hora. | Grade 7 |
| Knotion | 7.RAZ.A.2 | Reconocen y representan relaciones de proporcionalidad entre cantidades. | Grade 7 |
| Knotion | 7.RAZ.A.3 | Utilizan relaciones de proporcionalidad para solucionar problemas de pasos multiple, sobre razones y porcentaje. Ejemplos: inter_s simple, impuestos, màrgenes de ganancias o rebajas, propinas y comisiones, honorarios, aumentos y disminuciones en los porcentajes, porcentaje de errores. | Grade 7 |
| Knotion | 7.SN.A.1 | Describen situaciones en las que se combinen cantidades opuestas para obtener 0. Por ejemplo, un àtomo de hidrÑgeno tiene una carga 0 debido a que sus dos elementos tienen tiene cargas opuestas. | Grade 7 |
| Knotion | 7.SN.A.2 | Comprenden que la multiplicaciÑn se extiende desde fracciones hasta nÏmeros racionales al requerir que las operaciones continÏen satisfaciendo las propiedades de las operaciones, particularmente la propiedad distributiva, dando resultado a productos tales como (-1) (-1) = 1, y las reglas para multiplicar nÏmeros con sus signos correspondientes. Interpretan los productos de nÏmeros racionales al describir contextos del mundo real. | Grade 7 |
| Knotion | 7.SN.A.3 | Resuelven problemas matemàticos y del mundo real relacionados con las cuatro operaciones con nÏmeros racionales. | Grade 7 |
| Knotion | 8.EXEC.A.3 | Usan nÏmeros expresados mediante un Ïnico dÕgito multiplicado por una potencia de 10 de un entero para estimar cantidades muy grandes o muy pequeÐas, y para expresar cuantas veces mayor es una cantidad con respecto a otra. Por ejemplo, al estimar la poblaciÑn de los Estados Unidos como 3 _ 108 y la poblaciÑn del mundo como 7 _ 109 , y determinar que la poblaciÑn del mundo es màs de 20 veces màs grande. | Grade 8 |
| Knotion | 8.EXEC.A.4 | Realizan operaciones con nÏmeros expresados en notaciÑn cientÕfica, incluyendo problemas donde se utilicen ambas la notaciÑn decimal y cientÕfica. Usan notaciÑn cientÕfica y escogen unidades de tamaÐo apropiado para medir cantidades muy grandes o muy pequeÐas (por ejemplo, usan milÕmetros por aÐo para la expansiÑn del lecho marino). Interpretan la notaciÑn cientÕfica que ha sido generada por medio de tecnologÕa. | Grade 8 |
| Knotion | 8.EXEC.B.5 | Grafican relaciones proporcionales, interpretando la tasa unitaria como la pendiente de la gràfica. Comparan dos relaciones proporcionales diferentes representadas de manera diferente. Por ejemplo, comparan una gràfica de tiempo-distancia con una ecuaciÑn de tiempo y distancia para determinar cuàl de los dos objetos en movimiento tiene una velocidad mayor. | Grade 8 |
| Knotion | 8.EXEC.B.6 | Usan triàngulos similares para explicar porqu_ la pendiente m es igual entre dos puntos definidos sobre una lÕnea no vertical en el plano de coordenadas; derivan la ecuaciÑn y = mx para una lÕnea a trav_s del origen y la ecuaciÑn y = mx + b para una lÕnea que interseca el eje vertical en b. | Grade 8 |
| Knotion | 8.EXEC.C.7 | Dan ejemplos de ecuaciones lineales de una variable con una soluciÑn, muchas soluciones infinitas, o sin soluciÑn. Demuestran cuàl de estas posibilidades es el caso al transformar sucesivamente la ecuaciÑn dada en formas màs simples, hasta que resulte una ecuaciÑn equivalente del tipo x = a, a = a, o a = b (donde a y b son nÏmeros diferentes). | Grade 8 |
| Knotion | 8.EXEC.C.8 | Comprenden que las soluciones para un sistema de dos ecuaciones lineales con dos variables corresponden a puntos de intersecciÑn de sus gràficas, porque los puntos de intersecciÑn satisfacen ambas ecuaciones simultàneamente. | Grade 8 |
| Knotion | 8.FUN.A.1 | Comprenden que una funciÑn es una regla que asigna exactamente una salida a cada entrada. La gràfica de una funciÑn es el conjunto de pares ordenados que consiste de una entrada y la salida correspondiente. | Grade 8 |
| Knotion | 8.FUN.A.2 | Comparan propiedades de dos funciones, cada una de las cuales està representada de manera diferente (algebraicamente, gràficamente, num_ricamente en tablas, o por descripciones verbales). Por ejemplo, dada una funciÑn lineal representada por una tabla de valores y una funciÑn lineal representada por una expresiÑn algebraica, determinan cual funciÑn tiene la mayor tasa de cambio. | Grade 8 |
| Knotion | 8.FUN.A.3 | Interpretan la ecuaciÑn y = mx + b como la definiciÑn de una funciÑn lineal, cuya gràfica es una lÕnea recta; dan ejemplos de funciones que no son lineales. Por ejemplo, la funciÑn A = s2 produce el àrea de un cuadrado como una funciÑn de su longitud lateral no es lineal porque su gràfica contiene los puntos (1,1), (2,4) y (3,9), que no estàn sobre una lÕnea recta | Grade 8 |
| Knotion | 8.FUN.B.4 | Construyen una funciÑn para representar una relaciÑn lineal entre dos cantidades. Determinan la tasa de cambio y el valor inicial de la funciÑn a partir de una descripciÑn de una relaciÑn o a partir de dos valores (x, y), incluyendo leerlas en una tabla o en una gràfica. Interpretan la tasa de cambio y el valor inicial de una funciÑn lineal en t_rminos de la situaciÑn que modela, y en t_rminos de su gràfica o de una tabla de valores. | Grade 8 |
| Knotion | 8.FUN.B.5 | Describen de manera cualitativa la relaciÑn funcional entre dos cantidades al analizar una gràfica (por ejemplo, donde la funciÑn crece o decrece, es lineal o no lineal). Esbozan una gràfica que exhibe las caracterÕsticas cualitativas de una funciÑn que ha sido descrita verbalmente. | Grade 8 |
| Knotion | 8.GE.A.2 | Entienden que una figura bidimensional es congruente con otra si se puede obtener la segunda a partir de la primera por una secuencia de rotaciones, reflexiones, y traslaciones; dadas dos figuras congruentes, describen una secuencia que exhibe la congruencia entre ellas. | Grade 8 |
| Knotion | 8.GE.A.4 | Entienden que una figura bidimensional es similar a otra si se puede obtener la segunda a partir de la primera por una secuencia de rotaciones, reflexiones, traslaciones, y dilataciones; dadas dos figuras bidimensionales similares, describen una secuencia que exhibe la semejanza entre ellas. | Grade 8 |
| Knotion | 8.GE.B.7 | Aplican el Teorema de Pitàgoras para determinar las longitudes laterales desconocidas en triàngulos rectos en problemas del mundo real y matemàticos en dos y tres dimensiones. | Grade 8 |
| Knotion | 8.GE.B.8 | Aplican el Teorema de Pitàgoras para encontrar la distancia entre dos puntos en un sistema de coordenadas. | Grade 8 |
| Knotion | 8.PRO.A.1 | Construyen e interpretan diagramas de dispersiÑn para datos bivariados entrada de mediciÑn para investigar patrones de asociaciÑn entre dos cantidades. Describen patrones como agrupaciones, valores atÕpicos, asociaciÑn positiva o negativa, asociaciÑn lineal, y asociaciÑn no lineal. | Grade 8 |
| Knotion | 8.PRO.A.2 | Saben que lÕneas rectas se utilizan ampliamente para modelar relaciones entre dos variables cuantitativas. Para diagramas de dispersiÑn que sugieren una asociaciÑn lineal, ajustan informalmente una lÕnea recta, y evalÏan informalmente el ajuste del modelo juzgando la cercanÕa de los puntos de datos a la lÕnea. | Grade 8 |
| Knotion | K1.CYCA.B.4 | Relaciona la acciÑn de aumentar una colecciÑn con agregar objetos. | Kindergarten |
| Knotion | K1.CYCA.C.6 | Identifican si el nÏmero de objetos de un grupo es mayor que, menor que, o igual que el nÏmero de objetos en otro grupo, por ejemplo, al usar estrategias para contar y para emparejar. | Kindergarten |
| Knotion | K2.CYCA.C.6 | Elige el conjunto que tiene màs o menos objetos despu_s de haber observado un par o una tercia de colecciones. | Kindergarten |
| Knotion | K2.OYPA.A.1 | Relaciona la acciÑn de aumentar una colecciÑn con agregar objetos. | Kindergarten |
| Knotion | K3.CYCA.A.1 | Identifica las regularidades de la sucesiÑn num_rica del 0 al 100. | Kindergarten |
| Knotion | K3.CYCA.A.2 | Cuentan hacia delante desde un nÏmero dado dentro de una secuencia conocida (en lugar de comenzar con el 1). | Kindergarten |
