RegionStandardDescriptionLevel
ArkansasK.CC.A.1Count to 100 by ones, fives, and tens.Kindergarten
ArkansasK.CC.A.2Count forward, by ones, from any given number up to 100.Kindergarten
ArkansasK.CC.B.4Understand 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
ArkansasK.CC.B.5Count 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
ArkansasK.CC.C.6Identify 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
ArkansasK.CC.C.7Compare two numbers between 0 and 20 presented as written numerals.Kindergarten
ArkansasK.CC.C.8Quickly identify a number of items in a set from 0-10 without counting (e.g., dominoes, dot cubes, tally marks, ten-frames).Kindergarten
ArkansasK.G.A.1Describe 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
ArkansasK.G.A.2Correctly name shapes regardless of their orientations or overall size.Kindergarten
ArkansasK.G.A.3Identify shapes as two-dimensional or three-dimensional.Kindergarten
ArkansasK.G.B.4Analyze 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
ArkansasK.G.B.5Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.Kindergarten
ArkansasK.G.B.6Compose two-dimensional shapes to form larger two-dimensional shapes.Kindergarten
ArkansasK.MD.A.1Describe several measurable attributes of a single object, including but not limited to length, weight, height, and temperature .Kindergarten
ArkansasK.MD.A.2Describe 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
ArkansasK.MD.B.3Classify, sort, and count objects using both measureable and non-measureable attributes such as size, number, color, or shape.Kindergarten
ArkansasK.MD.C.4Understand 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
ArkansasK.MD.C.6Identify pennies, nickels, and dimes, and know the vlaue of each.Kindergarten
ArkansasK.NBT.A.1Develop 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
ArkansasK.OA.A.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Kindergarten
ArkansasK.OA.A.2Solve real-world problems that involve addition and subtraction within 10 (e.g., by using objects or drawings to represent the problem).Kindergarten
ArkansasK.OA.A.3Use 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
ArkansasK.OA.A.4Find 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
ArkansasK.OA.A.5Fluently add and subtract within 10 by using various strategies and manipulatives.Kindergarten
Arkansas1.G.A.1Distinguish 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
Arkansas1.G.A.2Compose 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
Arkansas1.G.A.3Partition 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
Arkansas1.MD.A.1Order three objects by length; compare the lengths of two objects indirectly by using a third object.Grade 1
Arkansas1.MD.A.2Express 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
Arkansas1.MD.B.3Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
Arkansas1.MD.B.4Identify and know the value of a penny, nickel, dime and quarter.Grade 1
Arkansas1.MD.B.5Count collections of like coins (pennies, nickels, and dimes).Grade 1
Arkansas1.MD.C.6Organize, 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
Arkansas1.NBT.A.1Count 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
Arkansas1.NBT.B.2Understand 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
Arkansas1.NBT.B.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols.Grade 1
Arkansas1.NBT.C.4Add 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
Arkansas1.NBT.C.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Grade 1
Arkansas1.NBT.C.6Subtract 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
Arkansas1.OA.A.1Use 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
Arkansas1.OA.A.2Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 .Grade 1
Arkansas1.OA.B.3Apply 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
Arkansas1.OA.B.4Understand 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
Arkansas1.OA.C.6Add 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
Arkansas1.OA.D.7Understand 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
Arkansas1.OA.D.8Determine 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
Arkansas2.G.A.1Recognize 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
Arkansas2.G.A.2Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.Grade 2
Arkansas2.G.A.3Partition 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
Arkansas2.G.A.4Recognize that equal shares of identical wholes need not have the same shape.Grade 2
Arkansas2.MD.A.1Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.Grade 2
Arkansas2.MD.A.2Measure 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
Arkansas2.MD.A.3Estimate lengths using units of inches, feet, centimeters, and meters.Grade 2
Arkansas2.MD.A.4Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.Grade 2
Arkansas2.MD.B.5Use 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
Arkansas2.MD.B.6Represent 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
Arkansas2.MD.C.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Grade 2
Arkansas2.MD.C.8Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately.Grade 2
Arkansas2.MD.D.9Generate 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
Arkansas2.MD.D.10Draw 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
Arkansas2.NBT.A.1Understand 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
Arkansas2.NBT.A.2Count within 1000; skip-count by 5s, 10s, and 100s.Grade 2
Arkansas2.NBT.A.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Grade 2
Arkansas2.NBT.A.4Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons.Grade 2
Arkansas2.NBT.B.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Grade 2
Arkansas2.NBT.B.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Grade 2
Arkansas2.NBT.B.7Add 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
Arkansas2.NBT.B.8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.Grade 2
Arkansas2.NBT.B.9Explain why addition and subtraction strategies work, using place value and the properties of operations.Grade 2
Arkansas2.OA.A.1Use 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
Arkansas2.OA.B.2Fluently 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
Arkansas2.OA.C.3Determine 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
Arkansas2.OA.C.4Use 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
Arkansas3.G.A.1Understand 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
Arkansas3.G.A.2Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.Grade 3
Arkansas3.MD.A.1Tell 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
Arkansas3.MD.A.2Measure 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
Arkansas3.MD.B.3Draw 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
Arkansas3.MD.B.4Generate 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
Arkansas3.MD.C.5Recognize area as an attribute of plane figures and understand concepts of area measurement.Grade 3
Arkansas3.MD.C.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Grade 3
Arkansas3.MD.D.8Solve 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
Arkansas3.NBT.A.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
Arkansas3.NBT.A.2Fluently 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
Arkansas3.NBT.A.3Multiply 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
Arkansas3.NBT.A.4Understand that the four digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones.Grade 3
Arkansas3.NBT.A.5Read and write numbers to 10,000 using base-ten numerals, number names, and expanded form(s).Grade 3
Arkansas3.NBT.A.6Compare two four-digit numbers based on meanings of thousands, hundreds, tens, and ones digits using symbols (<, >, =) to record the results of comparisons.Grade 3
Arkansas3.NF.A.1Understand 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
Arkansas3.NF.A.2Understand 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
Arkansas3.NF.A.3Explain 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
Arkansas3.OA.A.1Interpret 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
Arkansas3.OA.A.2Interpret 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
Arkansas3.OA.A.3Use 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
Arkansas3.OA.A.4Determine 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
Arkansas3.OA.B.5Apply 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
Arkansas3.OA.B.6Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.Grade 3
Arkansas3.OA.C.7Fluently 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
Arkansas3.OA.D.8Solve 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
Arkansas3.OA.D.9Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.Grade 3
Arkansas4.G.A.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Grade 4
Arkansas4.G.A.2Classify 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
Arkansas4.G.A.3Recognize 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
Arkansas4.MD.A.1Know 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
Arkansas4.MD.A.2Use 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
Arkansas4.MD.A.3Apply the area and perimeter formulas for rectangles in real world and mathematical problems.Grade 4
Arkansas4.MD.B.4Make 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
Arkansas4.MD.C.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.Grade 4
Arkansas4.MD.C.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Grade 4
Arkansas4.MD.C.7Recognize 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
Arkansas4.NBT.A.1Recognize 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
Arkansas4.NBT.A.2Read 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
Arkansas4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.Grade 4
Arkansas4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.Grade 4
Arkansas4.NBT.B.5Multiply 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
Arkansas4.NBT.B.6Find 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
Arkansas4.NF.A.1Explain 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
Arkansas4.NF.A.2Compare 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
Arkansas4.NF.B.3Understand 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
Arkansas4.NF.B.4Apply 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
Arkansas4.NF.C.5Express 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
Arkansas4.NF.C.6Use 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
Arkansas4.NF.C.7Compare 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
Arkansas4.OA.A.1Interpret 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
Arkansas4.OA.A.2Multiply 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
Arkansas4.OA.A.3Solve 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
Arkansas4.OA.B.4Find 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
Arkansas4.OA.C.5Generate 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
Arkansas5.G.A.1Use 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
Arkansas5.G.A.2Represent 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
Arkansas5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Grade 5
Arkansas5.G.B.4Classify two-dimensional figures in a hierarchy based on properties.Grade 5
Arkansas5.MD.A.1Convert 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
Arkansas5.MD.B.2Make 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
Arkansas5.MD.C.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement.Grade 5
Arkansas5.MD.C.4Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.Grade 5
Arkansas5.MD.C.5Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.Grade 5
Arkansas5.NBT.A.1Recognize 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
Arkansas5.NBT.A.2Explain 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
Arkansas5.NBT.A.4Use place value understanding to round decimals to any place.Grade 5
Arkansas5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm.Grade 5
Arkansas5.NBT.B.6Find 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
Arkansas5.NBT.B.7Add, 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
Arkansas5.NF.A.1Add 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
Arkansas5.NF.A.2Solve 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
Arkansas5.NF.B.3Interpret 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
Arkansas5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Grade 5
Arkansas5.NF.B.5Interpret 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
Arkansas5.NF.B.6Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.Grade 5
Arkansas5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Grade 5
Arkansas5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Grade 5
Arkansas5.OA.A.2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.Grade 5
Arkansas5.OA.B.3Generate 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
Arkansas6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.Grade 6
Arkansas6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.Grade 6
Arkansas6.EE.A.3Apply the properties of operations to generate equivalent expressions.Grade 6
Arkansas6.EE.A.4Identify 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
Arkansas6.EE.B.5Understand 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
Arkansas6.EE.B.6Use 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
Arkansas6.EE.B.7Solve 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
Arkansas6.EE.B.8Write 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
Arkansas6.EE.C.9Use 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
Arkansas6.G.A.1Find 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
Arkansas6.G.A.2Find 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
Arkansas6.G.A.3Draw 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
Arkansas6.G.A.4Represent 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
Arkansas6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.Grade 6
Arkansas6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.Grade 6
Arkansas6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Grade 6
Arkansas6.NS.B.4Find 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
Arkansas6.NS.C.5Understand 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
Arkansas6.NS.C.6Understand 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
Arkansas6.NS.C.7Understand ordering and absolute value of rational numbers.Grade 6
Arkansas6.NS.C.8Solve 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
Arkansas6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.Grade 6
Arkansas6.RP.A.2Understand 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
Arkansas6.RP.A.3Use 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
Arkansas6.SP.A.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.Grade 6
Arkansas6.SP.A.2Understand 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
Arkansas6.SP.A.3Recognize 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
Arkansas6.SP.B.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.Grade 6
Arkansas6.SP.B.5Summarize numerical data sets in relation to their context.Grade 6
Arkansas7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Grade 7
Arkansas7.EE.A.2Understand 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
Arkansas7.EE.B.3Solve 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
Arkansas7.EE.B.4Use 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
Arkansas7.G.A.1Solve 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
Arkansas7.G.A.2Draw (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
Arkansas7.G.A.3Describe 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
Arkansas7.G.B.4Know 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
Arkansas7.G.B.5Use 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
Arkansas7.G.B.6Solve 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
Arkansas7.NS.A.1Apply 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
Arkansas7.NS.A.2Understand 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
Arkansas7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.Grade 7
Arkansas7.RP.A.1Compute 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
Arkansas7.RP.A.2Recognize and represent proportional relationships between quantities.Grade 7
Arkansas7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems.Grade 7
Arkansas7.SP.A.1Understand 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
Arkansas7.SP.A.2Use 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
Arkansas7.SP.B.3Informally 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
Arkansas7.SP.B.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.Grade 7
Arkansas7.SP.C.5Understand 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
Arkansas7.SP.C.6Approximate 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
Arkansas7.SP.C.7Develop 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
Arkansas7.SP.C.8Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.Grade 7
Arkansas8.EE.A.1Know and apply the properties of integer exponents to generate equivalent numerical expressions.Grade 8
Arkansas8.EE.A.2Use 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
Arkansas8.EE.A.3Use 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
Arkansas8.EE.A.4Perform 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
Arkansas8.EE.B.5Graph 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
Arkansas8.EE.B.6Use 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
Arkansas8.EE.C.7Give 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
Arkansas8.EE.C.8Understand 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
Arkansas8.F.A.1Understand 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
Arkansas8.F.A.2Compare 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
Arkansas8.F.A.3Interpret 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
Arkansas8.F.B.4Construct 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
Arkansas8.F.B.5Describe 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
Arkansas8.G.A.1Verify experimentally the properties of rotations, reflections, and translations.Grade 8
Arkansas8.G.A.2Understand 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
Arkansas8.G.A.3Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.Grade 8
Arkansas8.G.A.4Understand 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
Arkansas8.G.A.5Use 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
Arkansas8.G.B.6Explain a proof of the Pythagorean Theorem and its converse.Grade 8
Arkansas8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Grade 8
Arkansas8.G.B.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Grade 8
Arkansas8.G.C.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.Grade 8
Arkansas8.NS.A.1Know 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
Arkansas8.NS.A.2Use 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
Arkansas8.SP.A.1Construct 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
Arkansas8.SP.A.2Know 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
Arkansas8.SP.A.3Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.Grade 8
Arkansas8.SP.A.4Understand 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
ArkansasA-APR.B.3Identify 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
ArkansasA-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Algebra
ArkansasA-REI.C.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.Algebra
ArkansasA-REI.C.7Solve 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
ArkansasA-SSE.A.2Use the structure of an expression to identify ways to rewrite it.Algebra
ArkansasA-SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Algebra
ArkansasF-BF.A.1Write a function that describes a relationship between two quantities.Algebra
ArkansasF-IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Algebra
ArkansasF-IF.B.4For 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
ArkansasF-IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Algebra
ArkansasS-ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Algebra
ArkansasS-ID.C.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.Algebra
ArizonaA-APR.B.3Identify 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
ArizonaA-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Algebra
ArizonaA-SSE.A.2Use the structure of an expression to identify ways to rewrite it.Algebra
ArizonaA-SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Algebra
ArizonaF-BF.A.1Write a function that describes a relationship between two quantities.Algebra
ArizonaF-IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Algebra
ArizonaF-IF.B.4For 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
ArizonaF-IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Algebra
ArizonaS-ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Algebra
Arizona1.MD.B.3Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
Arizona1.MD.C.4Organize, 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
Arizona1.NBT.A.1Count 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
Arizona1.NBT.B.2Understand 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
Arizona1.NBT.B.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols.Grade 1
Arizona1.NBT.C.4Add 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
Arizona1.NBT.C.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Grade 1
Arizona1.NBT.C.6Subtract 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
Arizona1.OA.B.3Apply 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
Arizona1.OA.B.4Understand 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
Arizona1.OA.C.6Add 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
Arizona1.OA.D.7Understand 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
Arizona1.OA.D.8Determine 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
Arizona2.G.A.1Recognize 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
Arizona2.MD.C.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Grade 2
Arizona2.MD.D.10Draw 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
Arizona2.MD.D.9Generate 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
Arizona2.NBT.A.1Understand 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
Arizona2.NBT.A.2Count within 1000; skip-count by 5s, 10s, and 100s.Grade 2
Arizona2.NBT.A.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Grade 2
Arizona2.NBT.A.4Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons.Grade 2
Arizona2.NBT.B.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Grade 2
Arizona2.NBT.B.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Grade 2
Arizona2.NBT.B.7Add 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
Arizona2.NBT.B.8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.Grade 2
Arizona2.OA.A.1Use 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
Arizona2.OA.B.2Fluently 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
Arizona3.G.A.1Understand 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
Arizona3.MD.A.1Tell 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
Arizona3.MD.B.3Draw 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
Arizona3.MD.B.4Generate 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
Arizona3.MD.C.5Recognize area as an attribute of plane figures and understand concepts of area measurement.Grade 3
Arizona3.MD.C.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Grade 3
Arizona3.NBT.A.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
Arizona3.NBT.A.2Fluently 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
Arizona3.NBT.A.3Multiply 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
Arizona3.NF.A.1Understand 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
Arizona3.NF.A.2Understand 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
Arizona3.NF.A.3Explain 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 >, =, orGrade 3
Arizona3.OA.A.1Interpret 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
Arizona3.OA.A.2Interpret 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
Arizona3.OA.A.3Use 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
Arizona3.OA.A.4Determine 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
Arizona3.OA.B.5Apply 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
Arizona3.OA.B.6Understand division as an unknown-factor problem. For example, find 32  8 by finding the number that makes 32 when multiplied by 8.Grade 3
Arizona3.OA.C.7Fluently 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
Arizona4.G.A.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Grade 4
Arizona4.G.A.2Classify 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
Arizona4.MD.A.1Know 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
Arizona4.MD.A.2Use 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
Arizona4.MD.B.4Make 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
Arizona4.MD.C.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:Grade 4
Arizona4.MD.C.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Grade 4
Arizona4.MD.C.7Recognize 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
Arizona4.NBT.A.1Recognize 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
Arizona4.NBT.A.2Read 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
Arizona4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.Grade 4
Arizona4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.Grade 4
Arizona4.NBT.B.5Multiply 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
Arizona4.NBT.B.6Find 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
Arizona4.NF.A.1Explain 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
Arizona4.NF.A.2Compare 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 >, =, orGrade 4
Arizona4.NF.B.3Understand 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
Arizona4.NF.B.4Apply 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
Arizona4.NF.C.5Express 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
Arizona4.NF.C.6Use 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
Arizona4.NF.C.7Compare 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 >, =, orGrade 4
Arizona4.OA.A.1Interpret 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
Arizona4.OA.A.2Multiply 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
Arizona4.OA.B.4Find 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
Arizona4.OA.C.5Generate 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
Arizona5.G.A.1Use 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
Arizona5.G.A.2Represent 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
Arizona5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Grade 5
Arizona5.G.B.4Classify two-dimensional figures in a hierarchy based on properties.Grade 5
Arizona5.MD.B.2Make 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
Arizona5.NBT.A.1Recognize 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
Arizona5.NBT.A.2Explain 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
Arizona5.NBT.A.4Use place value understanding to round decimals to any place.Grade 5
Arizona5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm.Grade 5
Arizona5.NBT.B.6Find 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
Arizona5.NBT.B.7Add, 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
Arizona5.NF.B.3Interpret 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
Arizona5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Grade 5
Arizona5.NF.B.5Interpret 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
Arizona5.NF.B.6Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.Grade 5
Arizona5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Grade 5
Arizona5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Grade 5
Arizona5.OA.B.3Generate 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
Arizona6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.Grade 6
Arizona6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.Grade 6
Arizona6.EE.A.3Apply the properties of operations to generate equivalent expressions.Grade 6
Arizona6.EE.B.5Understand 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
Arizona6.EE.B.7Solve 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
Arizona6.EE.B.8Write 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
Arizona6.G.A.3Draw 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
Arizona6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.Grade 6
Arizona6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.Grade 6
Arizona6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Grade 6
Arizona6.NS.C.5Understand 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
Arizona6.NS.C.6Understand 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
Arizona6.NS.C.7Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.Grade 6
Arizona6.NS.C.8Solve 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
Arizona6.NS.C.9Convert between expressions for positive rational numbers, including fractions, decimals, and percents.Grade 6
Arizona6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.Grade 6
Arizona6.RP.A.2Understand 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
Arizona6.RP.A.3Use 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
Arizona7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Grade 7
Arizona7.EE.B.3Solve 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
Arizona7.G.A.1Solve 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
Arizona7.G.A.2Draw (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
Arizona7.G.B.5Use 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
Arizona7.NS.A.1Describe 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
Arizona7.NS.A.2Understand 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
Arizona7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.Grade 7
Arizona7.RP.A.1Compute 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
Arizona7.RP.A.2Recognize and represent proportional relationships between quantities.Grade 7
Arizona7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems.Grade 7
Arizona8.EE.A.3Use 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
Arizona8.EE.A.4Perform 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
Arizona8.EE.B.5Graph 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
Arizona8.EE.B.6Use 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
Arizona8.EE.C.7Give 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
Arizona8.EE.C.8Understand 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
Arizona8.F.A.1Understand 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
Arizona8.F.A.2Compare 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
Arizona8.F.A.3Interpret 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
Arizona8.F.B.4Construct 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
Arizona8.F.B.5Describe 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
Arizona8.G.A.1Verify experimentally the properties of rotations, reflections, and translations:Grade 8
Arizona8.G.A.2Understand 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
Arizona8.G.A.4Understand 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
Arizona8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Grade 8
Arizona8.G.B.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Grade 8
Arizona8.SP.A.1Construct 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
Arizona8.SP.A.2Know 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
ArizonaK.CC.A.1Count to 100 by ones and by tensKindergarten
ArizonaK.CC.A.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Kindergarten
ArizonaK.CC.A.3Write 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
ArizonaK.CC.B.4Understand 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
ArizonaK.CC.B.5Count 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
ArizonaK.CC.C.6Identify 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
ArizonaK.CC.C.7Compare two numbers between 1 and 10 presented as written numerals.Kindergarten
ArizonaK.NBT.A.1Compose 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
ArizonaK.OA.A.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Kindergarten
ArizonaK.OA.A.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.Kindergarten
ArizonaK.OA.A.3Decompose 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
ArizonaK.OA.A.4For 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
ArizonaK.OA.A.5Fluently add and subtract within 5.Kindergarten
CaliforniaK.CC.1Count to 100 by ones and by tens.Kindergarten
CaliforniaK.CC.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Kindergarten
CaliforniaK.CC.3Write 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
CaliforniaK.CC.4Understand the relationship between numbers and quantities; connect counting to cardinality.Kindergarten
CaliforniaK.CC.5Count 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
CaliforniaK.CC.6Identify 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
CaliforniaK.CC.7Compare two numbers between 1 and 10 presented as written numerals.Kindergarten
CaliforniaK.G.1Describe 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
CaliforniaK.G.2Correctly name shapes regardless of their orientations or overall size.Kindergarten
CaliforniaK.G.3Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).Kindergarten
CaliforniaK.G.4Analyze 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
CaliforniaK.G.5Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.Kindergarten
CaliforniaK.G.6Compose simple shapes to form larger shapes.Kindergarten
CaliforniaK.MD.1Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.Kindergarten
CaliforniaK.MD.2Directly 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
CaliforniaK.MD.3Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.Kindergarten
CaliforniaK.NBT.1Compose 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
CaliforniaK.OA.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Kindergarten
CaliforniaK.OA.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.Kindergarten
CaliforniaK.OA.3Decompose 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
CaliforniaK.OA.4For 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
CaliforniaK.OA.5Fluently add and subtract within 5.Kindergarten
California1.G.1Distinguish 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
California1.G.2Compose 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
California1.G.3Partition 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
California1.MD.1Order three objects by length; compare the lengths of two objects indirectly by using a third object.Grade 1
California1.MD.2Express 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
California1.MD.3Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
California1.MD.4Organize, 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
California1.NBT.1Count 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
California1.NBT.2Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:Grade 1
California1.NBT.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.Grade 1
California1.NBT.4Add 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
California1.NBT.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Grade 1
California1.NBT.6Subtract 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
California1.OA.1Use 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
California1.OA.2Solve 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
California1.OA.6Add 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
California1.OA.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.Grade 1
California1.OA.8Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.Grade 1
California2.G.1Recognize 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
California2.G.2Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.Grade 2
California2.G.3Partition 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
California2.MD.1Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.Grade 2
California2.MD.2Measure 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
California2.MD.3Estimate lengths using units of inches, feet, centimeters, and meters.Grade 2
California2.MD.4Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.Grade 2
California2.MD.5Use 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
California2.MD.6Represent 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
California2.MD.7Tell 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
California2.MD.8Solve word problems involving combinations of dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately.Grade 2
California2.MD.9Generate 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
California2.MD.10Draw 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
California2.NBT.1Understand 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
California2.NBT.2Count within 1000; skip-count by 2s, 5s, 10s, and 100s.Grade 2
California2.NBT.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Grade 2
California2.NBT.4Compare 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
California2.NBT.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Grade 2
California2.NBT.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Grade 2
California2.NBT.7Add 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
California2.NBT.7.1Use estimation strategies to make reasonable estimates in problem solving.Grade 2
California2.NBT.8Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.Grade 2
California2.NBT.9Explain why addition and subtraction strategies work, using place value and the properties of operations.Grade 2
California2.OA.1Use 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
California2.OA.2Fluently 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
California2.OA.3Determine 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
California2.OA.4Use 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
California3.G.1Understand 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
California3.G.2Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.Grade 3
California3.MD.1Tell 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
California3.MD.2Measure 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
California3.MD.3Draw 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
California3.MD.4Generate 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
California3.MD.5Recognize area as an attribute of plane figures and understand concepts of area measurement.Grade 3
California3.MD.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Grade 3
California3.MD.8Solve 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
California3.NBT.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
California3.NBT.2Fluently 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
California3.NBT.3Multiply 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
California3.NF.1Understand 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
California3.NF.2Understand a fraction as a number on the number line; represent fractions on a number line diagram.Grade 3
California3.NF.3Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.Grade 3
California3.OA.1Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.Grade 3
California3.OA.2Interpret 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
California3.OA.3Use 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
California3.OA.4Determine the unknown whole number in a multiplication or division equation relating three whole numbers.Grade 3
California3.OA.5Apply properties of operations as strategies to multiply and divide.Grade 3
California3.OA.6Understand division as an unknown-factor problem.Grade 3
California3.OA.7Fluently 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
California3.OA.8Solve 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
California3.OA.9Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.Grade 3
California4.G.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Grade 4
California4.G.2Classify 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
California4.G.3Recognize 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
California4.MD.1Know 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
California4.MD.2Use 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
California4.MD.3Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.Grade 4
California4.MD.4Make 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
California4.MD.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:Grade 4
California4.MD.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Grade 4
California4.MD.7Recognize 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
California4.NBT.1Recognize 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
California4.NBT.2Read 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
California4.NBT.3Use place value understanding to round multi-digit whole numbers to any place.Grade 4
California4.NBT.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.Grade 4
California4.NBT.5Multiply 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
California4.NBT.6Find 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
California4.NF.1Explain 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
California4.NF.2Compare 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
California4.NF.3Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣.Grade 4
California4.NF.4Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.Grade 4
California4.NF.5Express 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
California4.NF.6Use decimal notation for fractions with denominators 10 or 100.Grade 4
California4.NF.7Compare 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
California4.OA.1Interpret 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
California4.OA.2Multiply 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
California4.OA.3Solve 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
California4.OA.4Find 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
California4.OA.5Generate 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
California5.G.1Use 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
California5.G.2Represent 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
California5.G.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Grade 5
California5.G.4Classify two-dimensional figures in a hierarchy based on properties.Grade 5
California5.MD.1Convert 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
California5.MD.2Make 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
California5.MD.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement.Grade 5
California5.MD.4Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.Grade 5
California5.MD.5Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.Grade 5
California5.NBT.1Recognize 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
California5.NBT.2Explain 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
California5.NBT.4Use place value understanding to round decimals to any place.Grade 5
California5.NBT.5Fluently multiply multi-digit whole numbers using the standard algorithm.Grade 5
California5.NBT.6Find 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
California5.NBT.7Add, 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
California5.NF.1Add 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
California5.NF.2Solve 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
California5.NF.3Interpret 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
California5.NF.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Grade 5
California5.NF.5Interpret multiplication as scaling (resizing), by:Grade 5
California5.NF.6Solve 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
California5.NF.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Grade 5
California5.OA.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Grade 5
California5.OA.2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.Grade 5
California5.OA.2.1Express a whole number in the range 2-50 as a product of its prime factors.Grade 5
California5.OA.3Generate 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
California6.EE.1Write and evaluate numerical expressions involving whole-number exponents.Grade 6
California6.EE.2Write, read, and evaluate expressions in which letters stand for numbers.Grade 6
California6.EE.3Apply the properties of operations to generate equivalent expressions.Grade 6
California6.EE.4Identify 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
California6.EE.5Understand 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
California6.EE.6Use 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
California6.EE.7Solve 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
California6.EE.8Write 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
California6.EE.9Use 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
California6.G.1Find 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
California6.G.2Find 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
California6.G.3Draw 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
California6.G.4Represent 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
California6.RP.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.Grade 6
California6.RP.2Understand 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
California6.RP.3Use 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
California6.SP.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.Grade 6
California6.SP.2Understand 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
California6.SP.3Recognize 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
California6.SP.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.Grade 6
California6.SP.5Summarize numerical data sets in relation to their context, such as by:Grade 6
California6.NS.1Interpret 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
California6.NS.2Fluently divide multi-digit numbers using the standard algorithm.Grade 6
California6.NS.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Grade 6
California6.NS.4Find 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
California6.NS.5Understand 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
California6.NS.6Understand 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
California6.NS.7Understand ordering and absolute value of rational numbers.Grade 6
California6.NS.8Solve 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
California7.EE.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Grade 7
California7.EE.2Understand 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
California7.EE.3Solve 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
California7.EE.4Use 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
California7.G.1Solve 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
California7.G.2Draw (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
California7.G.3Describe 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
California7.G.4Know 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
California7.G.5Use 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
California7.G.6Solve 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
California7.RP.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.Grade 7
California7.RP.2Recognize and represent proportional relationships between quantities.Grade 7
California7.RP.3Use proportional relationships to solve multistep ratio and percent problems.Grade 7
California7.SP.1Understand 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
California7.SP.2Use 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
California7.SP.3Informally 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
California7.SP.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.Grade 7
California7.SP.5Understand 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
California7.SP.6Approximate 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
California7.SP.7Develop 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
California7.SP.8Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.Grade 7
California7.NS.1Apply 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
California7.NS.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.Grade 7
California7.NS.3Solve real-world and mathematical problems involving the four operations with rational numbers.Grade 7
California8.EE.1Know and apply the properties of integer exponents to generate equivalent numerical expressions.Grade 8
California8.EE.2Use 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
California8.EE.3Use 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
California8.EE.4Perform 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
California8.EE.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.Grade 8
California8.EE.6Use 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
California8.EE.7Solve linear equations in one variable.Grade 8
California8.EE.8Analyze and solve pairs of simultaneous linear equations.Grade 8
California8.F.1Understand 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
California8.F.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Grade 8
California8.F.3Interpret 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
California8.F.4Construct 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
California8.F.5Describe 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
California8.G.1Verify experimentally the properties of rotations, reflections, and translations:Grade 8
California8.G.2Understand 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
California8.G.3Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.Grade 8
California8.G.4Understand 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
California8.G.5Use 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
California8.G.6Explain a proof of the Pythagorean Theorem and its converse.Grade 8
California8.G.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Grade 8
California8.G.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Grade 8
California8.G.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.Grade 8
California8.SP.1Construct 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
California8.SP.2Know 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
California8.SP.3Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.Grade 8
California8.SP.4Understand 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
California8.NS.1Know 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
California8.NS.2Use 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
CaliforniaA-SSE.1Interpret expressions that represent a quantity in terms of its context.Algebra I
CaliforniaA-SSE.2Use the structure of an expression to identify ways to rewrite it.Algebra I
CaliforniaA-SSE.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Algebra I
CaliforniaA-APR.1Understand 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
CaliforniaA-CED.1Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.Algebra I
CaliforniaA-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Algebra I
CaliforniaA-CED.3Represent 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
CaliforniaA-CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.Algebra I
CaliforniaA-REI.1Explain 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
CaliforniaA-REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.Algebra I
CaliforniaA-REI.3.1Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.Algebra I
CaliforniaA-REI.4Solve quadratic equations in one variable.Algebra I
CaliforniaA-REI.5Prove 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
CaliforniaA-REI.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.Algebra I
CaliforniaA-REI.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.Algebra I
CaliforniaA-REI.10Understand 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
CaliforniaA-REI.11Explain 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
CaliforniaA-REI.12Graph 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
CaliforniaF-IF.1Understand 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
CaliforniaF-IF.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Algebra I
CaliforniaF-IF.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.Algebra I
CaliforniaF-IF.4For 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
CaliforniaF-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.Algebra I
CaliforniaF-IF.6Calculate 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
CaliforniaF-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Algebra I
CaliforniaF-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.Algebra I
CaliforniaF-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Algebra I
CaliforniaF-BF.1Write a function that describes a relationship between two quantities.Algebra I
CaliforniaF-BF.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.Algebra I
CaliforniaF-BF.3Identify 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
CaliforniaF-BF.4Find inverse functions.Algebra I
CaliforniaF-LE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.Algebra I
CaliforniaF-LE.2Construct 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
CaliforniaF-LE.3Observe 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
CaliforniaF-LE.5Interpret the parameters in a linear or exponential function in terms of a context.Algebra I
CaliforniaF-LE.6Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity.Algebra I
CaliforniaN-RN.1Explain 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
CaliforniaN-RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.Algebra I
CaliforniaN-RN.3Explain 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
CaliforniaN-Q.1Use 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
CaliforniaN-Q.2Define appropriate quantities for the purpose of descriptive modeling.Algebra I
CaliforniaN-Q.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.Algebra I
CaliforniaS-ID.1Represent data with plots on the real number line (dot plots, histograms, and box plots).Algebra I
CaliforniaS-ID.2Use 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
CaliforniaS-ID.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).Algebra I
CaliforniaS-ID.5Summarize 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
CaliforniaS-ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Algebra I
CaliforniaS-ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.Algebra I
CaliforniaS-ID.8Compute (using technology) and interpret the correlation coefficient of a linear fit.Algebra I
CaliforniaS-ID.9Distinguish between correlation and causation.Algebra I
CaliforniaG-CO.1Know 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
CaliforniaG-CO.2Represent 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
CaliforniaG-CO.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.Geometry
CaliforniaG-CO.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.Geometry
CaliforniaG-CO.5Given 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
CaliforniaG-CO.6Use 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
CaliforniaG-CO.7Use 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
CaliforniaG-CO.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.Geometry
CaliforniaG-CO.9Prove theorems about lines and angles.Geometry
CaliforniaG-CO.12Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).Geometry
CaliforniaG-CO.13Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.Geometry
CaliforniaG-SRT.1Verify experimentally the properties of dilations given by a center and a scale factor:Geometry
CaliforniaG-SRT.2Given 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
CaliforniaG-SRT.3Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.Geometry