| Knotion | K3.CYCA.A.3 | Escribe y lee los nÏmeros (1 a 20). | Kindergarten |
| Knotion | K3.CYCA.B.4 | Escribe y lee un listado de nÏmeros que inician despu_s del uno y lo completa, ya sea en la parte intermedia o lo continÏa. | Kindergarten |
| Knotion | K3.CYCA.B.5 | Completa el elemento faltante de una secuencia de nÏmeros o figuras incompleta. | Kindergarten |
| Knotion | K3.OYPA.A.1 | Relaciona las acciones de aumentar y disminuir con la suma y con la resta. | Kindergarten |
| Knotion | K3.OYPA.A.2 | Resuelven problemas verbales de sumal y resta, y suman y restan hasta 10, por ejemplo, utilizar objetos o dibujos para representar el problema. | Kindergarten |
| Knotion | K3.OYPA.A.3 | Utiliza material concreto, dibujos y/o nÏmeros para descomponer nÏmeros menores a veinte como la suma de una decena y las unidades faltantes. | Kindergarten |
| Knotion | K3.OYPA.A.4 | Para cualquier nÏmero entre el 1 al 9, encuentran el nÏmero que llega al 10 cuando se le suma al nÏmero determinado, por ejemplo, al utiizar objetos o dibujos, y representar la respuesta con un dibujo o una ecuaciÑn. | Kindergarten |
| Knotion | K3.OYPA.A.5 | Suman y restan con fluidez de y hasta el nÏmero 5. | Kindergarten |
| Knotion | K3.SND.A.1 | Componen y descomponen nÏmeros del 11 al 19 en diez unidades y algunas màs, por ejemplo, al utilizar objetos o dibujos, y representar cada composiciÑn o descomposiciÑn por medio de un dibujo o ecuaciÑn (por ejemplo, 18 = 10 + 8); comprenden que estos nÏmeros estàn compuestos por diez unidades y una, dos, tres, cuatro, cinco, seis, siete, ocho o nueve unidades. | Kindergarten |
| Knotion | A-APR.B.3 | Identifica los ceros de los polinomios cuando haya factorizaciones apropiadas y utiliza los ceros para construir un bosquejo gràfico de la funciÑn que define el polinomio. | lgebra |
| Knotion | A-CED.A.2 | Crea ecuaciones en dos variables o màs para representar relaciones entre cantidades; representa ecuaciones de forma gràfica en los ejes con etiquetas de referencia y escalas. | lgebra |
| Knotion | A-SSE.A.2 | Utiliza la estructura de una expresiÑn para identificar formas de volver a escribirla. | lgebra |
| Knotion | A-SSE.B.3 | Elige y produce una forma equivalente de la expresiÑn para revelar y explicar propiedades de la cantidad que representa. | lgebra |
| Knotion | F-BF.A.1 | Escribe una funciÑn que describa la relaciÑn entre dos cantidades. | lgebra |
| Knotion | F-IF.A.2 | Utiliza la notaciÑn, evalÏa las funciones de las variables independientes en sus dominios e interpreta las expresiones que usen la notaciÑn en t_rminos del contexto. | lgebra |
| Knotion | F-IF.B.4 | Para una funciÑn que modela una relaciÑn entre dos cantidades, interpreta las caracterÕsticas fundamentales de las gràficas y las tablas en t_rminos de las cantidades, y realiza bocetos de gràficas que muestren las caracterÕsticas fundamentales tras recibir una descripciÑn verbal de la relaciÑn. Entre las caracterÕsticas fundamentales estàn: intersecciones; intervalos en los que la funciÑn es creciente, decreciente, positiva o negativa; màximos y mÕnimos relativos; simetrÕas; comportamiento en los extremos; y periodicidad. | lgebra |
| Knotion | F-IF.C.7 | Realiza gràficas de funciones expresadas de manera simbÑlica y muestra caracterÕsticas fundamentales de la gràfica, a mano en casos sencillos y usando la tecnologÕa para casos màs complicados. | lgebra |
| Knotion | S-ID.B.6 | Representa los datos en dos variables cuantitativas en un gràfico de dispersiÑn y describe cÑmo se relacionan las variables. | lgebra |
| Manitoba | K.N.1 | Say the number sequence by 1s, starting anywhere from 1 to 30 and from 10 to 1. | Kindergarten |
| Manitoba | K.N.2 | Subitize and name familiar arrangements of 1 to 6 dots (or objects). | Kindergarten |
| Manitoba | K.N.3 | Relate a numeral, 1 to 10, to its respective quantity. | Kindergarten |
| Manitoba | K.N.4 | Represent and describe numbers 2 to 10 in two parts, concretely and pictorially. | Kindergarten |
| Manitoba | K.N.5.1 | Demonstrate an understanding of counting to 10 by indicating that the last number said identifies how many. | Kindergarten |
| Manitoba | K.N.5.2 | Demonstrate an understanding of counting to 10 by showing that any set has only one count. | Kindergarten |
| Manitoba | K.N.6.1 | Compare quantities, 1 to 10, using one-to-one correspondence. | Kindergarten |
| Manitoba | K.N.6.2 | Compare quantities, 1 to 10, by ordering numbers representing different quantities. | Kindergarten |
| Manitoba | K.PR.1 | Demonstrate an understanding of repeating patterns (two or three elements) by, identifying, reproducing, extending, creating, patterns using manipulatives, sounds, and actions. | Kindergarten |
| Manitoba | K.SS.1 | Use direct comparison to compare two objects based on a single attribute, such as length (height), mass (weight), and volume (capacity). | Kindergarten |
| Manitoba | K.SS.2 | Sort 3-D objects using a single attribute. | Kindergarten |
| Manitoba | K.SS.3 | Build and describe 3-D objects. | Kindergarten |
| Manitoba | 1.N.1.1 | Say the number sequence by 1s forward and backward between any two given numbers (0 to 100). | Grade 1 |
| Manitoba | 1.N.1.2 | Say the number sequence by 2s to 30, forward starting at 0. | Grade 1 |
| Manitoba | 1.N.1.3 | Say the number sequence by 5s and 10s to 100, forward starting at 0. | Grade 1 |
| Manitoba | 1.N.2 | Subitize and name familiar arrangements of 1 to 10 dots (or objects). | Grade 1 |
| Manitoba | 1.N.3.1 | Demonstrate an understanding of counting by using the counting-on strategy. | Grade 1 |
| Manitoba | 1.N.3.2 | Demonstrate an understanding of counting by using parts or equal groups to count sets. | Grade 1 |
| Manitoba | 1.N.4 | Represent and describe numbers to 20, concretely, pictorially, and symbolically. | Grade 1 |
| Manitoba | 1.N.5 | Compare and order sets containing up to 20 elements to solve problems using referents and one-to-one correspondence. | Grade 1 |
| Manitoba | 1.N.6 | Estimate quantities to 20 by using referents. | Grade 1 |
| Manitoba | 1.N.7 | Demonstrate, concretely and pictorially, how a number, up to 30, can be represented by a variety of equal groups with and without singles. | Grade 1 |
| Manitoba | 1.N.8 | Identify the number, up to 20, that is one more, two more, one less, and two less than a given number. | Grade 1 |
| Manitoba | 1.N.9.1 | Demonstrate an understanding of addition of numbers with answers to 20 and their corresponding subtraction facts, concretely, pictorially, and symbolically, by using familiar and mathematical language to describe additive and subtractive actions from their experience. | Grade 1 |
| Manitoba | 1.N.9.2 | Demonstrate an understanding of addition of numbers with answers to 20 and their corresponding subtraction facts, concretely, pictorially, and symbolically, by creating and solving problems in context that involve addition and subtraction. | Grade 1 |
| Manitoba | 1.N.9.3 | Demonstrate an understanding of addition of numbers with answers to 20 and their corresponding subtraction facts, concretely, pictorially, and symbolically, by modelling addition and subtraction using a variety of concrete and visual representations, and recording the process symbolically. | Grade 1 |
| Manitoba | 1.N.10 | Describe and use mental mathematics strategies including counting on, counting back, using one more, one less, making 10, starting from known doubles, using addition to subtract to determine the basic addition and related subtractions facts to 18. | Grade 1 |
| Manitoba | 1.PR.1 | Demonstrate an understanding of repeating patterns (two to four elements). | Grade 1 |
| Manitoba | 1.PR.2 | Translate repeating patterns from one representation to another. | Grade 1 |
| Manitoba | 1.PR.3 | Describe equality as a balance and inequality as an imbalance, concretely and pictorially (0 to 20). | Grade 1 |
| Manitoba | 1.PR.4 | Record equalities using the equal symbol (0 to 20). | Grade 1 |
| Manitoba | 1.SS.1 | Demonstrate an understanding of measurement as a process of comparing. | Grade 1 |
| Manitoba | 1.SS.2 | Sort 3-D objects and 2-D shapes using one attribute, and explain the sorting rule. | Grade 1 |
| Manitoba | 1.SS.3 | Replicate composite 2-D shapes and 3-D objects. | Grade 1 |
| Manitoba | 1.SS.4 | Compare 2-D shapes to parts of 3-D objects in the environment. | Grade 1 |
| Manitoba | 2.N.1.1 | Say the number sequence from 0 to 100 by 2s, 5s, and 10s, forward and backward, using starting points that are multiples of 2, 5, and 10 respectively. | Grade 2 |
| Manitoba | 2.N.1.2 | Say the number sequence from 0 to 100 by 10s using starting points from 1 to 9. | Grade 2 |
| Manitoba | 2.N.1.3 | Say the number sequence from 0 to 100 by 2s starting from 1. | Grade 2 |
| Manitoba | 2.N.2 | Demonstrate if a number (up to 100) is even or odd. | Grade 2 |
| Manitoba | 2.N.3 | Describe order or relative position using ordinal numbers. | Grade 2 |
| Manitoba | 2.N.4 | Represent and describe numbers to 100, concretely, pictorially, and symbolically. | Grade 2 |
| Manitoba | 2.N.5 | Compare and order numbers up to 100. | Grade 2 |
| Manitoba | 2.N.6 | Estimate quantities to 100 using referents. | Grade 2 |
| Manitoba | 2.N.7 | Illustrate, concretely and pictorially, the meaning of place value for numbers to 100. | Grade 2 |
| Manitoba | 2.N.8 | Demonstrate and explain the effect of adding zero to or subtracting zero from any number. | Grade 2 |
| Manitoba | 2.N.9.1 | Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by using personal strategies for adding and subtracting with and without the support of manipulatives. | Grade 2 |
| Manitoba | 2.N.9.2 | Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by creating and solving problems that involve addition and subtraction. | Grade 2 |
| Manitoba | 2.N.9.3 | Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by explaining that the order in which numbers are added does not affect the sum. | Grade 2 |
| Manitoba | 2.N.9.4 | Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by explaining that the order in which numbers are subtracted may affect the difference. | Grade 2 |
| Manitoba | 2.N.10 | Apply mental mathematics strategies, including using doubles, using one more, one less, using two more, two less, building on a known double, using addition for subtraction to develop recall of basic addition facts to 18 and related subtractions facts. | Grade 2 |
| Manitoba | 2.PR.1 | Predict an element in a repeating pattern using a variety of strategies. | Grade 2 |
| Manitoba | 2.PR.2 | Demonstrate an understanding of increasing patters by describing, reproducing, extending and creating patterns using manipulatives, diagrams, sounds and actions (numbers to 100). | Grade 2 |
| Manitoba | 2.PR.3 | Demonstrate and explain the meaning of equality and inequality by using manipulatives and diagrams (0 to 100). | Grade 2 |
| Manitoba | 2.PR.4 | Record equalities and inequalities symbolically using the equal symbol or the not-equal symbol. | Grade 2 |
| Manitoba | 2.SS.1 | Relate the number of days to a week and the number of months to a year in a problem-solving context. | Grade 2 |
| Manitoba | 2.SS.2 | Relate the size of a unit of measure to the number of units (limited to non-standard units) used to measure length and mass (weight). | Grade 2 |
| Manitoba | 2.SS.3 | Compare and order objects by length, height, distance around, and mass (weight) using non-standard units, and make statements of comparison. | Grade 2 |
| Manitoba | 2.SS.4 | Measure length to the nearest non-standard unit by using multiple copies of a unit or using a single copy of a unit. | Grade 2 |
| Manitoba | 2.SS.5 | Demonstrate that changing the orientation of an object does not alter the measurements of its attributes. | Grade 2 |
| Manitoba | 2.SS.6 | Sort 2-D shapes and 3-D objects using two attributes, and explain the sorting rule. | Grade 2 |
| Manitoba | 2.SS.7 | Describe, compare, and construct 3-D objects, including cubes, spheres, cones, cylinders, prisms and pyramids. | Grade 2 |
| Manitoba | 2.SS.8 | Describe, compare, and construct 2-D shapes, including triangles, squares, rectangels and circles. | Grade 2 |
| Manitoba | 2.SS.9 | Identify 2-D shapes as parts of 3-D objects in the environment. | Grade 2 |
| Manitoba | 2.SP.1 | Gather and record data about self and others to answer questions. | Grade 2 |
| Manitoba | 2.SP.2 | Construct and interpret concrete graphs and pictographs to solve problems. | Grade 2 |
| Manitoba | 3.N.1.1 | Say the number sequence between any two given numbers forward and backward from 0 to 1000 by 10s or 100s, using any starting point. | Grade 3 |
| Manitoba | 3.N.1.2 | Say the number sequence between any two given numbers forward and backward from 0 to 1000 by 5s, using starting points that are multiples of 5. | Grade 3 |
| Manitoba | 3.N.1.3 | Say the number sequence between any two given numbers forward and backward from 0 to 1000 by 25s, using starting points that are multiples of 25. | Grade 3 |
| Manitoba | 3.N.1.4 | Say the number sequence between any two given numbers forward and backward from 0 to 100 by 3s, using starting points that are multiples of 3. | Grade 3 |
| Manitoba | 3.N.1.5 | Say the number sequence between any two given numbers forward and backward from 0 to 100 by 4s, using starting points that are multiples of 4. | Grade 3 |
| Manitoba | 3.N.2 | Represent and describe numbers to 1000, concretely, pictorially, and symbolically. | Grade 3 |
| Manitoba | 3.N.3 | Compare and order numbers to 1000. | Grade 3 |
| Manitoba | 3.N.4 | Estimate quantities less than 1000 using referents. | Grade 3 |
| Manitoba | 3.N.5 | Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000. | Grade 3 |
| Manitoba | 3.N.6.1 | Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as adding from left to right. | Grade 3 |
| Manitoba | 3.N.6.2 | Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as taking one addend to the nearest multiple of ten and then compensating. | Grade 3 |
| Manitoba | 3.N.6.3 | Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as using doubles. | Grade 3 |
| Manitoba | 3.N.7.1 | Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as taking the subtrahend to the nearest multiple of ten and then compensating. | Grade 3 |
| Manitoba | 3.N.7.2 | Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as thinking of addition. | Grade 3 |
| Manitoba | 3.N.7.3 | Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as using doubles. | Grade 3 |
| Manitoba | 3.N.8 | Apply estimation strategies to predict sums and differences of two 2-digit numerals in a problem-solving context. | Grade 3 |
| Manitoba | 3.N.9.1 | Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1-, 2-, and 3-digit numerals) by using personal strategies for adding and subtracting with and without the support of maniplulatives. | Grade 3 |
| Manitoba | 3.N.9.2 | Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1-, 2-, and 3-digit numerals) by creating and solving problems in contexts that involve addition and subtraction of numbers concretely, pictorially, and symbolically. | Grade 3 |
| Manitoba | 3.N.10 | Apply mental math strategies to determine addition facts and related subtraction facts to 18 (9 + 9). | Grade 3 |
| Manitoba | 3.N.11.1 | Demonstrate an understanding of multiplication to 5 × 5 by representing and explaining multiplication using equal grouping and arrays. | Grade 3 |
| Manitoba | 3.N.11.2 | Demonstrate an understanding of multiplication to 5 × 5 by creating and solving problems in context that involve multiplication. | Grade 3 |
| Manitoba | 3.N.11.3 | Demonstrate an understanding of multiplication to 5 × 5 by modelling multiplication using concrete and visual representations, and recording the process symbolically. | Grade 3 |
| Manitoba | 3.N.11.4 | Demonstrate an understanding of multiplication to 5 × 5 by relating multiplication to repeated addition. | Grade 3 |