CaliforniaG-SRT.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.Geometry
CaliforniaG-SRT.6Understand 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
CaliforniaG-SRT.7Explain and use the relationship between the sine and cosine of complementary angles.Geometry
CaliforniaG-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.Geometry
CaliforniaG-SRT.8.1Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90° and 45°, 45°, 90°).Geometry
CaliforniaG-SRT.9Derive 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
CaliforniaG-SRT.10Prove the Laws of Sines and Cosines and use them to solve problems.Geometry
CaliforniaG-SRT.11Understand 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
CaliforniaG-C.1Prove that all circles are similar.Geometry
CaliforniaG-C.2Identify and describe relationships among inscribed angles, radii, and chords.Geometry
CaliforniaG-C.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.Geometry
CaliforniaG-C.4Construct a tangent line from a point outside a given circle to the circle.Geometry
CaliforniaG-C.5Derive 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
CaliforniaG-GPE.1Derive 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
CaliforniaG-GPE.2Derive the equation of a parabola given a focus and directrix.Geometry
CaliforniaG-GPE.4Use coordinates to prove simple geometric theorems algebraically.Geometry
CaliforniaG-GPE.5Prove 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
CaliforniaG-GPE.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.Geometry
CaliforniaG-GPE.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.Geometry
CaliforniaG-GMD.1Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.Geometry
CaliforniaG-GMD.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.Geometry
CaliforniaG-GMD.4Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.Geometry
CaliforniaG-GMD.5Know 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
CaliforniaG-GMD.6Verify 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
CaliforniaG-MG.1Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).Geometry
CaliforniaG-MG.2Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).Geometry
CaliforniaG-MG.3Apply 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
CaliforniaS-CP.1Describe 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
CaliforniaS-CP.2Understand 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
CaliforniaS-CP.3Understand 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
CaliforniaS-CP.4Construct 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
CaliforniaS-CP.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.Geometry
CaliforniaS-CP.6Find 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
CaliforniaS-CP.7Apply 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
CaliforniaS-CP.8Apply 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
CaliforniaS-CP.9Use permutations and combinations to compute probabilities of compound events and solve problems.Geometry
CaliforniaS-MD.6Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).Geometry
CaliforniaS-MD.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).Geometry
CaliforniaA-SSE.1Interpret expressions that represent a quantity in terms of its context.Algebra II
CaliforniaA-SSE.2Use the structure of an expression to identify ways to rewrite it.Algebra II
CaliforniaA-SSE.4Derive 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
CaliforniaA-APR.1Understand 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
CaliforniaA-APR.2Know 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
CaliforniaA-APR.3Identify 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
CaliforniaA-APR.4Prove polynomial identities and use them to describe numerical relationships.Algebra II
CaliforniaA-APR.5Know 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
CaliforniaA-APR.6Rewrite 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
CaliforniaA-APR.7Understand 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
CaliforniaA-CED.1Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.Algebra II
CaliforniaA-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Algebra II
CaliforniaA-CED.3Represent 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
CaliforniaA-CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.Algebra II
CaliforniaA-REI.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.Algebra II
CaliforniaA-REI.3.1Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.Algebra II
CaliforniaA-REI.11Explain 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
CaliforniaF-IF.4For 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
CaliforniaF-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.Algebra II
CaliforniaF-IF.6Calculate 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
CaliforniaF-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Algebra II
CaliforniaF-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.Algebra II
CaliforniaF-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Algebra II
CaliforniaF-BF.1Write a function that describes a relationship between two quantities.Algebra II
CaliforniaF-BF.3Identify 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
CaliforniaF-BF.4Find inverse functions.Algebra II
CaliforniaF-LE.4For 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
CaliforniaF-LE.4.1Prove simple laws of logarithms.Algebra II
CaliforniaF-LE.4.2Use the definition of logarithms to translate between logarithms in any base.Algebra II
CaliforniaF-LE.4.3Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.Algebra II
CaliforniaF-TF.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.Algebra II
CaliforniaF-TF.2Explain 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
CaliforniaF-TF.2.1Graph all 6 basic trigonometric functions.Algebra II
CaliforniaF-TF.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.Algebra II
CaliforniaF-TF.8Prove 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
CaliforniaG-GPE.3.1Given 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
CaliforniaN-CN.1Know 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
CaliforniaN-CN.2Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.Algebra II
CaliforniaN-CN.7Solve quadratic equations with real coefficients that have complex solutions.Algebra II
CaliforniaN-CN.8Extend polynomial identities to the complex numbers.Algebra II
CaliforniaN-CN.9Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.Algebra II
CaliforniaS-ID.4Use 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
CaliforniaS-IC.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.Algebra II
CaliforniaS-IC.2Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.Algebra II
CaliforniaS-IC.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.Algebra II
CaliforniaS-IC.4Use 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
CaliforniaS-IC.5Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.Algebra II
CaliforniaS-IC.6Evaluate reports based on data.Algebra II
CaliforniaS-MD.6Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).Algebra II
CaliforniaS-MD.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).Algebra II
CaliforniaA-SSE.1Interpret expressions that represent a quantity in terms of its context.Mathematics I
CaliforniaA-CED.1Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.Mathematics I
CaliforniaA-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Mathematics I
CaliforniaA-CED.3Represent 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
CaliforniaA-CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.Mathematics I
CaliforniaA-REI.1Explain 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
CaliforniaA-REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.Mathematics I
CaliforniaA-REI.3.1Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.Mathematics I
CaliforniaA-REI.5Prove 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
CaliforniaA-REI.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.Mathematics I
CaliforniaA-REI.10Understand 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
CaliforniaA-REI.11Explain 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
CaliforniaA-REI.12Graph 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
CaliforniaF-IF.1Understand 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
CaliforniaF-IF.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Mathematics I
CaliforniaF-IF.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.Mathematics I
CaliforniaF-IF.4For 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
CaliforniaF-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.Mathematics I
CaliforniaF-IF.6Calculate 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
CaliforniaF-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Mathematics I
CaliforniaF-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Mathematics I
CaliforniaF-BF.1Write a function that describes a relationship between two quantities.Mathematics I
CaliforniaF-BF.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.Mathematics I
CaliforniaF-BF.3Identify 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
CaliforniaF-LE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.Mathematics I
CaliforniaF-LE.2Construct 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
CaliforniaF-LE.3Observe 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
CaliforniaF-LE.5Interpret the parameters in a linear or exponential function in terms of a context.Mathematics I
CaliforniaG-CO.1Know 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
CaliforniaG-CO.2Represent 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
CaliforniaG-CO.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.Mathematics I
CaliforniaG-CO.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.Mathematics I
CaliforniaG-CO.5Given 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
CaliforniaG-CO.6Use 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
CaliforniaG-CO.7Use 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
CaliforniaG-CO.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.Mathematics I
CaliforniaG-CO.12Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).Mathematics I
CaliforniaG-CO.13Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.Mathematics I
CaliforniaG-GPE.4Use coordinates to prove simple geometric theorems algebraically.Mathematics I
CaliforniaG-GPE.5Prove 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
CaliforniaG-GPE.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.Mathematics I
CaliforniaN-Q.1Use 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
CaliforniaN-Q.2Define appropriate quantities for the purpose of descriptive modeling.Mathematics I
CaliforniaN-Q.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.Mathematics I
CaliforniaS-ID.1Represent data with plots on the real number line (dot plots, histograms, and box plots).Mathematics I
CaliforniaS-ID.2Use 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
CaliforniaS-ID.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).Mathematics I
CaliforniaS-ID.5Summarize 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
CaliforniaS-ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Mathematics I
CaliforniaS-ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.Mathematics I
CaliforniaS-ID.8Compute (using technology) and interpret the correlation coefficient of a linear fit.Mathematics I
CaliforniaS-ID.9Distinguish between correlation and causation.Mathematics I
CaliforniaA-SSE.1Interpret expressions that represent a quantity in terms of its context.Mathematics II
CaliforniaA-SSE.2Use the structure of an expression to identify ways to rewrite it.Mathematics II
CaliforniaA-SSE.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Mathematics II
CaliforniaA-APR.1Understand 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
CaliforniaA-CED.1Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.Mathematics II
CaliforniaA-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Mathematics II
CaliforniaA-CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.Mathematics II
CaliforniaA-REI.4Solve quadratic equations in one variable.Mathematics II
CaliforniaA-REI.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.Mathematics II
CaliforniaF-IF.4For 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
CaliforniaF-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.Mathematics II
CaliforniaF-IF.6Calculate 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
CaliforniaF-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Mathematics II
CaliforniaF-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.Mathematics II
CaliforniaF-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Mathematics II
CaliforniaF-BF.1Write a function that describes a relationship between two quantities.Mathematics II
CaliforniaF-BF.3Identify 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
CaliforniaF-BF.4Find inverse functions.Mathematics II
CaliforniaF-LE.3Observe 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
CaliforniaF-LE.6Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity.Mathematics II
CaliforniaF-TF.8Prove 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
CaliforniaG-CO.9Prove theorems about lines and angles.Mathematics II
CaliforniaG-SRT.1Verify experimentally the properties of dilations given by a center and a scale factor:Mathematics II
CaliforniaG-SRT.2Given 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
CaliforniaG-SRT.3Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.Mathematics II
CaliforniaG-SRT.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.Mathematics II
CaliforniaG-SRT.6Understand 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
CaliforniaG-SRT.7Explain and use the relationship between the sine and cosine of complementary angles.Mathematics II
CaliforniaG-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.Mathematics II
CaliforniaG-SRT.8.1Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90° and 45°, 45°, 90°).Mathematics II
CaliforniaG-C.1Prove that all circles are similar.Mathematics II
CaliforniaG-C.2Identify and describe relationships among inscribed angles, radii, and chords.Mathematics II
CaliforniaG-C.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.Mathematics II
CaliforniaG-C.4Construct a tangent line from a point outside a given circle to the circle.Mathematics II
CaliforniaG-C.5Derive 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
CaliforniaG-GPE.1Derive 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
CaliforniaG-GPE.2Derive the equation of a parabola given a focus and directrix.Mathematics II
CaliforniaG-GPE.4Use coordinates to prove simple geometric theorems algebraically.Mathematics II
CaliforniaG-GPE.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.Mathematics II
CaliforniaG-GMD.1Give 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
CaliforniaG-GMD.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.Mathematics II
CaliforniaG-GMD.5Know 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
CaliforniaG-GMD.6Verify 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
CaliforniaN-RN.1Explain 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
CaliforniaN-RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.Mathematics II
CaliforniaN-RN.3Explain 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
CaliforniaN-CN.1Know 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
CaliforniaN-CN.2Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.Mathematics II
CaliforniaN-CN.7Solve quadratic equations with real coefficients that have complex solutions.Mathematics II
CaliforniaN-CN.8Extend polynomial identities to the complex numbers.Mathematics II
CaliforniaN-CN.9Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.Mathematics II
CaliforniaS-CP.1Describe 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
CaliforniaS-CP.2Understand 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
CaliforniaS-CP.3Understand 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
CaliforniaS-CP.4Construct 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
CaliforniaS-CP.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.Mathematics II
CaliforniaS-CP.6Find 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
CaliforniaS-CP.7Apply 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
CaliforniaS-CP.8Apply 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
CaliforniaS-CP.9Use permutations and combinations to compute probabilities of compound events and solve problems.Mathematics II
CaliforniaS-MD.6Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).Mathematics II
CaliforniaS-MD.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).Mathematics II
CaliforniaA-SSE.1Interpret expressions that represent a quantity in terms of its context.Mathematics III
CaliforniaA-SSE.2Use the structure of an expression to identify ways to rewrite it.Mathematics III
CaliforniaA-SSE.4Derive 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
CaliforniaA-APR.1Understand 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
CaliforniaA-APR.2Know 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
CaliforniaA-APR.3Identify 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
CaliforniaA-APR.4Prove polynomial identities and use them to describe numerical relationships.Mathematics III
CaliforniaA-APR.5Know 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
CaliforniaA-APR.6Rewrite 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
CaliforniaA-APR.7Understand 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
CaliforniaA-CED.1Create 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
CaliforniaA-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Mathematics III
CaliforniaA-CED.3Represent 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
CaliforniaA-CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.Mathematics III
CaliforniaA-REI.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.Mathematics III
CaliforniaA-REI.11Explain 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
CaliforniaF-IF.4For 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
CaliforniaF-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.Mathematics III
CaliforniaF-IF.6Calculate 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
CaliforniaF-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Mathematics III
CaliforniaF-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.Mathematics III
CaliforniaF-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Mathematics III
CaliforniaF-BF.1Write a function that describes a relationship between two quantities.Mathematics III
CaliforniaF-BF.3Identify 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
CaliforniaF-BF.4Find inverse functions.Mathematics III
CaliforniaF-LE.4For 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
CaliforniaF-LE.4.1Prove simple laws of logarithms.Mathematics III
CaliforniaF-LE.4.2Use the definition of logarithms to translate between logarithms in any base.Mathematics III
CaliforniaF-LE.4.3Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.Mathematics III
CaliforniaF-TF.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.Mathematics III
CaliforniaF-TF.2Explain 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
CaliforniaF-TF.2.1Graph all 6 basic trigonometric functions.Mathematics III
CaliforniaF-TF.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.Mathematics III
CaliforniaG-SRT.9Derive 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
CaliforniaG-SRT.10Prove the Laws of Sines and Cosines and use them to solve problems.Mathematics III
CaliforniaG-SRT.11Understand 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
CaliforniaG-GPE.3.1Given 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 equationMathematics III
CaliforniaG-GMD.4Identify 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
CaliforniaG-MG.1Use 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
CaliforniaG-MG.2Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).Mathematics III
CaliforniaG-MG.3Apply 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
CaliforniaN-CN.8Extend polynomial identities to the complex numbers.Mathematics III
CaliforniaN-CN.9Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.Mathematics III
CaliforniaS-ID.4Use 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
CaliforniaS-IC.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.Mathematics III
CaliforniaS-IC.2Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.Mathematics III
CaliforniaS-IC.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.Mathematics III
CaliforniaS-IC.4Use 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
CaliforniaS-IC.5Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.Mathematics III
CaliforniaS-IC.6Evaluate reports based on data.Mathematics III
CaliforniaS-MD.6Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).Mathematics III
CaliforniaS-MD.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).Mathematics III
CaliforniaN-Q.1Use 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
CaliforniaN-Q.2Define appropriate quantities for the purpose of descriptive modeling.High School - Number and Quantity
CaliforniaN-Q.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.High School - Number and Quantity
CaliforniaN-CN.1Know 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
CaliforniaN-CN.2Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.High School - Number and Quantity
CaliforniaN-CN.3Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.High School - Number and Quantity
CaliforniaN-CN.4Represent 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
CaliforniaN-CN.5Represent 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
CaliforniaN-CN.6Calculate 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
CaliforniaN-CN.7Solve quadratic equations with real coefficients that have complex solutions.High School - Number and Quantity
CaliforniaN-CN.8Extend polynomial identities to the complex numbers.High School - Number and Quantity
CaliforniaN-CN.9Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.High School - Number and Quantity
CaliforniaN-RN.1Explain 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
CaliforniaN-RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.High School - Number and Quantity
CaliforniaN-RN.3Explain 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
CaliforniaN-VM.1Recognize 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
CaliforniaN-VM.2Find 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
CaliforniaN-VM.3Solve problems involving velocity and other quantities that can be represented by vectors.High School - Number and Quantity
CaliforniaN-VM.4Add and subtract vectors.High School - Number and Quantity
CaliforniaN-VM.5Multiply a vector by a scalar.High School - Number and Quantity
CaliforniaN-VM.6Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.High School - Number and Quantity
CaliforniaN-VM.7Multiply 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
CaliforniaN-VM.8Add, subtract, and multiply matrices of appropriate dimensions.High School - Number and Quantity
CaliforniaN-VM.9Understand 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
CaliforniaN-VM.10Understand 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
CaliforniaN-VM.11Multiply 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
CaliforniaN-VM.12Work 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
CaliforniaA-APR.1Understand 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
CaliforniaA-APR.2Know 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
CaliforniaA-APR.3Identify 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
CaliforniaA-APR.4Prove polynomial identities and use them to describe numerical relationships.High School - Algebra
CaliforniaA-APR.5Know 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
CaliforniaA-APR.6Rewrite 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
CaliforniaA-APR.7Understand 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
CaliforniaA-CED.1Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.High School - Algebra
CaliforniaA-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.High School - Algebra
CaliforniaA-CED.3Represent 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
CaliforniaA-CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.High School - Algebra
CaliforniaA-REI.1Explain 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
CaliforniaA-REI.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.High School - Algebra
CaliforniaA-REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.High School - Algebra
CaliforniaA-REI.3.1Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.High School - Algebra
CaliforniaA-REI.4Solve quadratic equations in one variable.High School - Algebra
CaliforniaA-REI.5Prove 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
CaliforniaA-REI.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.High School - Algebra
CaliforniaA-REI.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.High School - Algebra
CaliforniaA-REI.8Represent a system of linear equations as a single matrix equation in a vector variable.High School - Algebra
CaliforniaA-REI.9Find 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
CaliforniaA-REI.10Understand 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
CaliforniaA-REI.11Explain 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
CaliforniaA-REI.12Graph 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
CaliforniaA-SSE.1Interpret expressions that represent a quantity in terms of its context.High School - Algebra
CaliforniaA-SSE.2Use the structure of an expression to identify ways to rewrite it.High School - Algebra
CaliforniaA-SSE.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.High School - Algebra
CaliforniaA-SSE.4Derive 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
CaliforniaF-BF.1Write a function that describes a relationship between two quantities.High School - Functions
CaliforniaF-BF.2Write 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
CaliforniaF-BF.3Identify 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
CaliforniaF-BF.4Find inverse functions.High School - Functions
CaliforniaF-BF.5Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.High School - Functions
CaliforniaF-IF.1Understand 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
CaliforniaF-IF.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.High School - Functions
CaliforniaF-IF.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.High School - Functions
CaliforniaF-IF.4For 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
CaliforniaF-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.High School - Functions
CaliforniaF-IF.6Calculate 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
CaliforniaF-IF.7Graph 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
CaliforniaF-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.High School - Functions
CaliforniaF-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).High School - Functions
CaliforniaF-IF.10Demonstrate an understanding of functions and equations defined parametrically and graph them.High School - Functions
CaliforniaF-IF.11Graph polar coordinates and curves. Convert between polar and rectangular coordinate systems.High School - Functions
CaliforniaF-LE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.High School - Functions
CaliforniaF-LE.2Construct 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
CaliforniaF-LE.3Observe 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
CaliforniaF-LE.4For 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