| Manitoba | 3.N.11.5 | Demonstrate an understanding of multiplication to 5 × 5 by relating multiplication to division. | Grade 3 |
| Manitoba | 3.N.12.1 | Demonstrate an understanding of division by representing and explaining division using equal sharing and equal grouping limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.12.2 | Demonstrate an understanding of division by creating and solving problems in context that involve equal sharing and equal grouping limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.12.3 | Demonstrate an understanding of division by modelling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.12.4 | Demonstrate an understanding of division by relating division to repeated subtraction limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.12.5 | Demonstrate an understanding of division by relating division to multiplication limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.13.1 | Demonstrate an understanding of fractions by explaining that a fraction represents a portion of a whole divided into equal parts. | Grade 3 |
| Manitoba | 3.N.13.2 | Demonstrate an understanding of fractions by describing situations in which fractions are used. | Grade 3 |
| Manitoba | 3.N.13.3 | Demonstrate an understanding of fractions by comparing fractions of the same whole with like denominators. | Grade 3 |
| Manitoba | 3.PR.1 | Demonstrate an understanding of increasing patterns by describing, extending, comparing, and creating patterns using manipulatives, diagrams, and numbers to 1000. | Grade 3 |
| Manitoba | 3.PR.2 | Demonstrate an understanding of decreasing patterns by describing, extending, comparing, and creating patterns using manipulatives, diagrams, and numbers starting from 1000 or less. | Grade 3 |
| Manitoba | 3.PR.3 | Solve one-step addition and subtraction equations involving symbols representing an unknown number. | Grade 3 |
| Manitoba | 3.SS.1 | Relate the passage of time to common activities using non- standard and standard units (minutes, hours, days, weeks, months, years). | Grade 3 |
| Manitoba | 3.SS.2 | Relate the number of seconds to a minute, the number of minutes to an hour, and the number of days to a month in a problem-solving context. | Grade 3 |
| Manitoba | 3.SS.3.1 | Demonstrate an understanding of measuring length (cm, m) by selecting and justifying referents for the units cm and m. | Grade 3 |
| Manitoba | 3.SS.3.2 | Demonstrate an understanding of measuring length (cm, m) by modelling and describing the relationship between the units cm and m. | Grade 3 |
| Manitoba | 3.SS.3.3 | Demonstrate an understanding of measuring length (cm, m) by estimating length using referents. | Grade 3 |
| Manitoba | 3.SS.3.4 | Demonstrate an understanding of measuring length (cm, m) by measuring and recording length, width, and height. | Grade 3 |
| Manitoba | 3.SS.4.1 | Demonstrate an understanding of measuring mass (g, kg) by selecting and justifying referents for the units g and kg. | Grade 3 |
| Manitoba | 3.SS.4.2 | Demonstrate an understanding of measuring mass (g, kg) by modelling and describing the relationship between the units g and kg. | Grade 3 |
| Manitoba | 3.SS.4.3 | Demonstrate an understanding of measuring mass (g, kg) by estimating mass using referents. | Grade 3 |
| Manitoba | 3.SS.4.4 | Demonstrate an understanding of measuring mass (g, kg) by measuring and recording mass. | Grade 3 |
| Manitoba | 3.SS.5.1 | Demonstrate an understanding of perimeter of regular and irregular shapes by estimating perimeter using referents for centimetre or metre. | Grade 3 |
| Manitoba | 3.SS.5.2 | Demonstrate an understanding of perimeter of regular and irregular shapes by measuring and recording perimeter (cm, m). | Grade 3 |
| Manitoba | 3.SS.5.3 | Demonstrate an understanding of perimeter of regular and irregular shapes by constructing different shapes for a given perimeter (cm | Grade 3 |
| Manitoba | 3.SS.6 | Describe 3-D objects according to the shape of the faces, and the number of edges and vertices. | Grade 3 |
| Manitoba | 3.SS.7 | Sort regular and irregular polygons, including triangles, quadrilaterals, pentagons, hexagons, and octagons according to the number of sides. | Grade 3 |
| Manitoba | 3.SP.1 | Collect first-hand data and organize it using tally marks, line plots, charts, and lists to answer questions. | Grade 3 |
| Manitoba | 3.SP.2 | Construct, label, and interpret bar graphs to solve problems. | Grade 3 |
| Manitoba | 4.N.1 | Represent and describe whole numbers to 10,000 pictorally and symbolically. | Grade 4 |
| Manitoba | 4.N.2 | Compare and order numbers to 10,000 | Grade 4 |
| Manitoba | 4.N.3.1 | Demonstrate and understanding of addition of numbers with answers to 10,000 and their corresponding subtractions (limited to 3 and 4 digit numbers), concretly, pictorially, and cymbolically, by using personal strategies. | Grade 4 |
| Manitoba | 4.N.3.2 | Demonstrate and understanding of addition of numbers with answers to 10,000 and their corresponding subtractions (limited to 3 and 4 digit numbers), concretly, pictorially, and cymbolically, by using the standard algorithms. | Grade 4 |
| Manitoba | 4.N.3.3 | Demonstrate and understanding of addition of numbers with answers to 10,000 and their corresponding subtractions (limited to 3 and 4 digit numbers), concretly, pictorially, and cymbolically, by estimating sums and differences. | Grade 4 |
| Manitoba | 4.N.3.4 | Demonstrate and understanding of addition of numbers with answers to 10,000 and their corresponding subtractions (limited to 3 and 4 digit numbers), concretly, pictorially, and cymbolically, by solving problems. | Grade 4 |
| Manitoba | 4.N.4 | Explain the properties of 0 and 1 for multiplication and the property of 1 for division. | Grade 4 |
| Manitoba | 4.N.5.1 | Describe and apply mental mathematics strategies, such as skip-counting from a known fact to develop an understanding of basic multiplication facts to 9 × 9 and related division facts. | Grade 4 |
| Manitoba | 4.N.5.2 | Describe and apply mental mathematics strategies, such as using halving/doubling to develop an understanding of basic multiplication facts to 9 × 9 and related division facts. | Grade 4 |
| Manitoba | 4.N.5.3 | Describe and apply mental mathematics strategies, such as using doubling and adding one more group to develop an understanding of basic multiplication facts to 9 × 9 and related division facts. | Grade 4 |
| Manitoba | 4.N.5.4 | Describe and apply mental mathematics strategies, such as using patterns in the 9s facts to develop an understanding of basic multiplication facts to 9 × 9 and related division facts. | Grade 4 |
| Manitoba | 4.N.5.5 | Describe and apply mental mathematics strategies, such as using repeated doubling to develop an understanding of basic multiplication facts to 9 × 9 and related division facts. | Grade 4 |
| Manitoba | 4.N.6.1 | Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by using personal strategies for multiplication with and without concrete materials. | Grade 4 |
| Manitoba | 4.N.6.2 | Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by using arrays to represent multiplication. | Grade 4 |
| Manitoba | 4.N.6.3 | Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by connecting concrete representations to symbolic representations. | Grade 4 |
| Manitoba | 4.N.6.4 | Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by estimating products. | Grade 4 |
| Manitoba | 4.N.7.1 | Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by using personal strategies for dividing with and without concrete materials. | Grade 4 |
| Manitoba | 4.N.7.2 | Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by estimating quotients. | Grade 4 |
| Manitoba | 4.N.7.3 | Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by relating division to multiplication. | Grade 4 |
| Manitoba | 4.N.8.1 | Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to name and record fractions for parts of a whole or a set. | Grade 4 |