CaliforniaF-LE.4.1Prove simple laws of logarithms.High School - Functions
CaliforniaF-LE.4.2Use the definition of logarithms to translate between logarithms in any base.High School - Functions
CaliforniaF-LE.4.3Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.High School - Functions
CaliforniaF-LE.5Interpret the parameters in a linear or exponential function in terms of a context.High School - Functions
CaliforniaF-LE.6Apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.High School - Functions
CaliforniaF-TF.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.High School - Functions
CaliforniaF-TF.2Explain 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
CaliforniaF-TF.2.1Graph all 6 basic trigonometric functions.High School - Functions
CaliforniaF-TF.3Use 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
CaliforniaF-TF.4Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.High School - Functions
CaliforniaF-TF.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.High School - Functions
CaliforniaF-TF.6Understand 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
CaliforniaF-TF.7Use 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
CaliforniaF-TF.8Prove 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
CaliforniaF-TF.9Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.High School - Functions
CaliforniaF-TF.10Prove the half angle and double angle identities for sine and cosine and use them to solve problems.High School - Functions
CaliforniaG-C.1Prove that all circles are similar.High School - Geometry
CaliforniaG-C.2Identify and describe relationships among inscribed angles, radii, and chords.High School - Geometry
CaliforniaG-C.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.High School - Geometry
CaliforniaG-C.4Construct a tangent line from a point outside a given circle to the circle.High School - Geometry
CaliforniaG-C.5Derive 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
CaliforniaG-CO.1Know 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
CaliforniaG-CO.2Represent 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
CaliforniaG-CO.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.High School - Geometry
CaliforniaG-CO.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.High School - Geometry
CaliforniaG-CO.5Given 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
CaliforniaG-CO.6Use 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
CaliforniaG-CO.7Use 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
CaliforniaG-CO.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.High School - Geometry
CaliforniaG-CO.9Prove theorems about lines and angles.High School - Geometry
CaliforniaG-CO.10Prove theorems about triangles.High School - Geometry
CaliforniaG-CO.11Prove theorems about parallelograms.High School - Geometry
CaliforniaG-CO.12Make 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
CaliforniaG-CO.13Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.High School - Geometry
CaliforniaG-GPE.1Derive 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
CaliforniaG-GPE.2Derive the equation of a parabola given a focus and directrix.High School - Geometry
CaliforniaG-GPE.3Derive 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
CaliforniaG-GPE.3.1Given 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
CaliforniaG-GPE.4Use coordinates to prove simple geometric theorems algebraically.High School - Geometry
CaliforniaG-GPE.5Prove 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
CaliforniaG-GPE.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.High School - Geometry
CaliforniaG-GPE.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.High School - Geometry
CaliforniaG-GMD.1Give 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
CaliforniaG-GMD.2Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.High School - Geometry
CaliforniaG-GMD.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.High School - Geometry
CaliforniaG-GMD.4Identify 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
CaliforniaG-GMD.5Know 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
CaliforniaG-GMD.6Verify 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
CaliforniaG-MG.1Use 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
CaliforniaG-MG.2Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).High School - Geometry
CaliforniaG-MG.3Apply 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
CaliforniaG-SRT.1Verify experimentally the properties of dilations given by a center and a scale factor:High School - Geometry
CaliforniaG-SRT.2Given 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
CaliforniaG-SRT.3Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.High School - Geometry
CaliforniaG-SRT.4Prove theorems about triangles.High School - Geometry
CaliforniaG-SRT.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.High School - Geometry
CaliforniaG-SRT.6Understand 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
CaliforniaG-SRT.7Explain and use the relationship between the sine and cosine of complementary angles.High School - Geometry
CaliforniaG-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.High School - Geometry
CaliforniaG-SRT.8.1Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90° and 45°, 45°, 90°).High School - Geometry
CaliforniaG-SRT.9Derive 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
CaliforniaG-SRT.10Prove the Laws of Sines and Cosines and use them to solve problems.High School - Geometry
CaliforniaG-SRT.11Understand 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
CaliforniaS-CP.1Describe 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
CaliforniaS-CP.2Understand 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
CaliforniaS-CP.3Understand 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
CaliforniaS-CP.4Construct 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
CaliforniaS-CP.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.High School - Statistics and Probability
CaliforniaS-CP.6Find 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
CaliforniaS-CP.7Apply 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
CaliforniaS-CP.8Apply 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
CaliforniaS-CP.9Use permutations and combinations to compute probabilities of compound events and solve problems.High School - Statistics and Probability
CaliforniaS-ID.1Represent data with plots on the real number line (dot plots, histograms, and box plots).High School - Statistics and Probability
CaliforniaS-ID.2Use 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
CaliforniaS-ID.3Interpret 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
CaliforniaS-ID.4Use 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
CaliforniaS-ID.5Summarize 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
CaliforniaS-ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.High School - Statistics and Probability
CaliforniaS-ID.7Interpret 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
CaliforniaS-ID.8Compute (using technology) and interpret the correlation coefficient of a linear fit.High School - Statistics and Probability
CaliforniaS-ID.9Distinguish between correlation and causation.High School - Statistics and Probability
CaliforniaS-IC.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.High School - Statistics and Probability
CaliforniaS-IC.2Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.High School - Statistics and Probability
CaliforniaS-IC.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.High School - Statistics and Probability
CaliforniaS-IC.4Use 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
CaliforniaS-IC.5Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.High School - Statistics and Probability
CaliforniaS-IC.6Evaluate reports based on data.High School - Statistics and Probability
CaliforniaS-MD.1Define 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
CaliforniaS-MD.2Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.High School - Statistics and Probability
CaliforniaS-MD.3Develop 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
CaliforniaS-MD.4Develop 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
CaliforniaS-MD.5Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.High School - Statistics and Probability
CaliforniaS-MD.6Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).High School - Statistics and Probability
CaliforniaS-MD.7Analyze 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
CCSSMA-APR.B.3Identify 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
CCSSMA-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Algebra
CCSSMA-SSE.A.2Use the structure of an expression to identify ways to rewrite it.Algebra
CCSSMA-SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Algebra
CCSSMF-BF.A.1Write a function that describes a relationship between two quantities.Algebra
CCSSMF-IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Algebra
CCSSMF-IF.B.4For 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
CCSSMF-IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Algebra
CCSSMS-ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Algebra
CCSSM1.MD.B.3Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
CCSSM1.MD.C.4Organize, 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
CCSSM1.NBT.A.1Count 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
CCSSM1.NBT.B.2Understand 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
CCSSM1.NBT.B.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols.Grade 1
CCSSM1.NBT.C.4Add 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
CCSSM1.NBT.C.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Grade 1
CCSSM1.NBT.C.6Subtract 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
CCSSM1.OA.B.3Apply 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
CCSSM1.OA.B.4Understand 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
CCSSM1.OA.C.6Add 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
CCSSM1.OA.D.7Understand 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
CCSSM1.OA.D.8Determine 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
CCSSM2.G.A.1Recognize 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
CCSSM2.MD.C.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Grade 2
CCSSM2.MD.D.10Draw 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
CCSSM2.MD.D.9Generate 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
CCSSM2.NBT.A.1Understand 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
CCSSM2.NBT.A.2Count within 1000; skip-count by 5s, 10s, and 100s.Grade 2
CCSSM2.NBT.A.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Grade 2
CCSSM2.NBT.A.4Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons.Grade 2
CCSSM2.NBT.B.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Grade 2
CCSSM2.NBT.B.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Grade 2
CCSSM2.NBT.B.7Add 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
CCSSM2.NBT.B.8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.Grade 2
CCSSM2.OA.A.1Use 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
CCSSM2.OA.B.2Fluently 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
CCSSM3.G.A.1Understand 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
CCSSM3.MD.A.1Tell 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
CCSSM3.MD.B.3Draw 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
CCSSM3.MD.B.4Generate 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
CCSSM3.MD.C.5Recognize area as an attribute of plane figures and understand concepts of area measurement.Grade 3
CCSSM3.MD.C.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Grade 3
CCSSM3.NBT.A.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
CCSSM3.NBT.A.2Fluently 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
CCSSM3.NBT.A.3Multiply 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
CCSSM3.NF.A.1Understand 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
CCSSM3.NF.A.2Understand 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
CCSSM3.NF.A.3Explain 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 >, =, orGrade 3
CCSSM3.OA.A.1Interpret 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
CCSSM3.OA.A.2Interpret 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
CCSSM3.OA.A.3Use 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
CCSSM3.OA.A.4Determine 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
CCSSM3.OA.B.5Apply 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
CCSSM3.OA.B.6Understand division as an unknown-factor problem. For example, find 32  8 by finding the number that makes 32 when multiplied by 8.Grade 3
CCSSM3.OA.C.7Fluently 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
CCSSM4.G.A.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Grade 4
CCSSM4.G.A.2Classify 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
CCSSM4.MD.A.1Know 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
CCSSM4.MD.A.2Use 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
CCSSM4.MD.B.4Make 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
CCSSM4.MD.C.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.Grade 4
CCSSM4.MD.C.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Grade 4
CCSSM4.MD.C.7Recognize 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
CCSSM4.NBT.A.1Recognize 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
CCSSM4.NBT.A.2Read 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
CCSSM4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.Grade 4
CCSSM4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.Grade 4
CCSSM4.NBT.B.5Multiply 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
CCSSM4.NBT.B.6Find 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
CCSSM4.NF.A.1Explain 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
CCSSM4.NF.A.2Compare 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 >, =, orGrade 4
CCSSM4.NF.B.3Understand 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
CCSSM4.NF.B.4Apply 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
CCSSM4.NF.C.5Express 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
CCSSM4.NF.C.6Use 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
CCSSM4.NF.C.7Compare 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 >, =, orGrade 4
CCSSM4.OA.A.1Interpret 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
CCSSM4.OA.A.2Multiply 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
CCSSM4.OA.B.4Find 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
CCSSM4.OA.C.5Generate 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
CCSSM5.G.A.1Use 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
CCSSM5.G.A.2Represent 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
CCSSM5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Grade 5
CCSSM5.G.B.4Classify two-dimensional figures in a hierarchy based on properties.Grade 5
CCSSM5.MD.B.2Make 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
CCSSM5.NBT.A.1Recognize 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
CCSSM5.NBT.A.2Explain 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
CCSSM5.NBT.A.4Use place value understanding to round decimals to any place.Grade 5
CCSSM5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm.Grade 5
CCSSM5.NBT.B.6Find 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
CCSSM5.NBT.B.7Add, 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
CCSSM5.NF.B.3Interpret 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
CCSSM5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Grade 5
CCSSM5.NF.B.5Interpret 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
CCSSM5.NF.B.6Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.Grade 5
CCSSM5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Grade 5
CCSSM5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Grade 5
CCSSM5.OA.B.3Generate 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
CCSSM6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.Grade 6
CCSSM6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.Grade 6
CCSSM6.EE.A.3Apply the properties of operations to generate equivalent expressions.Grade 6
CCSSM6.EE.B.5Understand 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
CCSSM6.EE.B.7Solve 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
CCSSM6.EE.B.8Write 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
CCSSM6.G.A.3Draw 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
CCSSM6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.Grade 6
CCSSM6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.Grade 6
CCSSM6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Grade 6
CCSSM6.NS.C.5Understand 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
CCSSM6.NS.C.6Understand 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
CCSSM6.NS.C.7Understand ordering and absolute value of rational numbers.Grade 6
CCSSM6.NS.C.8Solve 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
CCSSM6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.Grade 6
CCSSM6.RP.A.2Understand 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
CCSSM6.RP.A.3Use 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
CCSSM7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Grade 7
CCSSM7.EE.B.3Solve 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
CCSSM7.G.A.1Solve 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
CCSSM7.G.A.2Draw (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
CCSSM7.G.B.5Use 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
CCSSM7.NS.A.1Apply 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
CCSSM7.NS.A.2Understand 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
CCSSM7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.Grade 7
CCSSM7.RP.A.1Compute 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
CCSSM7.RP.A.2Recognize and represent proportional relationships between quantities.Grade 7
CCSSM7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems.Grade 7
CCSSM8.EE.A.3Use 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
CCSSM8.EE.A.4Perform 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
CCSSM8.EE.B.5Graph 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
CCSSM8.EE.B.6Use 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
CCSSM8.EE.C.7Give 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
CCSSM8.EE.C.8Understand 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
CCSSM8.F.A.1Understand 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
CCSSM8.F.A.2Compare 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
CCSSM8.F.A.3Interpret 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
CCSSM8.F.B.4Construct 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
CCSSM8.F.B.5Describe 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
CCSSM8.G.A.1Verify experimentally the properties of rotations, reflections, and translations.Grade 8
CCSSM8.G.A.2Understand 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
CCSSM8.G.A.4Understand 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
CCSSM8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Grade 8
CCSSM8.G.B.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Grade 8
CCSSM8.SP.A.1Construct 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
CCSSM8.SP.A.2Know 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
CCSSMK.CC.A.1Count to 100 by ones and by tensKindergarten
CCSSMK.CC.A.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Kindergarten
CCSSMK.CC.A.3Write 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
CCSSMK.CC.B.4Understand 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
CCSSMK.CC.B.5Count 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
CCSSMK.CC.C.6Identify 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
CCSSMK.CC.C.7Compare two numbers between 1 and 10 presented as written numerals.Kindergarten
CCSSMK.NBT.A.1Compose 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
CCSSMK.OA.A.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Kindergarten
CCSSMK.OA.A.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.Kindergarten
CCSSMK.OA.A.3Decompose 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
CCSSMK.OA.A.4For 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
CCSSMK.OA.A.5Fluently add and subtract within 5.Kindergarten
FloridaA-APR.B.3Identify 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
FloridaA-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Algebra
FloridaA-SSE.A.2Use the structure of an expression to identify ways to rewrite it.Algebra
FloridaA-SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Algebra
FloridaF-BF.A.1Write a function that describes a relationship between two quantities.Algebra
FloridaF-IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Algebra
FloridaF-IF.B.4For 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
FloridaF-IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Algebra
FloridaS-ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Algebra
Florida1.MD.2.3Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
Florida1.MD.3.4Organize, 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
Florida1.NBT.1.1Count 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
Florida1.NBT.2.2Understand 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
Florida1.NBT.2.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.Grade 1
Florida1.NBT.3.4Add 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
Florida1.NBT.3.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Grade 1
Florida1.NBT.3.6Subtract 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
Florida1.OA.2.3Apply 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
Florida1.OA.2.4Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.Grade 1
Florida1.OA.3.6Add 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
Florida1.OA.4.7Understand 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
Florida1.OA.4.8Determine 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
Florida2.G.1.1Recognize 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
Florida2.MD.3.7Tell and write time from analog and digital clocks to the nearest five minutes.Grade 2
Florida2.MD.4.10Draw 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
Florida2.MD.4.9Generate 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
Florida2.NBT.1.1Understand 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
Florida2.NBT.1.2Count within 1000; skip-count by 5s, 10s, and 100s.Grade 2
Florida2.NBT.1.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Grade 2
Florida2.NBT.1.4Compare 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
Florida2.NBT.2.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Grade 2
Florida2.NBT.2.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Grade 2
Florida2.NBT.2.7Add 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
Florida2.NBT.2.8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.Grade 2
Florida2.OA.1.1Use 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
Florida2.OA.1.aDetermine 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
Florida2.OA.2.2Fluently 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
Florida3.G.1.1Understand 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
Florida3.MD.1.1Tell 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
Florida3.MD.2.3Draw 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
Florida3.MD.2.4Generate 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
Florida3.MD.3.5Recognize 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
Florida3.MD.3.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Grade 3
Florida3.MD.3.7Relate 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
Florida3.NBT.1.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
Florida3.NBT.1.2Fluently 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
Florida3.NBT.1.3Multiply 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
Florida3.NF.1.1Understand 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
Florida3.NF.1.2Understand 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
Florida3.NF.1.3Explain 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 >, =, orGrade 3
Florida3.OA.1.1Interpret 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
Florida3.OA.1.2Interpret 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
Florida3.OA.1.3Use 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
Florida3.OA.1.4Determine 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
Florida3.OA.2.5Apply 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
Florida3.OA.2.6Understand division as an unknown-factor problem. For example, find 32  8 by finding the number that makes 32 when multiplied by 8.Grade 3
Florida3.OA.3.7Fluently 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
Florida4.G.1.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Grade 4
Florida4.G.1.2Classify 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
Florida4.MD.1.1Know 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
Florida4.MD.1.2Use 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
Florida4.MD.2.4Make 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
Florida4.MD.3.5Recognize 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
Florida4.MD.3.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Grade 4
Florida4.MD.3.7Recognize 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
Florida4.NBT.1.1Recognize 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
Florida4.NBT.1.2Read 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
Florida4.NBT.1.3Use place value understanding to round multi-digit whole numbers to any place.Grade 4
Florida4.NBT.2.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.Grade 4
Florida4.NBT.2.5Multiply 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
Florida4.NBT.2.6Find 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
Florida4.NF.1.1Explain 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
Florida4.NF.1.2Compare 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 >, =, orGrade 4
Florida4.NF.2.3Understand 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
Florida4.NF.2.4Apply 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
Florida4.NF.3.5Express 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
Florida4.NF.3.6Use 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
Florida4.NF.3.7Compare 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 >, =, orGrade 4
Florida4.OA.1.1Interpret 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
Florida4.OA.1.2Multiply 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
Florida4.OA.2.4Investigate 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
Florida4.OA.3.5Generate 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
Florida5.G.1.1Use 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
Florida5.G.1.2Represent 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
Florida5.G.2.3Understand 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
Florida5.G.2.4Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures.Grade 5
Florida5.MD.2.2Make 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
Florida5.NBT.1.1Recognize 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
Florida5.NBT.1.2Explain 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
Florida5.NBT.1.3Read, 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
Florida5.NBT.1.4Use place value understanding to round decimals to any place.Grade 5
Florida5.NBT.2.5Fluently multiply multi-digit whole numbers using the standard algorithm.Grade 5
Florida5.NBT.2.6Find 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
Florida5.NBT.2.7Add, 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
Florida5.NF.2.3Interpret 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
Florida5.NF.2.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Grade 5
Florida5.NF.2.5Interpret 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
Florida5.NF.2.6Solve 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
Florida5.NF.2.7Apply 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
Florida5.OA.1.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Grade 5
Florida5.OA.2.3Generate 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
Florida6.EE.1.1Write and evaluate numerical expressions involving whole-number exponents.Grade 6
Florida6.EE.1.2Write, read, and evaluate expressions in which letters stand for numbers.Grade 6
Florida6.EE.1.3Apply the properties of operations to generate equivalent expressions.Grade 6
Florida6.EE.2.5Understand 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
Florida6.EE.2.7Solve 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
Florida6.EE.2.8Write 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
Florida6.G.1.3Draw 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
Florida6.NS.1.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.Grade 6
Florida6.NS.2.2Fluently divide multi-digit numbers using the standard algorithm.Grade 6
Florida6.NS.2.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Grade 6
Florida6.NS.3.5Understand 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
Florida6.NS.3.6Understand 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
Florida6.NS.3.7Understand ordering and absolute value of rational numbers.Grade 6
Florida6.NS.3.8Solve 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
Florida6.RP.1.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.Grade 6
Florida6.RP.1.2Understand 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
Florida6.RP.1.3Use 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
Florida7.EE.1.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Grade 7
Florida7.EE.2.3Solve 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
Florida7.G.1.1Solve 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
Florida7.G.1.2Draw (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
Florida7.G.2.5Use 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
Florida7.NS.1.1Apply 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
Florida7.NS.1.2Understand 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
Florida7.NS.1.3Solve real-world and mathematical problems involving the four operations with rational numbers.Grade 7
Florida7.RP.1.1Compute 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
Florida7.RP.1.2Recognize and represent proportional relationships between quantities.Grade 7
Florida7.RP.1.3Use proportional relationships to solve multistep ratio and percent problems.Grade 7
Florida8.EE.1.3Use 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
Florida8.EE.1.4Perform 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
Florida8.EE.2.5Graph 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
Florida8.EE.2.6Use 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
Florida8.EE.3.7Give 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
Florida8.EE.3.8Understand 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
Florida8.F.1.1Understand 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
Florida8.F.1.2Compare 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
Florida8.F.1.3Interpret 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
Florida8.F.2.4Construct 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
Florida8.F.2.5Describe 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
Florida8.G.1.1Verify experimentally the properties of rotations, reflections, and translations.Grade 8
Florida8.G.1.2Understand 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
Florida8.G.1.4Understand 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
Florida8.G.2.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Grade 8
Florida8.G.2.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Grade 8
Florida8.SP.1.1Construct 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
Florida8.SP.1.2Know 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
FloridaK.CC.1.1Count to 100 by ones and by tens.Kindergarten
FloridaK.CC.1.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Kindergarten
FloridaK.CC.1.3Read 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
FloridaK.CC.2.4Understand 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
FloridaK.CC.2.5Count 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
FloridaK.CC.3.6Identify 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
FloridaK.CC.3.7Compare two numbers between 1 and 10 presented as written numerals.Kindergarten
FloridaK.NBT.1.1Compose 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
FloridaK.OA.1.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Kindergarten
FloridaK.OA.1.2Solve 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
FloridaK.OA.1.4For 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
FloridaK.OA.1.5Fluently add and subtract within 5.Kindergarten
FloridaK.OA.1.aUse 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
GeorgiaA.APR.B.3Identify 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
GeorgiaA.CED.A.2Create 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
GeorgiaA.SSE.A.2Use the structure of an expression to rewrite it in different equivalent forms.Algebra
GeorgiaA.SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Algebra
GeorgiaF.BF.A.1Write a function that describes a relationship between two quantities.Algebra
GeorgiaF.IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Algebra
GeorgiaF.IF.B.4Using 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
GeorgiaF.IF.C.7Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.Algebra
GeorgiaS.ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Algebra
Georgia1.MD.B.3Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
Georgia1.MD.C.4Organize, 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
Georgia1.NBT.A.1Count 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
Georgia1.NBT.B.2Understand that the two digits of a two-digit number represent amounts of tens and ones.Grade 1
Georgia1.NBT.B.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols.Grade 1
Georgia1.NBT.C.4Add 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
Georgia1.NBT.C.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Grade 1
Georgia1.NBT.C.6Subtract 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
Georgia1.OA.B.4Understand 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
Georgia1.OA.D.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.Grade 1
Georgia1.OA.D.8Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.Grade 1
Georgia2.G.A.1Recognize 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
Georgia2.MD.C.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Grade 2
Georgia2.MD.D.10Draw 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
Georgia2.MD.D.9Generate 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
Georgia2.NBT.A.1Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.Grade 2
Georgia2.NBT.A.2Count within 1000; skip-count by 5s, 10s, and 100s.Grade 2
Georgia2.NBT.A.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Grade 2
Georgia2.NBT.A.4Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, < symbols to record the results of comparisons.Grade 2
Georgia2.NBT.B.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Grade 2
Georgia2.NBT.B.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Grade 2
Georgia2.NBT.B.7Add 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
Georgia2.NBT.B.8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.Grade 2
Georgia2.OA.A.1Use 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
Georgia2.OA.B.2Fluently 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
Georgia3.G.A.1Understand 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
Georgia3.MD.A.1Tell 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
Georgia3.MD.B.3Draw 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
Georgia3.MD.B.4Generate 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
Georgia3.MD.C.5Recognize area as an attribute of plane figures and understand concepts of area measurement.Grade 3
Georgia3.MD.C.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Grade 3
Georgia3.NBT.A.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
Georgia3.NBT.A.2Fluently 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
Georgia3.NBT.A.3Multiply 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
Georgia3.NF.A.1Understand 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
Georgia3.NF.A.2Understand a fraction as a number on the number line; represent fractions on a number line diagram.Grade 3
Georgia3.NF.A.3Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.Grade 3
Georgia3.OA.A.1Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each.Grade 3
Georgia3.OA.A.2Interpret 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
Georgia3.OA.A.3Use 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
Georgia3.OA.A.4Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division.Grade 3
Georgia3.OA.B.5Apply properties of operations as strategies to multiply and divide.Grade 3
Georgia3.OA.B.6Understand division as an unknown-factor problem.Grade 3
Georgia3.OA.C.7Fluently 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
Georgia4.G.A.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Grade 4
Georgia4.G.A.2Classify 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
Georgia4.MD.A.1Know 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
Georgia4.MD.A.2Use 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
Georgia4.MD.B.4Make 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
Georgia4.MD.C.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.Grade 4
Georgia4.MD.C.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Grade 4
Georgia4.MD.C.7Recognize 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
Georgia4.MD.C.8Recognize 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
Georgia4.NBT.A.1Recognize 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
Georgia4.NBT.A.2Read 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
Georgia4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.Grade 4
Georgia4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.Grade 4
Georgia4.NBT.B.5Multiply 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
Georgia4.NBT.B.6Find 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
Georgia4.NF.A.1Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b).Grade 4
Georgia4.NF.A.2Compare 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 >, =, orGrade 4
Georgia4.NF.B.3Understand a fraction a/b with a > 1 as a sum of fractions 1/b.Grade 4
Georgia4.NF.B.4Apply 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
Georgia4.NF.C.5Express 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
Georgia4.NF.C.6Use decimal notation for fractions with denominators 10 or 100.Grade 4
Georgia4.NF.C.7Compare 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 >, =, orGrade 4
Georgia4.OA.A.1Understand that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity.Grade 4
Georgia4.OA.A.2Multiply 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
Georgia4.OA.B.4Find 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
Georgia4.OA.C.5Generate 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
Georgia5.G.A.1Use 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
Georgia5.G.A.2Represent 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
Georgia5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Grade 5
Georgia5.G.B.4Classify two-dimensional figures in a hierarchy based on properties.Grade 5
Georgia5.MD.B.2Make 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
Georgia5.NBT.A.1Recognize 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
Georgia5.NBT.A.2Explain 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
Georgia5.NBT.A.4Use place value understanding to round decimals up to the hundredths place.Grade 5
Georgia5.NBT.B.5Fluently 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
Georgia5.NBT.B.6Fluently 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
Georgia5.NBT.B.7Add, 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
Georgia5.NF.B.3Interpret 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
Georgia5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Grade 5
Georgia5.NF.B.5Interpret multiplication as scaling (resizing).Grade 5
Georgia5.NF.B.6Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.Grade 5
Georgia5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Grade 5
Georgia5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Grade 5
Georgia5.OA.B.3Generate 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
Georgia6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.Grade 6
Georgia6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.Grade 6
Georgia6.EE.A.3Apply the properties of operations to generate equivalent expressions.Grade 6
Georgia6.EE.B.5Understand 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
Georgia6.EE.B.7Solve 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
Georgia6.EE.B.8Write 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
Georgia6.G.A.3Draw 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
Georgia6.NS.A.1Interpret 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
Georgia6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.Grade 6
Georgia6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Grade 6
Georgia6.NS.C.5Understand 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
Georgia6.NS.C.6Understand 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
Georgia6.NS.C.7Understand ordering and absolute value of rational numbers.Grade 6
Georgia6.NS.C.8Solve 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
Georgia6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.Grade 6
Georgia6.RP.A.2Understand 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
Georgia6.RP.A.3Use 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
Georgia7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Grade 7
Georgia7.EE.B.3Solve 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
Georgia7.G.A.1Solve 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
Georgia7.G.A.2Explore 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
Georgia7.G.B.5Use 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
Georgia7.NS.A.1Apply 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
Georgia7.NS.A.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.Grade 7
Georgia7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.Grade 7
Georgia7.RP.A.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.Grade 7
Georgia7.RP.A.2Recognize and represent proportional relationships between quantities.Grade 7
Georgia7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems.Grade 7
Georgia8.EE.A.3Use 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
Georgia8.EE.A.4Add, 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
Georgia8.EE.B.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.Grade 8
Georgia8.EE.B.6Use 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
Georgia8.EE.C.7Give examples of linear equations in one variable.Grade 8
Georgia8.EE.C.8Analyze and solve pairs of simultaneous linear equations (systems of linear equations).Grade 8
Georgia8.F.A.1Understand 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
Georgia8.F.A.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Grade 8
Georgia8.F.A.3Interpret 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
Georgia8.F.B.4Construct 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
Georgia8.F.B.5Describe 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
Georgia8.G.A.1Verify 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
Georgia8.G.A.2Understand 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
Georgia8.G.A.4Understand 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
Georgia8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Grade 8
Georgia8.G.B.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Grade 8
Georgia8.SP.A.1Construct 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
Georgia8.SP.A.2Know 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
GeorgiaK.CC.A.1Count to 100 by ones and by tens.Kindergarten
GeorgiaK.CC.A.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Kindergarten
GeorgiaK.CC.A.3Write 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
GeorgiaK.CC.B.4Understand the relationship between numbers and quantities.Kindergarten
GeorgiaK.CC.B.5Count to answer ïhow many?î questions.Kindergarten
GeorgiaK.CC.C.6Identify 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
GeorgiaK.CC.C.7Compare two numbers between 1 and 10 presented as written numerals.Kindergarten
GeorgiaK.NBT.A.1Compose 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
GeorgiaK.OA.A.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Kindergarten
GeorgiaK.OA.A.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.Kindergarten
GeorgiaK.OA.A.3Decompose 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
GeorgiaK.OA.A.4For 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
GeorgiaK.OA.A.5Fluently add and subtract within 5.Kindergarten
IllinoisK.CC.A.1Count to 100 by ones and by tens.Kindergarten
IllinoisK.CC.A.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Kindergarten
IllinoisK.CC.A.3Write 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
IllinoisK.CC.B.4Understand the relationship between numbers and quantities; connect counting to cardinality.Kindergarten
IllinoisK.CC.B.5Count 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
IllinoisK.CC.C.6Identify 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
IllinoisK.CC.C.7Compare two numbers between 1 and 10 presented as written numerals.Kindergarten
IllinoisK.G.A.1Describe 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
IllinoisK.G.A.2Correctly name shapes regardless of their orientations or overall size.Kindergarten
IllinoisK.G.A.3Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).Kindergarten
IllinoisK.G.B.4Analyze 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
IllinoisK.G.B.5Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.Kindergarten
IllinoisK.G.B.6Compose simple shapes to form larger shapes.Kindergarten
IllinoisK.MD.A.1Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.Kindergarten
IllinoisK.MD.A.2Directly 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
IllinoisK.MD.B.3Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.Kindergarten
IllinoisK.NBT.A.1Compose 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
IllinoisK.OA.A.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Kindergarten
IllinoisK.OA.A.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.Kindergarten
IllinoisK.OA.A.3Decompose 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
IllinoisK.OA.A.4For 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
IllinoisK.OA.A.5Fluently add and subtract within 5.Kindergarten
Illinois1.G.A.1Distinguish 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
Illinois1.G.A.2Compose 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
Illinois1.G.A.3Partition 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
Illinois1.MD.A.1Order three objects by length; compare the lengths of two objects indirectly by using a third object.Grade 1
Illinois1.MD.A.2Express 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
Illinois1.MD.B.3Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
Illinois1.MD.C.4Organize, 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
Illinois1.NBT.A.1Count 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
Illinois1.NBT.B.2Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:Grade 1
Illinois1.NBT.B.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.Grade 1
Illinois1.NBT.C.4Add 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
Illinois1.NBT.C.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Grade 1
Illinois1.NBT.C.6Subtract 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
Illinois1.OA.A.1Use 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
Illinois1.OA.A.2Solve 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
Illinois1.OA.C.6Add 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
Illinois1.OA.D.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.Grade 1
Illinois1.OA.D.8Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.Grade 1
Illinois2.G.A.1Recognize 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
Illinois2.G.A.2Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.Grade 2
Illinois2.G.A.3Partition 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
Illinois2.MD.A.1Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.Grade 2
Illinois2.MD.A.2Measure 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
Illinois2.MD.A.3Estimate lengths using units of inches, feet, centimeters, and meters.Grade 2
Illinois2.MD.A.4Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.Grade 2
Illinois2.MD.B.5Use 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
Illinois2.MD.B.6Represent 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
Illinois2.MD.C.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Grade 2
Illinois2.MD.C.8Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately.Grade 2
Illinois2.MD.D.9Generate 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
Illinois2.MD.D.10Draw 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
Illinois2.NBT.A.1Understand 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
Illinois2.NBT.A.2Count within 1000; skip-count by 5s, 10s, and 100s.Grade 2
Illinois2.NBT.A.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Grade 2
Illinois2.NBT.A.4Compare 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
Illinois2.NBT.B.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Grade 2
Illinois2.NBT.B.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Grade 2
Illinois2.NBT.B.7Add 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
Illinois2.NBT.B.8Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.Grade 2
Illinois2.NBT.B.9Explain why addition and subtraction strategies work, using place value and the properties of operations.Grade 2
Illinois2.OA.A.1Use 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
Illinois2.OA.B.2Fluently 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
Illinois2.OA.C.3Determine 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
Illinois2.OA.C.4Use 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
Illinois3.G.A.1Understand 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
Illinois3.G.A.2Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.Grade 3
Illinois3.MD.A.1Tell 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
Illinois3.MD.A.2Measure 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
Illinois3.MD.B.3Draw 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
Illinois3.MD.B.4Generate 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
Illinois3.MD.C.5Recognize area as an attribute of plane figures and understand concepts of area measurement.Grade 3
Illinois3.MD.C.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Grade 3
Illinois3.MD.D.8Solve 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
Illinois3.NBT.A.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
Illinois3.NBT.A.2Fluently 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
Illinois3.NBT.A.3Multiply 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
Illinois3.NF.A.1Understand 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
Illinois3.NF.A.2Understand a fraction as a number on the number line; represent fractions on a number line diagram.Grade 3
Illinois3.NF.A.3Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.Grade 3
Illinois3.OA.A.1Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.Grade 3
Illinois3.OA.A.2Interpret 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
Illinois3.OA.A.3Use 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
Illinois3.OA.A.4Determine the unknown whole number in a multiplication or division equation relating three whole numbers.Grade 3
Illinois3.OA.B.5Apply properties of operations as strategies to multiply and divide.Grade 3
Illinois3.OA.B.6Understand division as an unknown-factor problem.Grade 3
Illinois3.OA.C.7Fluently 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
Illinois3.OA.D.8Solve 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
Illinois3.OA.D.9Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.Grade 3
Illinois4.G.A.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Grade 4
Illinois4.G.A.2Classify 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
Illinois4.G.A.3Recognize 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
Illinois4.MD.A.1Know 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
Illinois4.MD.A.2Use 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
Illinois4.MD.A.3Apply the area and perimeter formulas for rectangles in real world and mathematical problems.Grade 4
Illinois4.MD.B.4Make 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
Illinois4.MD.C.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:Grade 4
Illinois4.MD.C.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Grade 4
Illinois4.MD.C.7Recognize 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
Illinois4.NBT.A.1Recognize 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
Illinois4.NBT.A.2Read 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
Illinois4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.Grade 4
Illinois4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.Grade 4
Illinois4.NBT.B.5Multiply 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
Illinois4.NBT.B.6Find 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
Illinois4.NF.A.1Explain 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
Illinois4.NF.A.2Compare 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
Illinois4.NF.B.3Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣.Grade 4
Illinois4.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.Grade 4
Illinois4.NF.C.5Express 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
Illinois4.NF.C.6Use decimal notation for fractions with denominators 10 or 100.Grade 4
Illinois4.NF.C.7Compare 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
Illinois4.OA.A.1Interpret 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
Illinois4.OA.A.2Multiply 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
Illinois4.OA.A.3Solve 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
Illinois4.OA.B.4Find 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
Illinois4.OA.C.5Generate 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
Illinois5.G.A.1Use 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
Illinois5.G.A.2Represent 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
Illinois5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Grade 5
Illinois5.G.B.4Classify two-dimensional figures in a hierarchy based on properties.Grade 5
Illinois5.MD.A.1Convert 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
Illinois5.MD.B.2Make 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
Illinois5.MD.C.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement.Grade 5
Illinois5.MD.C.4Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.Grade 5
Illinois5.MD.C.5Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.Grade 5
Illinois5.NBT.A.1Recognize 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
Illinois5.NBT.A.2Explain 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