| Manitoba | 4.N.8.2 | Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to compare and order fractions. | Grade 4 |
| Manitoba | 4.N.8.3 | Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to model and explain that for different wholes, two identical fractions may not represent the same quantity. | Grade 4 |
| Manitoba | 4.N.8.4 | Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to provide examples of where fractions are used. | Grade 4 |
| Manitoba | 4.N.9 | Describe and represent decimals (tenths and hundredths), concretely, pictorially, and symbolically. | Grade 4 |
| Manitoba | 4.N.10 | Relate decimals to fractions (to hundredths). | Grade 4 |
| Manitoba | 4.N.11.1 | Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by using compatible numbers. | Grade 4 |
| Manitoba | 4.N.11.2 | Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by estimating sums and differences. | Grade 4 |
| Manitoba | 4.N.11.3 | Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by using mental math strategies to solve problems. | Grade 4 |
| Manitoba | 4.PR.1 | Identify and describe patterns found in tables and charts, including a multiplication chart. | Grade 4 |
| Manitoba | 4.PR.2 | Reproduce a pattern shown in a table or chart using concrete materials. | Grade 4 |
| Manitoba | 4.PR.3 | Represent and describe patterns and relationships using charts and tables to solve problems. | Grade 4 |
| Manitoba | 4.PR.4 | Identify and explain mathematical relationships using charts and diagrams to solve problems. | Grade 4 |
| Manitoba | 4.PR.5 | Express a problem as an equation in which a symbol is used to represent an unknown number. | Grade 4 |
| Manitoba | 4.PR.6 | Solve one-step equations involving a symbol to represent an unknown number. | Grade 4 |
| Manitoba | 4.SS.1 | Read and record time using digital and analog clocks, including 24-hour clocks. | Grade 4 |
| Manitoba | 4.SS.2 | Read and record calendar dates in a variety of formats. | Grade 4 |
| Manitoba | 4.SS.3.1 | Demonstrate an understanding of area of regular and irregular 2-D shapes by recognizing that area is measured in square units. | Grade 4 |
| Manitoba | 4.SS.3.2 | Demonstrate an understanding of area of regular and irregular 2-D shapes by selecting and justifying referents for the units cm2 or m2. | Grade 4 |
| Manitoba | 4.SS.3.3 | Demonstrate an understanding of area of regular and irregular 2-D shapes by estimating area by using referents for cm2 or m2. | Grade 4 |
| Manitoba | 4.SS.3.4 | Demonstrate an understanding of area of regular and irregular 2-D shapes by determining and recording area (cm2 or m2). | Grade 4 |
| Manitoba | 4.SS.3.5 | Demonstrate an understanding of area of regular and irregular 2-D shapes by constructing different rectangles for a given area (cm2 or m2) in order to demonstrate that many different rectangles may have the same area. | Grade 4 |
| Manitoba | 4.SS.4 | Solve problems involving 2-D shapes and 3-D objects. | Grade 4 |
| Manitoba | 4.SS.5 | Describe and construct rectangular and triangular prisms. | Grade 4 |
| Manitoba | 4.SS.6.1 | Demonstrate an understanding of line symmetry by identifying symmetrical 2-D shapes. | Grade 4 |
| Manitoba | 4.SS.6.2 | Demonstrate an understanding of line symmetry by creating symmetrical 2-D shapes. | Grade 4 |
| Manitoba | 4.SS.6.3 | Demonstrate an understanding of line symmetry by drawing one or more lines of symmetry in a 2-D shape. | Grade 4 |
| Manitoba | 4.SP.1 | Demonstrate an understanding of many-to-one correspondence. | Grade 4 |
| Manitoba | 4.SP.2 | Construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions. | Grade 4 |
| Manitoba | 5.N.1 | Represent and describe whole numbers to 1 000 000. | Grade 5 |
| Manitoba | 5.N.2 | Apply estimation strategies, including front-end rounding, compensation, compatible numbers, and in problem-solving contexts. | Grade 5 |
| Manitoba | 5.N.3 | Apply mental math strategies to determine multiplication and related division facts to 81 (9 × 9). | Grade 5 |
| Manitoba | 5.N.4.1 | Apply mental mathematics strategies for multiplication, such as annexing then adding zeros. | Grade 5 |
| Manitoba | 5.N.4.2 | Apply mental mathematics strategies for multiplication, such as halving and doubling. | Grade 5 |
| Manitoba | 5.N.4.3 | Apply mental mathematics strategies for multiplication, such as using the distributive property. | Grade 5 |
| Manitoba | 5.N.5.1 | Demonstrate an understanding of multiplication (1- and 2-digit multipliers and up to 4-digit multiplicands), concretely, pictorially, and symbolically, by using personal strategies to solve problems. | Grade 5 |
| Manitoba | 5.N.5.2 | Demonstrate an understanding of multiplication (1- and 2-digit multipliers and up to 4-digit multiplicands), concretely, pictorially, and symbolically, by using the standard algorithm to solve problems. | Grade 5 |
| Manitoba | 5.N.5.3 | Demonstrate an understanding of multiplication (1- and 2-digit multipliers and up to 4-digit multiplicands), concretely, pictorially, and symbolically, by estimating products to solve problems. | Grade 5 |
| Manitoba | 5.N.6.1 | Demonstrate an understanding of division (1- and 2-digit divisors and up to 4-digit dividends), concretely, pictorially, and symbolically, and interpret remainders by using personal strategies to solve problems. | Grade 5 |
| Manitoba | 5.N.6.2 | Demonstrate an understanding of division (1- and 2-digit divisors and up to 4-digit dividends), concretely, pictorially, and symbolically, and interpret remainders by using the standard algorithm to solve problems. | Grade 5 |
| Manitoba | 5.N.6.3 | Demonstrate an understanding of division (1- and 2-digit divisors and up to 4-digit dividends), concretely, pictorially, and symbolically, and interpret remainders by estimating quotients to solve problems. | Grade 5 |
| Manitoba | 5.N.7.1 | Demonstrate an understanding of fractions by using concrete and pictorial representations to create sets of equivalent fractions. | Grade 5 |
| Manitoba | 5.N.7.2 | Demonstrate an understanding of fractions by using concrete and pictorial representations to compare fractions with like and unlike denominators. | Grade 5 |
| Manitoba | 5.N.8 | Describe and represent decimals (tenths, hundredths, thousandths) concretely, pictorially, and symbolically. | Grade 5 |
| Manitoba | 5.N.9 | Relate decimals to fractions (tenths, hundredths, thousandths). | Grade 5 |
| Manitoba | 5.N.10 | Compare and order decimals (tenths, hundredths, thousandths) by using benchmarks, place value, and equivalent decimals. | Grade 5 |
| Manitoba | 5.N.11 | Demonstrate an understanding of addition and subtraction of decimals (to thousandths), concretely, pictorially, and symbolically, by using personal strategies, using the standard algorithms, using estimation, and solving problems. | Grade 5 |
| Manitoba | 5.PR.1 | Determine the pattern rule to make predictions about subsequent elements. | Grade 5 |
| Manitoba | 5.PR.2 | Solve problems involving single-variable (expressed as symbols or letters), one-step equations with whole-number coefficients, and whole-number solutions. | Grade 5 |
| Manitoba | 5.SS.1 | Design and construct different rectangles given either perimeter or area or both (whole numbers), and draw conclusions. | Grade 5 |
| Manitoba | 5.SS.2 | Demonstrate an understanding of measuring length (mm) by selecting and justifying referents for the unit mm and by modelling and describing the relationship between mm and cm units, and between mm and m units. | Grade 5 |
| Manitoba | 5.SS.3.1 | Demonstrate an understanding of volume by selecting and justifying referents for cm3 or m3 units. | Grade 5 |
| Manitoba | 5.SS.3.2 | Demonstrate an understanding of volume by estimating volume by using referents for cm3 or m3. | Grade 5 |
| Manitoba | 5.SS.3.3 | Demonstrate an understanding of volume by measuring and recording volume (cm3 or m3). | Grade 5 |
| Manitoba | 5.SS.3.4 | Demonstrate an understanding of volume by constructing rectangular prisms for a given volume. | Grade 5 |