Illinois5.NBT.A.4Use place value understanding to round decimals to any place.Grade 5
Illinois5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm.Grade 5
Illinois5.NBT.B.6Find 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
Illinois5.NBT.B.7Add, 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
Illinois5.NF.A.1Add 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
Illinois5.NF.A.2Solve 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
Illinois5.NF.B.3Interpret 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
Illinois5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Grade 5
Illinois5.NF.B.5Interpret multiplication as scaling (resizing), by:Grade 5
Illinois5.NF.B.6Solve 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
Illinois5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Grade 5
Illinois5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Grade 5
Illinois5.OA.A.2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.Grade 5
Illinois5.OA.B.3Generate 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
Illinois6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.Grade 6
Illinois6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.Grade 6
Illinois6.EE.A.3Apply the properties of operations to generate equivalent expressions.Grade 6
Illinois6.EE.A.4Identify 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
Illinois6.EE.B.5Understand 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
Illinois6.EE.B.6Use 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
Illinois6.EE.B.7Solve 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
Illinois6.EE.B.8Write 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
Illinois6.EE.C.9Use 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
Illinois6.G.A.1Find 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
Illinois6.G.A.2Find 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
Illinois6.G.A.3Draw 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
Illinois6.G.A.4Represent 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
Illinois6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.Grade 6
Illinois6.RP.A.2Understand 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
Illinois6.RP.A.3Use 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
Illinois6.SP.A.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.Grade 6
Illinois6.SP.A.2Understand 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
Illinois6.SP.A.3Recognize 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
Illinois6.SP.B.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.Grade 6
Illinois6.SP.B.5Summarize numerical data sets in relation to their context, such as by:Grade 6
Illinois6.NS.A.1Interpret 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
Illinois6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.Grade 6
Illinois6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Grade 6
Illinois6.NS.B.4Find 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
Illinois6.NS.C.5Understand 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
Illinois6.NS.C.6Understand 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
Illinois6.NS.C.7Understand ordering and absolute value of rational numbers.Grade 6
Illinois6.NS.C.8Solve 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
Illinois7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Grade 7
Illinois7.EE.A.2Understand 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
Illinois7.EE.B.3Solve 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
Illinois7.EE.B.4Use 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
Illinois7.G.A.1Solve 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
Illinois7.G.A.2Draw (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
Illinois7.G.A.3Describe 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
Illinois7.G.B.4Know 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
Illinois7.G.B.5Use 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
Illinois7.G.B.6Solve 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
Illinois7.RP.A.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.Grade 7
Illinois7.RP.A.2Recognize and represent proportional relationships between quantities.Grade 7
Illinois7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems.Grade 7
Illinois7.SP.A.1Understand 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
Illinois7.SP.A.2Use 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
Illinois7.SP.B.3Informally 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
Illinois7.SP.B.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.Grade 7
Illinois7.SP.C.5Understand 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
Illinois7.SP.C.6Approximate 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
Illinois7.SP.C.7Develop 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
Illinois7.SP.C.8Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.Grade 7
Illinois7.NS.A.1Apply 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
Illinois7.NS.A.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.Grade 7
Illinois7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.Grade 7
Illinois8.EE.A.1Know and apply the properties of integer exponents to generate equivalent numerical expressions.Grade 8
Illinois8.EE.A.2Use 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
Illinois8.EE.A.3Use 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
Illinois8.EE.A.4Perform 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
Illinois8.EE.B.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.Grade 8
Illinois8.EE.B.6Use 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
Illinois8.EE.C.7Solve linear equations in one variable.Grade 8
Illinois8.EE.C.8Analyze and solve pairs of simultaneous linear equations.Grade 8
Illinois8.F.A.1Understand 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
Illinois8.F.A.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Grade 8
Illinois8.F.A.3Interpret 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
Illinois8.F.B.4Construct 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
Illinois8.F.B.5Describe 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
Illinois8.G.A.1Verify experimentally the properties of rotations, reflections, and translations:Grade 8
Illinois8.G.A.2Understand 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
Illinois8.G.A.3Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.Grade 8
Illinois8.G.A.4Understand 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
Illinois8.G.A.5Use 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
Illinois8.G.B.6Explain a proof of the Pythagorean Theorem and its converse.Grade 8
Illinois8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Grade 8
Illinois8.G.B.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Grade 8
Illinois8.G.C.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.Grade 8
Illinois8.SP.A.1Construct 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
Illinois8.SP.A.2Know 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
Illinois8.SP.A.3Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.Grade 8
Illinois8.SP.A.4Understand 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
Illinois8.NS.A.1Know 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
Illinois8.NS.A.2Use 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
IllinoisHSN-Q.A.1Use 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
IllinoisHSN-Q.A.2Define appropriate quantities for the purpose of descriptive modeling.High School - Number and Quantity
IllinoisHSN-Q.A.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.High School - Number and Quantity
IllinoisHSN-CN.A.1Know 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
IllinoisHSN-CN.A.2Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.High School - Number and Quantity
IllinoisHSN-CN.A.3Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.High School - Number and Quantity
IllinoisHSN-CN.B.4Represent 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
IllinoisHSN-CN.B.5Represent 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
IllinoisHSN-CN.B.6Calculate 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
IllinoisHSN-CN.C.7Solve quadratic equations with real coefficients that have complex solutions.High School - Number and Quantity
IllinoisHSN-CN.C.8Extend polynomial identities to the complex numbers.High School - Number and Quantity
IllinoisHSN-CN.C.9Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.High School - Number and Quantity
IllinoisHSN-RN.A.1Explain 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
IllinoisHSN-RN.A.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.High School - Number and Quantity
IllinoisHSN-RN.B.3Explain 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
IllinoisHSN-VM.A.1Recognize 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
IllinoisHSN-VM.A.2Find 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
IllinoisHSN-VM.A.3Solve problems involving velocity and other quantities that can be represented by vectors.High School - Number and Quantity
IllinoisHSN-VM.B.4Add and subtract vectors.High School - Number and Quantity
IllinoisHSN-VM.B.5Multiply a vector by a scalar.High School - Number and Quantity
IllinoisHSN-VM.C.6Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.High School - Number and Quantity
IllinoisHSN-VM.C.7Multiply 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
IllinoisHSN-VM.C.8Add, subtract, and multiply matrices of appropriate dimensions.High School - Number and Quantity
IllinoisHSN-VM.C.9Understand 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
IllinoisHSN-VM.C.10Understand 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
IllinoisHSN-VM.C.11Multiply 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
IllinoisHSN-VM.C.12Work 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
IllinoisHSA-APR.A.1Understand 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
IllinoisHSA-APR.B.2Know 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
IllinoisHSA-APR.B.3Identify 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
IllinoisHSA-APR.C.4Prove polynomial identities and use them to describe numerical relationships.High School - Algebra
IllinoisHSA-APR.C.5Know 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
IllinoisHSA-APR.D.6Rewrite 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
IllinoisHSA-APR.D.7Understand 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
IllinoisHSA-CED.A.1Create equations and inequalities in one variable and use them to solve problems.High School - Algebra
IllinoisHSA-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.High School - Algebra
IllinoisHSA-CED.A.3Represent 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
IllinoisHSA-CED.A.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.High School - Algebra
IllinoisHSA-REI.A.1Explain 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
IllinoisHSA-REI.A.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.High School - Algebra
IllinoisHSA-REI.B.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.High School - Algebra
IllinoisHSA-REI.B.4Solve quadratic equations in one variable.High School - Algebra
IllinoisHSA-REI.C.5Prove 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
IllinoisHSA-REI.C.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.High School - Algebra
IllinoisHSA-REI.C.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.High School - Algebra
IllinoisHSA-REI.C.8Represent a system of linear equations as a single matrix equation in a vector variable.High School - Algebra
IllinoisHSA-REI.C.9Find 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
IllinoisHSA-REI.D.10Understand 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
IllinoisHSA-REI.D.11Explain 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
IllinoisHSA-REI.D.12Graph 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
IllinoisHSA-SSE.A.1Interpret expressions that represent a quantity in terms of its context.High School - Algebra
IllinoisHSA-SSE.A.2Use the structure of an expression to identify ways to rewrite it.High School - Algebra
IllinoisHSA-SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.High School - Algebra
IllinoisHSA-SSE.B.4Derive 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
IllinoisHSF-BF.A.1Write a function that describes a relationship between two quantities.High School - Functions
IllinoisHSF-BF.A.2Write 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
IllinoisHSF-BF.B.3Identify 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
IllinoisHSF-BF.B.4Find inverse functions.High School - Functions
IllinoisHSF-BF.B.5Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.High School - Functions
IllinoisHSF-IF.A.1Understand 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
IllinoisHSF-IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.High School - Functions
IllinoisHSF-IF.A.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.High School - Functions
IllinoisHSF-IF.B.4For 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
IllinoisHSF-IF.B.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.High School - Functions
IllinoisHSF-IF.B.6Calculate 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
IllinoisHSF-IF.C.7Graph 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
IllinoisHSF-IF.C.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.High School - Functions
IllinoisHSF-IF.C.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).High School - Functions
IllinoisHSF-LE.A.1Distinguish between situations that can be modeled with linear functions and with exponential functions.High School - Functions
IllinoisHSF-LE.A.2Construct 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
IllinoisHSF-LE.A.3Observe 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
IllinoisHSF-LE.A.4For 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
IllinoisHSF-LE.B.5Interpret the parameters in a linear or exponential function in terms of a context.High School - Functions
IllinoisHSF-TF.A.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.High School - Functions
IllinoisHSF-TF.A.2Explain 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
IllinoisHSF-TF.A.3Use 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
IllinoisHSF-TF.A.4Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.High School - Functions
IllinoisHSF-TF.B.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.High School - Functions
IllinoisHSF-TF.B.6Understand 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
IllinoisHSF-TF.B.7Use 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
IllinoisHSF-TF.C.8Prove 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
IllinoisHSF-TF.C.9Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.High School - Functions
IllinoisHSG-C.A.1Prove that all circles are similar.High School - Geometry
IllinoisHSG-C.A.2Identify and describe relationships among inscribed angles, radii, and chords.High School - Geometry
IllinoisHSG-C.A.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.High School - Geometry
IllinoisHSG-C.A.4Construct a tangent line from a point outside a given circle to the circle.High School - Geometry
IllinoisHSG-C.B.5Derive 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
IllinoisHSG-CO.A.1Know 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
IllinoisHSG-CO.A.2Represent 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
IllinoisHSG-CO.A.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.High School - Geometry
IllinoisHSG-CO.A.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.High School - Geometry
IllinoisHSG-CO.A.5Given 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
IllinoisHSG-CO.B.6Use 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
IllinoisHSG-CO.B.7Use 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
IllinoisHSG-CO.B.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.High School - Geometry
IllinoisHSG-CO.C.9Prove theorems about lines and angles.High School - Geometry
IllinoisHSG-CO.C.10Prove theorems about triangles.High School - Geometry
IllinoisHSG-CO.C.11Prove theorems about parallelograms.High School - Geometry
IllinoisHSG-CO.D.12Make 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
IllinoisHSG-CO.D.13Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.High School - Geometry
IllinoisHSG-GPE.A.1Derive 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
IllinoisHSG-GPE.A.2Derive the equation of a parabola given a focus and directrix.High School - Geometry
IllinoisHSG-GPE.A.3Derive 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
IllinoisHSG-GPE.B.4Use coordinates to prove simple geometric theorems algebraically.High School - Geometry
IllinoisHSG-GPE.B.5Prove 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
IllinoisHSG-GPE.B.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.High School - Geometry
IllinoisHSG-GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.High School - Geometry
IllinoisHSG-GMD.A.1Give 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
IllinoisHSG-GMD.A.2Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.High School - Geometry
IllinoisHSG-GMD.A.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.High School - Geometry
IllinoisHSG-GMD.B.4Identify 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
IllinoisHSG-MG.A.1Use 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
IllinoisHSG-MG.A.2Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).High School - Geometry
IllinoisHSG-MG.A.3Apply 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
IllinoisHSG-SRT.A.1Verify experimentally the properties of dilations given by a center and a scale factor:High School - Geometry
IllinoisHSG-SRT.A.2Given 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
IllinoisHSG-SRT.A.3Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.High School - Geometry
IllinoisHSG-SRT.B.4Prove theorems about triangles.High School - Geometry
IllinoisHSG-SRT.B.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.High School - Geometry
IllinoisHSG-SRT.C.6Understand 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
IllinoisHSG-SRT.C.7Explain and use the relationship between the sine and cosine of complementary angles.High School - Geometry
IllinoisHSG-SRT.C.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.High School - Geometry
IllinoisHSG-SRT.D.9Derive 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
IllinoisHSG-SRT.D.10Prove the Laws of Sines and Cosines and use them to solve problems.High School - Geometry
IllinoisHSG-SRT.D.11Understand 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
IllinoisHSS-CP.A.1Describe 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
IllinoisHSS-CP.A.2Understand 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
IllinoisHSS-CP.A.3Understand 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
IllinoisHSS-CP.A.4Construct 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
IllinoisHSS-CP.A.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.High School - Statistics and Probability
IllinoisHSS-CP.B.6Find 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
IllinoisHSS-CP.B.7Apply 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
IllinoisHSS-CP.B.8Apply 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
IllinoisHSS-CP.B.9Use permutations and combinations to compute probabilities of compound events and solve problems.High School - Statistics and Probability
IllinoisHSS-ID.A.1Represent data with plots on the real number line (dot plots, histograms, and box plots).High School - Statistics and Probability
IllinoisHSS-ID.A.2Use 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
IllinoisHSS-ID.A.3Interpret 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
IllinoisHSS-ID.A.4Use 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
IllinoisHSS-ID.B.5Summarize 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
IllinoisHSS-ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.High School - Statistics and Probability
IllinoisHSS-ID.C.7Interpret 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
IllinoisHSS-ID.C.8Compute (using technology) and interpret the correlation coefficient of a linear fit.High School - Statistics and Probability
IllinoisHSS-ID.C.9Distinguish between correlation and causation.High School - Statistics and Probability
IllinoisHSS-IC.A.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.High School - Statistics and Probability
IllinoisHSS-IC.A.2Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.High School - Statistics and Probability
IllinoisHSS-IC.B.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.High School - Statistics and Probability
IllinoisHSS-IC.B.4Use 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
IllinoisHSS-IC.B.5Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.High School - Statistics and Probability
IllinoisHSS-IC.B.6Evaluate reports based on data.High School - Statistics and Probability
IllinoisHSS-MD.A.1Define 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
IllinoisHSS-MD.A.2Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.High School - Statistics and Probability
IllinoisHSS-MD.A.3Develop 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
IllinoisHSS-MD.A.4Develop 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
IllinoisHSS-MD.B.5Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.High School - Statistics and Probability
IllinoisHSS-MD.B.6Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).High School - Statistics and Probability
IllinoisHSS-MD.B.7Analyze 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
IndianaAI.DS.2Graph bivariate data on a scatter plot and describe the relationship between the variables.Algebra
IndianaAI.DS.3Use 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
IndianaAI.F.2Describe 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
IndianaAI.F.4Understand 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
IndianaAI.QE.3Graph exponential and quadratic equations in two variables with and without technology.Algebra
IndianaAI.QE.5Represent 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
IndianaAI.QE.7Describe 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
IndianaAI.RNE.6Factor common terms from polynomials and factor polynomials completely. Factor the difference of two squares, perfect square trinomials, and other quadratic expressions.Algebra
IndianaAI.SEI.3Write 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
IndianaAII.CNE.4Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques).Algebra II
IndianaAII.DSP.2Use 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
IndianaAII.EL.2Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, and asymptotic and end behavior.Algebra II
IndianaAII.EL.4Use 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
IndianaAII.EL.7Represent 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
IndianaAII.F.2Understand composition of functions and combine functions by composition.Algebra II
IndianaAII.PR.2Graph 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
IndianaAII.Q.2Use 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
Indiana1.CA.1Demonstrate 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
Indiana1.CA.5Add 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
Indiana1.CA.6Understand 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
Indiana1.DA.1Organize 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
Indiana1.M.2Tell 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
Indiana1.NS.1Count 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
Indiana1.NS.2Understand 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
Indiana1.NS.4Use 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
Indiana1.NS.5Find 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
Indiana2.CA.2Solve 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
Indiana2.DA.1Draw 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
Indiana2.G.1Identify, 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
Indiana2.G.2Create squares, rectangles, triangles, cubes, and right rectangular prisms using appropriate materials.Grade 2
Indiana2.M.2Estimate 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
Indiana2.M.5Tell 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
Indiana2.NS.1Count by ones, twos, fives, tens, and hundreds up to at least 1,000 from any given number.Grade 2
Indiana2.NS.2Read 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
Indiana2.NS.6Understand 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
Indiana2.NS.7Use 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
Indiana3.AT.1Solve 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
Indiana3.AT.2Solve 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
Indiana3.AT.4Interpret 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
Indiana3.AT.5Determine the unknown whole number in a multiplication or division equation relating three whole numbers.Grade 3
Indiana3.C.3Represent 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
Indiana3.C.4Interpret 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
Indiana3.C.5Multiply 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
Indiana3.DA.1Create 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
Indiana3.DA.2Generate 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
Indiana3.G.2Understand 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
Indiana3.M.3Tell 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
Indiana3.M.5Find 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
Indiana3.M.6Multiply 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
Indiana3.NS.3Understand 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
Indiana3.NS.4Represent 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
Indiana3.NS.5Represent 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
Indiana3.NS.6Understand 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
Indiana3.NS.7Recognize 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
Indiana3.NS.8Compare 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 >, =, orGrade 3
Indiana3.NS.9Use place value understanding to round 2- and 3-digit whole numbers to the nearest 10 or 100.Grade 3
Indiana4.AT.3Interpret 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
Indiana4.AT.4Solve 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
Indiana4.AT.5Solve 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
Indiana4.AT.6Understand 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
Indiana4.C.1Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach.Grade 4
Indiana4.C.2Multiply 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
Indiana4.C.3Find 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
Indiana4.C.5Add 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
Indiana4.C.6Add 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
Indiana4.DA.2Make 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
Indiana4.G.4Identify, 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
Indiana4.G.5Classify 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
Indiana4.M.2Know 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
Indiana4.M.3Use 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
Indiana4.M.4Apply 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
Indiana4.M.5Understand 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
Indiana4.M.6Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure.Grade 4
Indiana4.NS.1Read 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
Indiana4.NS.2Compare two whole numbers up to 1,000,000 using >, =, and < symbols.Grade 4