| Manitoba | 5.SS.4.1 | Demonstrate an understanding of capacity by describing the relationship between mL and L. | Grade 5 |
| Manitoba | 5.SS.4.2 | Demonstrate an understanding of capacity by selecting and justifying referents for mL or L units. | Grade 5 |
| Manitoba | 5.SS.4.3 | Demonstrate an understanding of capacity by estimating capacity by using referents for mL or L. | Grade 5 |
| Manitoba | 5.SS.4.4 | Demonstrate an understanding of capacity by measuring and recording capacity (mL or L). | Grade 5 |
| Manitoba | 5.SS.5 | Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes, that are parallel, intersecting, perpendicular, vertical, and horizontal. | Grade 5 |
| Manitoba | 5.SS.6 | Identify and sort quadrilaterals, including rectangles, squares, trapezoids, parallelograms, and rhombuses according to their attributes. | Grade 5 |
| Manitoba | 5.SS.7 | Perform a single transformation (translation, rotation, or reflection) of a 2-D shape, and draw and describe the image. | Grade 5 |
| Manitoba | 5.SS.8 | Identify a single transformation (translation, rotation, or reflection) of 2-D shapes. | Grade 5 |
| Manitoba | 5.SP.1 | Differentiate between first-hand and second-hand data. | Grade 5 |
| Manitoba | 5.SP.2 | Construct and interpret double bar graphs to draw conclusions. | Grade 5 |
| Manitoba | 5.SP.3 | Describe the likelihood of a single outcome occurring, using words such as impossible, possible, and certain. | Grade 5 |
| Manitoba | 5.SP.4 | Compare the likelihood of two possible outcomes occurring, using words such as less likely, equally likely, and more likely. | Grade 5 |
| Manitoba | 6.N.1 | Demonstrate an understanding of place value for numbers greater than one million and numbers less than one-thousandth. | Grade 6 |
| Manitoba | 6.N.2 | Solve problems involving large numbers, using technology. | Grade 6 |
| Manitoba | 6.N.3.1 | Demonstrate an understanding of factors and multiples by determining multiples and factors of numbers less than 100. | Grade 6 |
| Manitoba | 6.N.3.2 | Demonstrate an understanding of factors and multiples by identifying prime and composite numbers. | Grade 6 |
| Manitoba | 6.N.3.3 | Demonstrate an understanding of factors and multiples by solving problems involving factors or multiples. | Grade 6 |
| Manitoba | 6.N.4 | Relate improper fractions to mixed numbers. | Grade 6 |
| Manitoba | 6.N.5 | Demonstrate an understanding of ratio, concretely, pictorially, and symbolically. | Grade 6 |
| Manitoba | 6.N.6 | Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially, and symbolically. | Grade 6 |
| Manitoba | 6.N.7 | Demonstrate an understanding of integers, concretely, pictorially, and symbolically. | Grade 6 |
| Manitoba | 6.N.8.1 | Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by using personal strategies. | Grade 6 |
| Manitoba | 6.N.8.2 | Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by using the standard algorithms. | Grade 6 |
| Manitoba | 6.N.8.3 | Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by using estimation. | Grade 6 |
| Manitoba | 6.N.8.4 | Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by solving problems. | Grade 6 |
| Manitoba | 6.N.9 | Explain and apply the order of operations, excluding exponents (limited to whole numbers). | Grade 6 |
| Manitoba | 6.PR.1 | Demonstrate an understanding of the relationships within tables of values to solve problems. | Grade 6 |
| Manitoba | 6.PR.2 | Represent and describe patterns and relationships using graphs and tables. | Grade 6 |
| Manitoba | 6.PR.3 | Represent generalizations arising from number relationships using equations with letter variables. | Grade 6 |
| Manitoba | 6.PR.4 | Demonstrate and explain the meaning of preservation of equality, concretely, pictorially, and symbolically. | Grade 6 |
| Manitoba | 6.SS.1.1 | Demonstrate an understanding of angles by identifying examples of angles in the environment. | Grade 6 |
| Manitoba | 6.SS.1.2 | Demonstrate an understanding of angles by classifying angles according to their measure. | Grade 6 |
| Manitoba | 6.SS.1.3 | Demonstrate an understanding of angles by estimating the measure of angles using 45°, 90°, and 180° as reference angles. | Grade 6 |
| Manitoba | 6.SS.1.4 | Demonstrate an understanding of angles by determining angle measures in degrees. | Grade 6 |
| Manitoba | 6.SS.1.5 | Demonstrate an understanding of angles by drawing and labelling angles when the measure is specified. | Grade 6 |
| Manitoba | 6.SS.2 | Demonstrate that the sum of interior angles is 180° in a triangle and 360° in a quadrilateral. | Grade 6 |
| Manitoba | 6.SS.3 | Develop and apply a formula for determining the perimeter of polygons, area of rectangles, and volume of right rectangular prisms. | Grade 6 |
| Manitoba | 6.SS.4 | Construct and compare triangles, including scalene, isosceles, equilateral, right, obtuse, and acute in different orientations. | Grade 6 |
| Manitoba | 6.SS.5 | Describe and compare the sides and angles of regular and irregular polygons. | Grade 6 |
| Manitoba | 6.SS.6 | Perform a combination of transformations (translations, rotations, or reflections) on a single 2-D shape, and draw and describe the image. | Grade 6 |
| Manitoba | 6.SS.7 | Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations. | Grade 6 |
| Manitoba | 6.SS.8 | Identify and plot points in the first quadrant of a Cartesian plane using whole-number ordered pairs. | Grade 6 |
| Manitoba | 6.SS.9 | Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole-number vertices). | Grade 6 |
| Manitoba | 6.SP.1 | Create, label, and interpret line graphs to draw conclusions. | Grade 6 |
| Manitoba | 6.SP.2 | Select, justify, and use appropriate methods of collecting data, including questionnaires, experiments, databases, and electronic media. | Grade 6 |
| Manitoba | 6.SP.3 | Graph collected data and analyze the graph to solve problems. | Grade 6 |
| Manitoba | 6.SP.4.1 | Demonstrate an understanding of probability by identifying all possible outcomes of a probability experiment. | Grade 6 |
| Manitoba | 6.SP.4.2 | Demonstrate an understanding of probability by differentiating between experimental and theoretical probability. | Grade 6 |
| Manitoba | 6.SP.4.3 | Demonstrate an understanding of probability by determining the theoretical probability of outcomes in a probability experiment. | Grade 6 |
| Manitoba | 6.SP.4.4 | Demonstrate an understanding of probability by determining the experimental probability of outcomes in a probability experiment. | Grade 6 |
| Manitoba | 6.SP.4.5 | Demonstrate an understanding of probability by comparing experimental results with the theoretical probability for an experiment. | Grade 6 |
| Manitoba | 7.N.1 | Determine and explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, and why a number cannot be divided by 0. | Grade 7 |
| Manitoba | 7.N.2 | Demonstrate an understanding of the addition, subtraction, multiplication, and division of decimals to solve problems (for more than 1-digit divisors or 2-digit multipliers, technology could be used). | Grade 7 |
| Manitoba | 7.N.3 | Solve problems involving percents from 1% to 100%. | Grade 7 |
| Manitoba | 7.N.4 | Demonstrate an understanding of the relationship between repeating decimals and fractions, and terminating decimals and fractions. | Grade 7 |
| Manitoba | 7.N.5 | Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially, and symbolically (limited to positive sums and differences). | Grade 7 |
| Manitoba | 7.N.6 | Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically. | Grade 7 |
| Manitoba | 7.N.7 | Compare and order fractions, decimals (to thousandths), and integers by using benchmarks, place value and equivalent fractions and/or decimals. | Grade 7 |
| Manitoba | 7.PR.1 | Demonstrate an understanding of oral and written patterns and their corresponding relations. | Grade 7 |
| Manitoba | 7.PR.2 | Construct a table of values from a relation, graph the table of values, and analyze the graph to draw conclusions and solve problems. | Grade 7 |
| Manitoba | 7.PR.3 | Demonstrate an understanding of preservation of equality by modelling preservation of equality, concretely, pictorially, and symbolically and applying preservation of equality to solve equations. | Grade 7 |
| Manitoba | 7.PR.4 | Explain the difference between an expression and an equation. | Grade 7 |
| Manitoba | 7.PR.5 | Evaluate an expression given the value of the variable(s). | Grade 7 |
| Manitoba | 7.PR.6 | Model and solve problems that can be represented by one-step linear equations of the form x + a = b, concretely, pictorially, and symbolically, where a and b are integers. | Grade 7 |
| Manitoba | 7.PR.7 | Model and solve problems that can be represented by linear equations of the form: ax + b = c, ax = b, concretely, pictorially, and symbolically, where a, b, and c, are whole numbers. | Grade 7 |
| Manitoba | 7.SS.1.1 | Demonstrate an understanding of circles by describing the relationships among radius, diameter, and circumference of circles. | Grade 7 |
| Manitoba | 7.SS.1.2 | Demonstrate an understanding of circles by relating circumference to pi. | Grade 7 |
| Manitoba | 7.SS.1.3 | Demonstrate an understanding of circles by determining the sum of the central angles. | Grade 7 |
| Manitoba | 7.SS.1.4 | Demonstrate an understanding of circles by constructing circles with a given radius or diameter. | Grade 7 |
| Manitoba | 7.SS.1.5 | Demonstrate an understanding of circles by solving problems involving the radii, diameters, and circumferences of circles. | Grade 7 |
| Manitoba | 7.SS.2.1 | Develop and apply a formula for determining the area of triangles. | Grade 7 |
| Manitoba | 7.SS.2.2 | Develop and apply a formula for determining the area of parallelograms. | Grade 7 |
| Manitoba | 7.SS.2.3 | Develop and apply a formula for determining the area of circles. | Grade 7 |
| Manitoba | 7.SS.3 | Perform geometric constructions, including perpendicular line segments, parallel line segments, perpendicular bisectors and angle bisectors. | Grade 7 |
| Manitoba | 7.SS.4 | Identify and plot points in the four quadrants of a Cartesian plane using ordered pairs. | Grade 7 |
| Manitoba | 7.SS.5 | Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events. | Grade 7 |
| Manitoba | 7.SP.1.1 | Demonstrate an understanding of central tendency and range by determining the measures of central tendency (mean, median, mode) and range. | Grade 7 |
| Manitoba | 7.SP.1.2 | Demonstrate an understanding of central tendency and range by determining the most appropriate measures of central tendency to report findings. | Grade 7 |
| Manitoba | 7.SP.2 | Determine the effect on the mean, median, and mode when an outlier is included in a data set. | Grade 7 |
| Manitoba | 7.SP.3 | Construct, label, and interpret circle graphs to solve problems. | Grade 7 |
| Manitoba | 7.SP.4 | Express probabilities as ratios, fractions, and percents. | Grade 7 |
| Manitoba | 7.SP.5 | Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events. | Grade 7 |
| Manitoba | 7.SP.6 | Conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table, or another graphic organizer) and experimental probability of two independent events. | Grade 7 |
| Manitoba | 8.N.1 | Demonstrate an understanding of perfect squares and square roots, concretely, pictorially, and symbolically (limited to whole numbers). | Grade 8 |
| Manitoba | 8.N.2 | Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers). | Grade 8 |
| Manitoba | 8.N.3 | Demonstrate an understanding of percents greater than or equalto 0%. | Grade 8 |
| Manitoba | 8.N.4 | Demonstrate an understanding of ratio and rate. | Grade 8 |
| Manitoba | 8.N.5 | Solve problems that involve rates, ratios, and proportionalreasoning. | Grade 8 |
| Manitoba | 8.N.6 | Demonstrate an understanding of multiplying and dividingpositive fractions and mixed numbers, concretely, pictorially,and symbolically. | Grade 8 |
| Manitoba | 8.N.7 | Demonstrate an understanding of multiplication and division ofintegers, concretely, pictorially, and symbolically. | Grade 8 |
| Manitoba | 8.N.8 | Solve problems involving positive rational numbers. | Grade 8 |
| Manitoba | 8.PR.1 | Graph and analyze two-variable linear relations. | Grade 8 |
| Manitoba | 8.PR.2 | Model and solve problems using linear equations concretely, pictorially, and symbolically, where a, b, and c, are integers | Grade 8 |
| Manitoba | 8.SS.1 | Develop and apply the Pythagorean theorem to solve problems. | Grade 8 |
| Manitoba | 8.SS.2 | Draw and construct nets for 3-D objects. | Grade 8 |
| Manitoba | 8.SS.3.1 | Determine the surface area of right rectangular prisms to solve problems. | Grade 8 |
| Manitoba | 8.SS.3.2 | Determine the surface area of right triangular prisms to solve problems. | Grade 8 |
| Manitoba | 8.SS.3.3 | Determine the surface area of right cylinders to solve problems. | Grade 8 |
| Manitoba | 8.SS.4 | Develop and apply formulas for determining the volume of right prisms and right cylinders. | Grade 8 |
| Manitoba | 8.SS.5 | Draw and interpret top, front, and side views of 3-D objects composed of right rectangular prisms. | Grade 8 |
| Manitoba | 8.SS.6.1 | Demonstrate an understanding of tessellation by explaining the properties of shapes that make tessellating possible. | Grade 8 |
| Manitoba | 8.SS.6.2 | Demonstrate an understanding of tessellation by creating tessellations. | Grade 8 |
| Manitoba | 8.SS.6.3 | Demonstrate an understanding of tessellation by identifying tessellations in the environment. | Grade 8 |
| Manitoba | 8.SP.1 | Critique ways in which data are presented. | Grade 8 |
| Manitoba | 8.SP.2 | Solve problems involving the probability of independent events. | Grade 8 |
| Manitoba | 10I.A.3 | Demonstrate an understanding of powers with integral and rational exponents. | Algebra |
| Manitoba | 9.PR.2 | Graph linear relations, analyze the graph, and interpolate or extrapolate to solve problems. | Algebra |
| Manitoba | 9.PR.4 | Explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context. | Algebra |
| Manitoba | 9.PR.5 | Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2). | Algebra |
| Manitoba | 9.PR.6 | Model, record, and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially, and symbolically (limited to polynomials of degree less than or equal to 2). | Algebra |
| Manitoba | 10I.R.2 | Demonstrate an understanding of relations and functions. | Algebra |
| Manitoba | 10I.R.4.4 | Describe and represent linear relations, using graphs. | Algebra |
| Manitoba | 10I.R.8 | Represent a linear function, using function notation. | Algebra |
| Manitoba | 10I.R.7.5 | Determine the equation of a linear relation, given a scatterplot | Algebra |
| Manitoba | 11P.R.4.5 | Analyze quadratic functions of the form y = ax2 + bx + c to identify characteristics of the corresponding graph, including x- and y-intercepts. | Algebra |
| Manitoba | 9.SS.4 | Draw and interpret scale diagrams of 2-D shapes. | Algebra |
| Minnesota | 9.2.1.1 | Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain. | Algebra |
| Minnesota | 9.2.1.4 | Obtain information and draw conclusions from graphs of functions and other relations. | Algebra |
| Minnesota | 9.2.1.6 | Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function. | Algebra |
| Minnesota | 9.2.1.8 | Make qualitative statements about the rate of change of a function, based on its graph or table of values. | Algebra |
| Minnesota | 9.2.2.3 | Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions. | Algebra |
| Minnesota | 9.2.2.4 | Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively. | Algebra |
| Minnesota | 9.2.2.6 | Sketch the graphs of common non-linear functions such as ??(??)= ???, ??(??) = |??|, ??(??)= 1/??, ??(??) = ??^3, and translations of these functions, such as ??(??) = ?(??-2) + 4. Know how to use graphing technology to graph these functions. | Algebra |