Indiana4.NS.3Express 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
Indiana4.NS.4Explain 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
Indiana4.NS.5Compare 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 >, =, orGrade 4
Indiana4.NS.6Write 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
Indiana4.NS.7Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, orGrade 4
Indiana4.NS.8Find 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
Indiana4.NS.9Use place value understanding to round multi-digit whole numbers to any given place value.Grade 4
Indiana5.AT.3Solve 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
Indiana5.AT.4Solve 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
Indiana5.AT.6Graph 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
Indiana5.AT.7Represent 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
Indiana5.C.1Multiply multi-digit whole numbers fluently using a standard algorithmic approach.Grade 5
Indiana5.C.2Find 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
Indiana5.C.3Compare 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
Indiana5.C.5Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.Grade 5
Indiana5.C.6Explain 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
Indiana5.C.7Use 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
Indiana5.C.8Add, 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
Indiana5.G.2Identify 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
Indiana5.M.2Find 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
Indiana5.NS.1Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols.Grade 5
Indiana5.NS.2Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.Grade 5
Indiana5.NS.3Recognize 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
Indiana5.NS.4Explain 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
Indiana5.NS.5Use place value understanding to round decimal numbers up to thousandths to any given place value.Grade 5
Indiana5.NS.6Understand, interpret, and model percents as part of a hundred (e.g. by using pictures, diagrams, and other visual models).Grade 5
Indiana6.AF.1Evaluate 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
Indiana6.AF.2Apply 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
Indiana6.AF.3Define and use multiple variables when writing expressions to represent real-world and other mathematical problems, and evaluate them for given values.Grade 6
Indiana6.AF.4Understand 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
Indiana6.AF.5Solve 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
Indiana6.AF.6Write 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
Indiana6.AF.7Understand 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
Indiana6.AF.8Solve 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
Indiana6.AF.9Make 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
Indiana6.C.1Divide multi-digit whole numbers fluently using a standard algorithmic approach.Grade 6
Indiana6.C.2Compute with positive fractions and positive decimals fluently using a standard algorithmic approach.Grade 6
Indiana6.C.4Compute 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
Indiana6.C.6Apply 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
Indiana6.GM.1Convert between measurement systems (English to metric and metric to English) given conversion factors, and use these conversions in solving real-world problems.Grade 6
Indiana6.GM.3Draw 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
Indiana6.NS.1Understand 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
Indiana6.NS.10Use 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
Indiana6.NS.2Understand 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
Indiana6.NS.3Compare 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
Indiana6.NS.4Understand 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
Indiana6.NS.8Interpret, 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
Indiana6.NS.9Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship.Grade 6
Indiana7.AF.1Apply 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
Indiana7.AF.6Decide 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
Indiana7.AF.7Identify the unit rate or constant of proportionality in tables, graphs, equations, and verbal descriptions of proportional relationships.Grade 7
Indiana7.AF.8Explain 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
Indiana7.AF.9Identify 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
Indiana7.C.1Understand 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
Indiana7.C.2Understand 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
Indiana7.C.3Understand 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
Indiana7.C.4Understand 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
Indiana7.C.5Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.Grade 7
Indiana7.C.6Use 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
Indiana7.C.7Compute with rational numbers fluently using a standard algorithmic approach.Grade 7
Indiana7.C.8Solve real-world problems with rational numbers by using one or two operations.Grade 7
Indiana7.GM.1Draw 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
Indiana7.GM.3Solve 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
Indiana7.GM.4Solve real-world and other mathematical problems that involve vertical, adjacent, complementary, and supplementary angles.Grade 7
Indiana8.AF.1Solve 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
Indiana8.AF.2Give 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
Indiana8.AF.3Understand 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
Indiana8.AF.4Describe 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
Indiana8.AF.5Interpret 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
Indiana8.AF.6Construct 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
Indiana8.AF.7Compare 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
Indiana8.AF.8Understand 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
Indiana8.C.2Solve 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
Indiana8.DSP.1Construct 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
Indiana8.DSP.2Know 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
Indiana8.GM.3Verify 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
Indiana8.GM.4Understand 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
Indiana8.GM.5Understand 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
Indiana8.GM.8Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and other mathematical problems in two dimensions.Grade 8
Indiana8.GM.9Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.Grade 8
Indiana8.NS.1Give 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
IndianaK.CA.1Use objects, drawings, mental images, sounds, etc., to represent addition and subtraction within 10.Kindergarten
IndianaK.CA.2Solve real-world problems that involve addition and subtraction within 10 (e.g., by using objects or drawings to represent the problem).Kindergarten
IndianaK.CA.3Use 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
IndianaK.CA.4Find 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
IndianaK.NS.1Count to at least 100 by ones and tens and count on by one from any number.Kindergarten
IndianaK.NS.2Write 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
IndianaK.NS.4Say 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
IndianaK.NS.5Count 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
IndianaK.NS.7Identify 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
IndianaK.NS.8Compare the values of two numbers from 1 to 20 presented as written numerals.Kindergarten
IndianaPC.EL.3Graph 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
IndianaPC.F.1For 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
IndianaPC.F.8Define 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
IndianaPC.QPR.2Graph rational functions with and without technology. Identify and describe features such as intercepts, domain and range, and asymptotic and end behavior.Pre-Calculus
IndianaPS.DA.11Find 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
IndianaTR.PF.2Graph 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
.KansasA-APR.B.3Identify 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
.KansasA-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Algebra
.KansasA-SSE.A.2Use the structure of an expression to identify ways to rewrite it.Algebra
.KansasA-SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Algebra
.KansasF-BF.A.1Write a function that describes a relationship between two quantities.Algebra
.KansasF-IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Algebra
.KansasF-IF.B.4For 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
.KansasF-IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Algebra
.KansasS-ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Algebra
.Kansas1.MD.B.3Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
.Kansas1.MD.C.4Organize, 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
.Kansas1.NBT.A.1Count 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
.Kansas1.NBT.B.2Understand 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
.Kansas1.NBT.B.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols.Grade 1
.Kansas1.NBT.C.4Add 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
.Kansas1.NBT.C.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Grade 1
.Kansas1.NBT.C.6Subtract 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
.Kansas1.OA.B.3Apply 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
.Kansas1.OA.B.4Understand 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
.Kansas1.OA.C.6Add 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
.Kansas1.OA.D.7Understand 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
.Kansas1.OA.D.8Determine 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
.Kansas2.G.A.1Recognize 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
.Kansas2.MD.C.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Grade 2
.Kansas2.MD.D.10Draw 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
.Kansas2.MD.D.9Generate 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
.Kansas2.NBT.A.1Understand 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
.Kansas2.NBT.A.2Count within 1000; skip-count by 5s, 10s, and 100s.Grade 2
.Kansas2.NBT.A.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Grade 2
.Kansas2.NBT.A.4Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons.Grade 2
.Kansas2.NBT.B.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Grade 2
.Kansas2.NBT.B.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Grade 2
.Kansas2.NBT.B.7Add 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
.Kansas2.NBT.B.8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.Grade 2
.Kansas2.OA.A.1Use 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
.Kansas2.OA.B.2Fluently 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
.Kansas3.G.A.1Understand 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
.Kansas3.MD.A.1Tell 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
.Kansas3.MD.B.3Draw 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
.Kansas3.MD.B.4Generate 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
.Kansas3.MD.C.5Recognize area as an attribute of plane figures and understand concepts of area measurement.Grade 3
.Kansas3.MD.C.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Grade 3
.Kansas3.NBT.A.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
.Kansas3.NBT.A.2Fluently 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
.Kansas3.NBT.A.3Multiply 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
.Kansas3.NF.A.1Understand 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
.Kansas3.NF.A.2Understand 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
.Kansas3.NF.A.3Explain 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 >, =, orGrade 3
.Kansas3.OA.A.1Interpret 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
.Kansas3.OA.A.2Interpret 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
.Kansas3.OA.A.3Use 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
.Kansas3.OA.A.4Determine 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
.Kansas3.OA.B.5Apply 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
.Kansas3.OA.B.6Understand division as an unknown-factor problem. For example, find 32  8 by finding the number that makes 32 when multiplied by 8.Grade 3
.Kansas3.OA.C.7Fluently 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
.Kansas4.G.A.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Grade 4
.Kansas4.G.A.2Classify 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
.Kansas4.MD.A.1Know 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
.Kansas4.MD.A.2Use 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
.Kansas4.MD.B.4Make 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
.Kansas4.MD.C.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:Grade 4
.Kansas4.MD.C.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Grade 4
.Kansas4.MD.C.7Recognize 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
.Kansas4.NBT.A.1Recognize 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
.Kansas4.NBT.A.2Read 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
.Kansas4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.Grade 4
.Kansas4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.Grade 4
.Kansas4.NBT.B.5Multiply 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
.Kansas4.NBT.B.6Find 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
.Kansas4.NF.A.1Explain 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
.Kansas4.NF.A.2Compare 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 >, =, orGrade 4
.Kansas4.NF.B.3Understand 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
.Kansas4.NF.B.4Apply 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
.Kansas4.NF.C.5Express 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
.Kansas4.NF.C.6Use 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
.Kansas4.NF.C.7Compare 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 >, =, orGrade 4
.Kansas4.OA.A.1Interpret 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
.Kansas4.OA.A.2Multiply 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
.Kansas4.OA.B.4Find 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
.Kansas4.OA.C.5Generate 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
.Kansas5.G.A.1Use 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
.Kansas5.G.A.2Represent 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
.Kansas5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Grade 5
.Kansas5.G.B.4Classify two-dimensional figures in a hierarchy based on properties.Grade 5
.Kansas5.MD.B.2Make 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
.Kansas5.NBT.A.1Recognize 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
.Kansas5.NBT.A.2Explain 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
.Kansas5.NBT.A.4Use place value understanding to round decimals to any place.Grade 5
.Kansas5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm.Grade 5
.Kansas5.NBT.B.6Find 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
.Kansas5.NBT.B.7Add, 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
.Kansas5.NF.B.3Interpret 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
.Kansas5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Grade 5
.Kansas5.NF.B.5Interpret 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
.Kansas5.NF.B.6Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.Grade 5
.Kansas5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Grade 5
.Kansas5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Grade 5
.Kansas5.OA.B.3Generate 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
.Kansas6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.Grade 6
.Kansas6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.Grade 6
.Kansas6.EE.A.3Apply the properties of operations to generate equivalent expressions.Grade 6
.Kansas6.EE.B.5Understand 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
.Kansas6.EE.B.7Solve 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
.Kansas6.EE.B.8Write 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
.Kansas6.G.A.3Draw 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
.Kansas6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.Grade 6
.Kansas6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.Grade 6
.Kansas6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Grade 6
.Kansas6.NS.C.5Understand 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
.Kansas6.NS.C.6Understand 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
.Kansas6.NS.C.7Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.Grade 6
.Kansas6.NS.C.8Solve 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
.Kansas6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.Grade 6
.Kansas6.RP.A.2Understand 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
.Kansas6.RP.A.3Use 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
.Kansas7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Grade 7
.Kansas7.EE.B.3Solve 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
.Kansas7.G.A.1Solve 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
.Kansas7.G.A.2Draw (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
.Kansas7.G.B.5Use 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
.Kansas7.NS.A.1Describe 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
.Kansas7.NS.A.2Understand 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
.Kansas7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.Grade 7
.Kansas7.RP.A.1Compute 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
.Kansas7.RP.A.2Recognize and represent proportional relationships between quantities.Grade 7
.Kansas7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems.Grade 7
.Kansas8.EE.A.3Use 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
.Kansas8.EE.A.4Perform 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
.Kansas8.EE.B.5Graph 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
.Kansas8.EE.B.6Use 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
.Kansas8.EE.C.7Give 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
.Kansas8.EE.C.8Understand 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
.Kansas8.F.A.1Understand 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
.Kansas8.F.A.2Compare 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
.Kansas8.F.A.3Interpret 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
.Kansas8.F.B.4Construct 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
.Kansas8.F.B.5Describe 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
.Kansas8.G.A.1Verify experimentally the properties of rotations, reflections, and translations:Grade 8
.Kansas8.G.A.2Understand 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
.Kansas8.G.A.4Understand 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
.Kansas8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Grade 8
.Kansas8.G.B.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Grade 8
.Kansas8.SP.A.1Construct 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
.Kansas8.SP.A.2Know 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
.KansasK.CC.A.1Count to 100 by ones and by tensKindergarten
.KansasK.CC.A.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Kindergarten
.KansasK.CC.A.3Write 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
.KansasK.CC.B.4Understand 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
.KansasK.CC.B.5Count 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
.KansasK.CC.C.6Identify 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
.KansasK.CC.C.7Compare two numbers between 1 and 10 presented as written numerals.Kindergarten
.KansasK.NBT.A.1Compose 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
.KansasK.OA.A.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Kindergarten
.KansasK.OA.A.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.Kindergarten
.KansasK.OA.A.3Decompose 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
.KansasK.OA.A.4For 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
Knotion1.MYD.B.3Dicen y escriben la hora en medias horas utilizando relojes anàlogos y digitales.Grade 1
Knotion1.MYD.C.4Organizan, 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
Knotion1.OYPA.B.3Aplican 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
Knotion1.OYPA.B.4Comprenden la resta como un problema de un sumando desconocido.Grade 1
Knotion1.OYPA.C.5Relacionan el conteo con la suma y la resta (por ejemplo, al contar de 2 en 2 para sumar 2).Grade 1
Knotion1.OYPA.C.6Suman 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
Knotion1.OYPA.D.7Entienden 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
Knotion1.OYPA.D.8Determinan 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
Knotion1.SND.A.1Cuentan 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
Knotion1.SND.B.2Entienden 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
Knotion1.SND.B.3Comparan 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
Knotion1.SND.C.4Suman 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
Knotion1.SND.C.5Dado 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
Knotion1.SND.C.6Restan 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
Knotion2.GE.A.1Reconocen 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
Knotion2.MYD.C.7Dicen y escriben la hora utilizando relojes anàlogos y digitales a los cinco minutos màs cercanos, usando a.m. y p.m.Grade 2
Knotion2.MYD.D.10Dibijan 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
Knotion2.MYD.D.9Generan 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
Knotion2.OYPA.A.1Usan 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
Knotion2.OYPA.B.2Suman 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
Knotion2.SND.A.1Comprenden 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
Knotion2.SND.A.2Cuentan hasta 1000; cuentan de 2 en 2, de 5 en 5, de 10 en 10, y de 100 en 100.Grade 2
Knotion2.SND.A.3Leen y escriben nÏmeros hasta 1000 usando numerales en base diez, los nombres de los nÏmeros, y en forma desarrollada.Grade 2
Knotion2.SND.A.4Comparan 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
Knotion2.SND.B.5Suman 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
Knotion2.SND.B.6Suman hasta cuatro nÏmeros de dos dÕgitos usando estrategias basadas en el valor decposiciona y las propiedades de las operaciones.Grade 2
Knotion2.SND.B.7Suman 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
Knotion2.SND.B.8Suman 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
Knotion3.FRA.A.1Comprenden 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
Knotion3.FRA.A.2Entienden 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
Knotion3.FRA.A.3Explican 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 >, = oGrade 3
Knotion3.GE.A.1Comprenden 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
Knotion3.MYD.A.1Dicen 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
Knotion3.MYD.B.3Trazan 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
Knotion3.MYD.C.7Relacionan el àrea con las operaciones de multiplicaciÑn y suma.Grade 3
Knotion3.OYPA.A.1Interpretan 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
Knotion3.OYPA.A.2Interpretan 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
Knotion3.OYPA.A.3Utilizan 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
Knotion3.OYPA.A.4Determinan 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
Knotion3.OYPA.B.5Aplican 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
Knotion3.OYPA.B.6Entender 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
Knotion3.OYPA.C.7Multiplican 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
Knotion3.SND.A.1Utilizan el entendimiento del valor posicional para redondear los nÏmeros enteros hasta la decena (10) o centena (100) màs prÑxima.Grade 3
Knotion3.SND.A.2Suman 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
Knotion3.SND.A.3Multiplican 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
Knotion4.FRA.A.1Explican 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
Knotion4.FRA.A.2Comparan 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 >, = ÑGrade 4
Knotion4.FRA.B.3Entienden 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
Knotion4.FRA.B.4Aplican 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
Knotion4.FRA.C.5Expresan 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
Knotion4.FRA.C.6Utilizan 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
Knotion4.FRA.C.7Comparan 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 >, = ÑGrade 4
Knotion4.GE.A.1Dibujan puntos, rectas, segmentos de rectas, semirrectas, àngulos (rectos, agudos, obtusos), y rectas perpendiculares y paralelas. Identifican estos elementos en las figuras bidimensionales.Grade 4
Knotion4.GE.A.2Clasifican 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
Knotion4.MYD.A.1Reconocen 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
Knotion4.MYD.A.2Utilizan 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
Knotion4.MYD.B.4Hacen 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
Knotion4.MYD.C.5Reconocen 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
Knotion4.MYD.C.7Reconocen 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
Knotion4.OYPA.A.1Interpretan 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
Knotion4.OYPA.A.2Multiplican 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
Knotion4.OYPA.B.4Hallan 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
Knotion4.OYPA.C.5Generan 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
Knotion4.SND.A.1Reconocen 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
Knotion4.SND.A.2Leen 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
Knotion4.SND.A.3Utilizan la comprensiÑn del valor de posiciÑn para redondear nÏmeros enteros con dÕgitos mÏltiples a cualquier lugar.Grade 4
Knotion4.SND.B.4Suman y restan con fluidez los nÏmeros enteros con dÕgitos mÏltiples utilizando el algoritmo convencional.Grade 4
Knotion4.SND.B.5Multiplican 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
Knotion4.SND.B.6Hallan 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
Knotion5.FRA.B.3Interpretan una fracciÑn como la divisiÑn del numerador por el denominador (a/b = ab). 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
Knotion5.FRA.B.5Interpretan 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
Knotion5.FRA.B.6Resuelven 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
Knotion5.FRA.B.7Aplican 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
Knotion5.GE.A.2Representan 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
Knotion5.GE.B.3Entienden 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
Knotion5.GE.B.4Clasifican las figuras bidimensionales dentro de una jerarquÕa, segÏn sus propiedades.Grade 5
Knotion5.MYD.B.2Hacen 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
Knotion5.OYPA.A.1Incorpora sÕmbolos de agrupaciÑn como par_ntesis, corchetes y llaves, para separar operaciones dentro de una expresiÑn y denotar jerarquÕa de resoluciÑn.Grade 5
Knotion5.OYPA.B.3Generan 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
Knotion5.SND.A.1Reconocen 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
Knotion5.SND.A.2Explican 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
Knotion5.SND.A.3Leen, escriben, y comparan decimales hasta las mil_simas.Grade 5
Knotion5.SND.A.4Utilizan el entendimiento del valor de posiciÑn para redondear decimales a cualquier lugar.Grade 5