| Minnesota | 9.2.3.2 | Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree. | Algebra |
| Minnesota | 9.2.3.3 | Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. | Algebra |
| Minnesota | 9.2.3.7 | Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables. | Algebra |
| Minnesota | 9.2.4.1 | Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities. | Algebra |
| Minnesota | 9.4.1.3 | Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions. | Algebra |
| Minnesota | 1.1.1.1 | Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. | Grade 1 |
| Minnesota | 1.1.1.2 | Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. | Grade 1 |
| Minnesota | 1.1.1.3 | Count, with and without objects, forward and backward from any given number up to 120. | Grade 1 |
| Minnesota | 1.1.1.4 | Find a number that is 10 more or 10 less than a given number. | Grade 1 |
| Minnesota | 1.1.1.5 | Compare and order whole numbers up to 100. | Grade 1 |
| Minnesota | 1.1.1.7 | Use counting and comparison skills to create and analyze bar graphs and tally charts. | Grade 1 |
| Minnesota | 1.1.2.1 | Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. | Grade 1 |
| Minnesota | 1.1.2.3 | Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s. | Grade 1 |
| Minnesota | 1.2.2.1 | Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. | Grade 1 |
| Minnesota | 1.2.2.2 | Determine if equations involving addition and subtraction are true. | Grade 1 |
| Minnesota | 1.3.2.2 | Tell time to the hour and half-hour. | Grade 1 |
| Minnesota | 2.1.1.1 | Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. | Grade 2 |
| Minnesota | 2.1.1.2 | Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. | Grade 2 |
| Minnesota | 2.1.1.3 | Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. | Grade 2 |
| Minnesota | 2.1.1.5 | Compare and order whole numbers up to 1000. | Grade 2 |
| Minnesota | 2.1.2.1 | Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts. | Grade 2 |
| Minnesota | 2.1.2.2 | Demonstrate fluency with basic addition facts and related subtraction facts. | Grade 2 |
| Minnesota | 2.1.2.4 | Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. | Grade 2 |
| Minnesota | 2.1.2.5 | Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. | Grade 2 |
| Minnesota | 2.1.2.6 | Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. | Grade 2 |
| Minnesota | 2.2.2.2 | Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. | Grade 2 |
| Minnesota | 2.3.1.2 | Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. | Grade 2 |
| Minnesota | 2.3.2.1 | Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. | Grade 2 |
| Minnesota | 3.1.1.2 | Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. | Grade 3 |
| Minnesota | 3.1.1.4 | Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. | Grade 3 |
| Minnesota | 3.1.2.1 | Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. | Grade 3 |
| Minnesota | 3.1.2.3 | Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. | Grade 3 |
| Minnesota | 3.1.2.4 | Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems. | Grade 3 |
| Minnesota | 3.1.2.5 | Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. | Grade 3 |
| Minnesota | 3.1.3.1 | Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. | Grade 3 |
| Minnesota | 3.1.3.2 | Understand that the size of a fractional part is relative to the size of the whole. | Grade 3 |
| Minnesota | 3.1.3.3 | Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. | Grade 3 |
| Minnesota | 3.3.1.1 | Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. | Grade 3 |
| Minnesota | 3.3.3.1 | Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. | Grade 3 |
| Minnesota | 3.4.1.1 | Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. | Grade 3 |
| Minnesota | 4.1.1.2 | Use an understanding of place value to multiply a number by 10, 100 and 1000. | Grade 4 |
| Minnesota | 4.1.1.3 | Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. | Grade 4 |
| Minnesota | 4.1.1.5 | Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. | Grade 4 |
| Minnesota | 4.1.1.6 | Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. | Grade 4 |
| Minnesota | 4.1.2.1 | Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. | Grade 4 |
| Minnesota | 4.1.2.2 | Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. | Grade 4 |
| Minnesota | 4.1.2.3 | Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. | Grade 4 |
| Minnesota | 4.1.2.5 | Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. | Grade 4 |
| Minnesota | 4.1.2.6 | Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. | Grade 4 |
| Minnesota | 4.2.1.1 | Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. | Grade 4 |
| Minnesota | 4.2.2.1 | Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. | Grade 4 |
| Minnesota | 4.2.2.2 | Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. | Grade 4 |
| Minnesota | 4.3.1.1 | Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. | Grade 4 |
| Minnesota | 4.3.1.2 | Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. | Grade 4 |
| Minnesota | 4.3.2.1 | Measure angles in geometric figures and real-world objects with a protractor or angle ruler. | Grade 4 |
| Minnesota | 4.3.2.3 | Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. | Grade 4 |
| Minnesota | 4.3.2.4 | Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. | Grade 4 |
| Minnesota | 5.1.1.4 | Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. | Grade 5 |
| Minnesota | 5.1.2.1 | Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. | Grade 5 |
| Minnesota | 5.1.2.3 | Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. | Grade 5 |
| Minnesota | 5.1.2.5 | Round numbers to the nearest 0.1, 0.01 and 0.001. | Grade 5 |
| Minnesota | 5.1.3.1 | Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. | Grade 5 |
| Minnesota | 5.1.3.4 | Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. | Grade 5 |
| Minnesota | 5.2.1.2 | Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. | Grade 5 |
| Minnesota | 5.2.2.1 | Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. | Grade 5 |
| Minnesota | 6.1.1.1 | Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. | Grade 6 |
| Minnesota | 6.1.1.2 | Compare positive rational numbers represented in various forms. Use the symbols . | Grade 6 |
| Minnesota | 6.1.1.3 | Understand that percent represents parts out of 100 and ratios to 100. | Grade 6 |
| Minnesota | 6.1.1.7 | Convert between equivalent representations of positive rational numbers. | Grade 6 |
| Minnesota | 6.1.2.1 | Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. | Grade 6 |
| Minnesota | 6.1.2.3 | Determine the rate for ratios of quantities with different units. | Grade 6 |
| Minnesota | 6.1.3.1 | Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. | Grade 6 |
| Minnesota | 6.1.3.4 | Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. | Grade 6 |
| Minnesota | 6.2.1.1 | Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. | Grade 6 |
| Minnesota | 6.2.3.1 | Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. | Grade 6 |
| Minnesota | 6.3.3.1 | Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. | Grade 6 |
| Minnesota | 7.1.1.2 | Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator. | Grade 7 |
| Minnesota | 7.1.1.3 | Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid. | Grade 7 |
| Minnesota | 7.1.2.1 | Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents. | Grade 7 |
| Minnesota | 7.1.2.4 | Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest. | Grade 7 |
| Minnesota | 7.1.2.6 | Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value. | Grade 7 |
| Minnesota | 7.2.1.2 | Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed. | Grade 7 |
| Minnesota | 7.2.2.1 | Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. | Grade 7 |
| Minnesota | 7.2.2.2 | Solve multi-step problems involving proportional relationships in numerous contexts. | Grade 7 |
| Minnesota | 7.2.2.4 | Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers. | Grade 7 |
| Minnesota |