Knotion5.SND.B.5Multiplican nÏmeros enteros de varios dÕgitos con fluidez, utilizando el algoritmo convencional.Grade 5
Knotion5.SND.B.6Encuentran 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
Knotion6.EXEC.A.1Escriben y evalÏan expresiones num_ricas relacionadas a los exponentes de nÏmeros enteros.Grade 6
Knotion6.EXEC.A.2Escriben, leen y evalÏan expresiones en las cuales las letras representan nÏmeros.Grade 6
Knotion6.EXEC.A.3Aplican 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
Knotion6.EXEC.B.5Entienden 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
Knotion6.EXEC.B.7Resuelven 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
Knotion6.EXEC.B.8Escriben 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
Knotion6.GE.A.3Dibujan 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
Knotion6.RAZ.A.1Relaciona la nociÑn de razÑn con proporciÑn.Grade 6
Knotion6.RAZ.A.2Entienden 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
Knotion6.RAZ.A.3Utilizan 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
Knotion6.SN.A.1Interpretan y calculan cocientes de fracciones, y resuelven problemas verbales relacionados a la divisiÑn de fracciones entre fracciones.Grade 6
Knotion6.SN.B.2Dividen con facilidad nÏmeros de mÏltiples dÕgito utilizando el algoritmo convencional.Grade 6
Knotion6.SN.B.3Suman, restan, multiplican y dividen decimales demÏltiples dÕgitos utilizando el algoritmo convencional para cada operaciÑn, con facilidad.Grade 6
Knotion6.SN.C.5Entienden 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
Knotion6.SN.C.6Entienden 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
Knotion6.SN.C.7Interpretan 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
Knotion6.SN.C.8Resuelven 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
Knotion7.EXEC.A.1Aplican las propiedades de operaciones como estrategias para sumar, restar, factorizar y expander expresiones lineales con coeficientes racionales.Grade 7
Knotion7.GE.A.1Resuelven 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
Knotion7.GE.A.2Dibujan (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
Knotion7.GE.B.5Utilizan 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
Knotion7.RAZ.A.1Calculan 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
Knotion7.RAZ.A.3Utilizan 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
Knotion7.SN.A.1Describen 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
Knotion7.SN.A.2Comprenden 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
Knotion7.SN.A.3Resuelven problemas matemàticos y del mundo real relacionados con las cuatro operaciones con nÏmeros racionales.Grade 7
Knotion8.EXEC.A.3Usan 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
Knotion8.EXEC.A.4Realizan 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
Knotion8.EXEC.B.5Grafican 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
Knotion8.EXEC.B.6Usan 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
Knotion8.EXEC.C.7Dan 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
Knotion8.EXEC.C.8Comprenden 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
Knotion8.FUN.A.1Comprenden 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
Knotion8.FUN.A.2Comparan 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
Knotion8.FUN.A.3Interpretan 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 rectaGrade 8
Knotion8.FUN.B.4Construyen 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
Knotion8.FUN.B.5Describen 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
Knotion8.GE.A.2Entienden 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
Knotion8.GE.A.4Entienden 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
Knotion8.GE.B.7Aplican 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
Knotion8.GE.B.8Aplican el Teorema de Pitàgoras para encontrar la distancia entre dos puntos en un sistema de coordenadas.Grade 8
Knotion8.PRO.A.1Construyen 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
Knotion8.PRO.A.2Saben 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
KnotionK1.CYCA.B.4Relaciona la acciÑn de aumentar una colecciÑn con agregar objetos.Kindergarten
KnotionK1.CYCA.C.6Identifican 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
KnotionK2.CYCA.C.6Elige el conjunto que tiene màs o menos objetos despu_s de haber observado un par o una tercia de colecciones.Kindergarten
KnotionK2.OYPA.A.1Relaciona la acciÑn de aumentar una colecciÑn con agregar objetos.Kindergarten
KnotionK3.CYCA.A.1Identifica las regularidades de la sucesiÑn num_rica del 0 al 100.Kindergarten
KnotionK3.CYCA.A.2Cuentan hacia delante desde un nÏmero dado dentro de una secuencia conocida (en lugar de comenzar con el 1).Kindergarten
KnotionK3.CYCA.A.3Escribe y lee los nÏmeros (1 a 20).Kindergarten
KnotionK3.CYCA.B.4Escribe 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
KnotionK3.CYCA.B.5Completa el elemento faltante de una secuencia de nÏmeros o figuras incompleta.Kindergarten
KnotionK3.OYPA.A.1Relaciona las acciones de aumentar y disminuir con la suma y con la resta.Kindergarten
KnotionK3.OYPA.A.2Resuelven problemas verbales de sumal y resta, y suman y restan hasta 10, por ejemplo, utilizar objetos o dibujos para representar el problema.Kindergarten
KnotionK3.OYPA.A.3Utiliza material concreto, dibujos y/o nÏmeros para descomponer nÏmeros menores a veinte como la suma de una decena y las unidades faltantes.Kindergarten
KnotionK3.OYPA.A.4Para 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
KnotionK3.OYPA.A.5Suman y restan con fluidez de y hasta el nÏmero 5.Kindergarten
KnotionK3.SND.A.1Componen 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
KnotionA-APR.B.3Identifica 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
KnotionA-CED.A.2Crea 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
KnotionA-SSE.A.2Utiliza la estructura de una expresiÑn para identificar formas de volver a escribirla.lgebra
KnotionA-SSE.B.3Elige y produce una forma equivalente de la expresiÑn para revelar y explicar propiedades de la cantidad que representa.lgebra
KnotionF-BF.A.1Escribe una funciÑn que describa la relaciÑn entre dos cantidades.lgebra
KnotionF-IF.A.2Utiliza 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
KnotionF-IF.B.4Para 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
KnotionF-IF.C.7Realiza 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
KnotionS-ID.B.6Representa los datos en dos variables cuantitativas en un gràfico de dispersiÑn y describe cÑmo se relacionan las variables.lgebra
ManitobaK.N.1Say the number sequence by 1s, starting anywhere from 1 to 30 and from 10 to 1.Kindergarten
ManitobaK.N.2Subitize and name familiar arrangements of 1 to 6 dots (or objects).Kindergarten
ManitobaK.N.3Relate a numeral, 1 to 10, to its respective quantity.Kindergarten
ManitobaK.N.4Represent and describe numbers 2 to 10 in two parts, concretely and pictorially.Kindergarten
ManitobaK.N.5.1Demonstrate an understanding of counting to 10 by indicating that the last number said identifies how many.Kindergarten
ManitobaK.N.5.2Demonstrate an understanding of counting to 10 by showing that any set has only one count.Kindergarten
ManitobaK.N.6.1Compare quantities, 1 to 10, using one-to-one correspondence.Kindergarten
ManitobaK.N.6.2Compare quantities, 1 to 10, by ordering numbers representing different quantities.Kindergarten
ManitobaK.PR.1Demonstrate an understanding of repeating patterns (two or three elements) by, identifying, reproducing, extending, creating, patterns using manipulatives, sounds, and actions.Kindergarten
ManitobaK.SS.1Use direct comparison to compare two objects based on a single attribute, such as length (height), mass (weight), and volume (capacity).Kindergarten
ManitobaK.SS.2Sort 3-D objects using a single attribute.Kindergarten
ManitobaK.SS.3Build and describe 3-D objects.Kindergarten
Manitoba1.N.1.1Say the number sequence by 1s forward and backward between any two given numbers (0 to 100).Grade 1
Manitoba1.N.1.2Say the number sequence by 2s to 30, forward starting at 0.Grade 1
Manitoba1.N.1.3Say the number sequence by 5s and 10s to 100, forward starting at 0.Grade 1
Manitoba1.N.2Subitize and name familiar arrangements of 1 to 10 dots (or objects).Grade 1
Manitoba1.N.3.1Demonstrate an understanding of counting by using the counting-on strategy.Grade 1
Manitoba1.N.3.2Demonstrate an understanding of counting by using parts or equal groups to count sets.Grade 1
Manitoba1.N.4Represent and describe numbers to 20, concretely, pictorially, and symbolically.Grade 1
Manitoba1.N.5Compare and order sets containing up to 20 elements to solve problems using referents and one-to-one correspondence.Grade 1
Manitoba1.N.6Estimate quantities to 20 by using referents.Grade 1
Manitoba1.N.7Demonstrate, concretely and pictorially, how a number, up to 30, can be represented by a variety of equal groups with and without singles.Grade 1
Manitoba1.N.8Identify the number, up to 20, that is one more, two more, one less, and two less than a given number.Grade 1
Manitoba1.N.9.1Demonstrate 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
Manitoba1.N.9.2Demonstrate 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
Manitoba1.N.9.3Demonstrate 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
Manitoba1.N.10Describe 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
Manitoba1.PR.1Demonstrate an understanding of repeating patterns (two to four elements).Grade 1
Manitoba1.PR.2Translate repeating patterns from one representation to another.Grade 1
Manitoba1.PR.3Describe equality as a balance and inequality as an imbalance, concretely and pictorially (0 to 20).Grade 1
Manitoba1.PR.4Record equalities using the equal symbol (0 to 20).Grade 1
Manitoba1.SS.1Demonstrate an understanding of measurement as a process of comparing.Grade 1
Manitoba1.SS.2Sort 3-D objects and 2-D shapes using one attribute, and explain the sorting rule.Grade 1
Manitoba1.SS.3Replicate composite 2-D shapes and 3-D objects.Grade 1
Manitoba1.SS.4Compare 2-D shapes to parts of 3-D objects in the environment.Grade 1
Manitoba2.N.1.1Say 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
Manitoba2.N.1.2Say the number sequence from 0 to 100 by 10s using starting points from 1 to 9.Grade 2
Manitoba2.N.1.3Say the number sequence from 0 to 100 by 2s starting from 1.Grade 2
Manitoba2.N.2Demonstrate if a number (up to 100) is even or odd.Grade 2
Manitoba2.N.3Describe order or relative position using ordinal numbers.Grade 2
Manitoba2.N.4Represent and describe numbers to 100, concretely, pictorially, and symbolically.Grade 2
Manitoba2.N.5Compare and order numbers up to 100.Grade 2
Manitoba2.N.6Estimate quantities to 100 using referents.Grade 2
Manitoba2.N.7Illustrate, concretely and pictorially, the meaning of place value for numbers to 100.Grade 2
Manitoba2.N.8Demonstrate and explain the effect of adding zero to or subtracting zero from any number.Grade 2
Manitoba2.N.9.1Demonstrate 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
Manitoba2.N.9.2Demonstrate 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
Manitoba2.N.9.3Demonstrate 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
Manitoba2.N.9.4Demonstrate 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
Manitoba2.N.10Apply 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
Manitoba2.PR.1Predict an element in a repeating pattern using a variety of strategies.Grade 2
Manitoba2.PR.2Demonstrate an understanding of increasing patters by describing, reproducing, extending and creating patterns using manipulatives, diagrams, sounds and actions (numbers to 100).Grade 2
Manitoba2.PR.3Demonstrate and explain the meaning of equality and inequality by using manipulatives and diagrams (0 to 100).Grade 2
Manitoba2.PR.4Record equalities and inequalities symbolically using the equal symbol or the not-equal symbol.Grade 2
Manitoba2.SS.1Relate the number of days to a week and the number of months to a year in a problem-solving context.Grade 2
Manitoba2.SS.2Relate 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
Manitoba2.SS.3Compare and order objects by length, height, distance around, and mass (weight) using non-standard units, and make statements of comparison.Grade 2
Manitoba2.SS.4Measure length to the nearest non-standard unit by using multiple copies of a unit or using a single copy of a unit.Grade 2
Manitoba2.SS.5Demonstrate that changing the orientation of an object does not alter the measurements of its attributes.Grade 2
Manitoba2.SS.6Sort 2-D shapes and 3-D objects using two attributes, and explain the sorting rule.Grade 2
Manitoba2.SS.7Describe, compare, and construct 3-D objects, including cubes, spheres, cones, cylinders, prisms and pyramids.Grade 2
Manitoba2.SS.8Describe, compare, and construct 2-D shapes, including triangles, squares, rectangels and circles.Grade 2
Manitoba2.SS.9Identify 2-D shapes as parts of 3-D objects in the environment.Grade 2
Manitoba2.SP.2Construct and interpret concrete graphs and pictographs to solve problems.Grade 2
Manitoba3.N.1.1Say 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
Manitoba3.N.1.2Say 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
Manitoba3.N.1.3Say 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
Manitoba3.N.1.4Say 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
Manitoba3.N.1.5Say 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
Manitoba3.N.2Represent and describe numbers to 1000, concretely, pictorially, and symbolically.Grade 3
Manitoba3.N.3Compare and order numbers to 1000.Grade 3
Manitoba3.N.4Estimate quantities less than 1000 using referents.Grade 3
Manitoba3.N.5Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000.Grade 3
Manitoba3.N.6.1Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as adding from left to right.Grade 3
Manitoba3.N.6.2Describe 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
Manitoba3.N.6.3Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as using doubles.Grade 3
Manitoba3.N.7.1Describe 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
Manitoba3.N.7.2Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as thinking of addition.Grade 3
Manitoba3.N.7.3Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as using doubles.Grade 3
Manitoba3.N.8Apply estimation strategies to predict sums and differences of two 2-digit numerals in a problem-solving context.Grade 3
Manitoba3.N.9.1Demonstrate 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
Manitoba3.N.9.2Demonstrate 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
Manitoba3.N.10Apply mental math strategies to determine addition facts and related subtraction facts to 18 (9 + 9).Grade 3
Manitoba3.N.11.1Demonstrate an understanding of multiplication to 5 × 5 by representing and explaining multiplication using equal grouping and arrays.Grade 3
Manitoba3.N.11.2Demonstrate an understanding of multiplication to 5 × 5 by creating and solving problems in context that involve multiplication.Grade 3
Manitoba3.N.11.3Demonstrate an understanding of multiplication to 5 × 5 by modelling multiplication using concrete and visual representations, and recording the process symbolically.Grade 3
Manitoba3.N.11.4Demonstrate an understanding of multiplication to 5 × 5 by relating multiplication to repeated addition.Grade 3
Manitoba3.N.11.5Demonstrate an understanding of multiplication to 5 × 5 by relating multiplication to division.Grade 3
Manitoba3.N.12.1Demonstrate 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
Manitoba3.N.12.2Demonstrate 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
Manitoba3.N.12.3Demonstrate 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
Manitoba3.N.12.4Demonstrate an understanding of division by relating division to repeated subtraction limited to division related to multiplication facts up to 5 × 5.Grade 3
Manitoba3.N.12.5Demonstrate an understanding of division by relating division to multiplication limited to division related to multiplication facts up to 5 × 5.Grade 3
Manitoba3.N.13.1Demonstrate an understanding of fractions by explaining that a fraction represents a portion of a whole divided into equal parts.Grade 3
Manitoba3.N.13.2Demonstrate an understanding of fractions by describing situations in which fractions are used.Grade 3
Manitoba3.N.13.3Demonstrate an understanding of fractions by comparing fractions of the same whole with like denominators.Grade 3
Manitoba3.PR.1Demonstrate an understanding of increasing patterns by describing, extending, comparing, and creating patterns using manipulatives, diagrams, and numbers to 1000.Grade 3
Manitoba3.PR.2Demonstrate an understanding of decreasing patterns by describing, extending, comparing, and creating patterns using manipulatives, diagrams, and numbers starting from 1000 or less.Grade 3
Manitoba3.PR.3Solve one-step addition and subtraction equations involving symbols representing an unknown number.Grade 3
Manitoba3.SS.1Relate the passage of time to common activities using non- standard and standard units (minutes, hours, days, weeks, months, years).Grade 3
Manitoba3.SS.2Relate 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
Manitoba3.SS.3.1Demonstrate an understanding of measuring length (cm, m) by selecting and justifying referents for the units cm and m.Grade 3
Manitoba3.SS.3.2Demonstrate an understanding of measuring length (cm, m) by modelling and describing the relationship between the units cm and m.Grade 3
Manitoba3.SS.3.3Demonstrate an understanding of measuring length (cm, m) by estimating length using referents.Grade 3
Manitoba3.SS.3.4Demonstrate an understanding of measuring length (cm, m) by measuring and recording length, width, and height.Grade 3
Manitoba3.SS.4.1Demonstrate an understanding of measuring mass (g, kg) by selecting and justifying referents for the units g and kg.Grade 3
Manitoba3.SS.4.2Demonstrate an understanding of measuring mass (g, kg) by modelling and describing the relationship between the units g and kg.Grade 3
Manitoba3.SS.4.3Demonstrate an understanding of measuring mass (g, kg) by estimating mass using referents.Grade 3
Manitoba3.SS.4.4Demonstrate an understanding of measuring mass (g, kg) by measuring and recording mass.Grade 3
Manitoba3.SS.5.1Demonstrate an understanding of perimeter of regular and irregular shapes by estimating perimeter using referents for centimetre or metre.Grade 3
Manitoba3.SS.5.2Demonstrate an understanding of perimeter of regular and irregular shapes by measuring and recording perimeter (cm, m).Grade 3
Manitoba3.SS.5.3Demonstrate an understanding of perimeter of regular and irregular shapes by constructing different shapes for a given perimeter (cmGrade 3
Manitoba3.SS.6Describe 3-D objects according to the shape of the faces, and the number of edges and vertices.Grade 3
Manitoba3.SS.7Sort regular and irregular polygons, including triangles, quadrilaterals, pentagons, hexagons, and octagons according to the number of sides.Grade 3
Manitoba3.SP.1Collect first-hand data and organize it using tally marks, line plots, charts, and lists to answer questions.Grade 3
Manitoba3.SP.2Construct, label, and interpret bar graphs to solve problems.Grade 3
Manitoba4.N.1Represent and describe whole numbers to 10,000 pictorally and symbolically.Grade 4
Manitoba4.N.2Compare and order numbers to 10,000Grade 4
Manitoba4.N.3.1Demonstrate 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
Manitoba4.N.3.2Demonstrate 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
Manitoba4.N.3.3Demonstrate 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
Manitoba4.N.3.4Demonstrate 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
Manitoba4.N.4Explain the properties of 0 and 1 for multiplication and the property of 1 for division.Grade 4
Manitoba4.N.5.1Describe 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
Manitoba4.N.5.2Describe 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
Manitoba4.N.5.3Describe 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
Manitoba4.N.5.4Describe 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
Manitoba4.N.5.5Describe 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
Manitoba4.N.6.1Demonstrate 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
Manitoba4.N.6.2Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by using arrays to represent multiplication.Grade 4
Manitoba4.N.6.3Demonstrate 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
Manitoba4.N.6.4Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by estimating products.Grade 4
Manitoba4.N.7.1Demonstrate 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
Manitoba4.N.7.2Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by estimating quotients.Grade 4
Manitoba4.N.7.3Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by relating division to multiplication.Grade 4
Manitoba4.N.8.1Demonstrate 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
Manitoba4.N.8.2Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to compare and order fractions.Grade 4
Manitoba4.N.8.3Demonstrate 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
Manitoba4.N.8.4Demonstrate 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
Manitoba4.N.9Describe and represent decimals (tenths and hundredths), concretely, pictorially, and symbolically.Grade 4
Manitoba4.N.10Relate decimals to fractions (to hundredths).Grade 4
Manitoba4.N.11.1Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by using compatible numbers.Grade 4
Manitoba4.N.11.2Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by estimating sums and differences.Grade 4
Manitoba4.N.11.3Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by using mental math strategies to solve problems.Grade 4
Manitoba4.PR.1Identify and describe patterns found in tables and charts, including a multiplication chart.Grade 4
Manitoba4.PR.2Reproduce a pattern shown in a table or chart using concrete materials.Grade 4
Manitoba4.PR.3Represent and describe patterns and relationships using charts and tables to solve problems.Grade 4
Manitoba4.PR.4Identify and explain mathematical relationships using charts and diagrams to solve problems.Grade 4
Manitoba4.PR.5Express a problem as an equation in which a symbol is used to represent an unknown number.Grade 4
Manitoba4.PR.6Solve one-step equations involving a symbol to represent an unknown number.Grade 4
Manitoba4.SS.1Read and record time using digital and analog clocks, including 24-hour clocks.Grade 4
Manitoba4.SS.3.1Demonstrate an understanding of area of regular and irregular 2-D shapes by recognizing that area is measured in square units.Grade 4
Manitoba4.SS.3.2Demonstrate an understanding of area of regular and irregular 2-D shapes by selecting and justifying referents for the units cm2 or m2.Grade 4
Manitoba4.SS.3.3Demonstrate an understanding of area of regular and irregular 2-D shapes by estimating area by using referents for cm2 or m2.Grade 4
Manitoba4.SS.3.4Demonstrate an understanding of area of regular and irregular 2-D shapes by determining and recording area (cm2 or m2).Grade 4
Manitoba4.SS.3.5Demonstrate 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
Manitoba4.SS.4Solve problems involving 2-D shapes and 3-D objects.Grade 4
Manitoba4.SS.5Describe and construct rectangular and triangular prisms.Grade 4
Manitoba4.SS.6.1Demonstrate an understanding of line symmetry by identifying symmetrical 2-D shapes.Grade 4
Manitoba4.SS.6.2Demonstrate an understanding of line symmetry by creating symmetrical 2-D shapes.Grade 4
Manitoba4.SS.6.3Demonstrate an understanding of line symmetry by drawing one or more lines of symmetry in a 2-D shape.Grade 4
Manitoba4.SP.1Demonstrate an understanding of many-to-one correspondence.Grade 4
Manitoba4.SP.2Construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions.Grade 4
Manitoba5.N.1Represent and describe whole numbers to 1 000 000.Grade 5
Manitoba5.N.2Apply estimation strategies, including front-end rounding, compensation, compatible numbers, and in problem-solving contexts.Grade 5
Manitoba5.N.3Apply mental math strategies to determine multiplication and related division facts to 81 (9 × 9).Grade 5
Manitoba5.N.4.1Apply mental mathematics strategies for multiplication, such as annexing then adding zeros.Grade 5
Manitoba5.N.4.2Apply mental mathematics strategies for multiplication, such as halving and doubling.Grade 5
Manitoba5.N.4.3Apply mental mathematics strategies for multiplication, such as using the distributive property.Grade 5
Manitoba5.N.5.1Demonstrate 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
Manitoba5.N.5.2Demonstrate 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
Manitoba5.N.5.3Demonstrate 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
Manitoba5.N.6.1Demonstrate 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
Manitoba5.N.6.2Demonstrate 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
Manitoba5.N.6.3Demonstrate 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
Manitoba5.N.7.1Demonstrate an understanding of fractions by using concrete and pictorial representations to create sets of equivalent fractions.Grade 5
Manitoba5.N.7.2Demonstrate an understanding of fractions by using concrete and pictorial representations to compare fractions with like and unlike denominators.Grade 5
Manitoba5.N.8Describe and represent decimals (tenths, hundredths, thousandths) concretely, pictorially, and symbolically.Grade 5
Manitoba5.N.9Relate decimals to fractions (tenths, hundredths, thousandths).Grade 5
Manitoba5.N.10Compare and order decimals (tenths, hundredths, thousandths) by using benchmarks, place value, and equivalent decimals.Grade 5
Manitoba5.N.11Demonstrate 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
Manitoba5.PR.2Solve problems involving single-variable (expressed as symbols or letters), one-step equations with whole-number coefficients, and whole-number solutions.Grade 5
Manitoba5.SS.1Design and construct different rectangles given either perimeter or area or both (whole numbers), and draw conclusions.Grade 5
Manitoba5.SS.2Demonstrate 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
Manitoba5.SS.3.1Demonstrate an understanding of volume by selecting and justifying referents for cm3 or m3 units.Grade 5
Manitoba5.SS.3.2Demonstrate an understanding of volume by estimating volume by using referents for cm3 or m3.Grade 5
Manitoba5.SS.3.3Demonstrate an understanding of volume by measuring and recording volume (cm3 or m3).Grade 5
Manitoba5.SS.3.4Demonstrate an understanding of volume by constructing rectangular prisms for a given volume.Grade 5
Manitoba5.SS.4.1Demonstrate an understanding of capacity by describing the relationship between mL and L.Grade 5
Manitoba5.SS.4.2Demonstrate an understanding of capacity by selecting and justifying referents for mL or L units.Grade 5
Manitoba5.SS.4.3Demonstrate an understanding of capacity by estimating capacity by using referents for mL or L.Grade 5
Manitoba5.SS.4.4Demonstrate an understanding of capacity by measuring and recording capacity (mL or L).Grade 5
Manitoba5.SS.5Describe 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
Manitoba5.SS.6Identify and sort quadrilaterals, including rectangles, squares, trapezoids, parallelograms, and rhombuses according to their attributes.Grade 5
Manitoba5.SS.7Perform a single transformation (translation, rotation, or reflection) of a 2-D shape, and draw and describe the image.Grade 5
Manitoba5.SS.8Identify a single transformation (translation, rotation, or reflection) of 2-D shapes.Grade 5
Manitoba5.SP.1Differentiate between first-hand and second-hand data.Grade 5
Manitoba5.SP.2Construct and interpret double bar graphs to draw conclusions.Grade 5
Manitoba5.SP.3Describe the likelihood of a single outcome occurring, using words such as impossible, possible, and certain.Grade 5
Manitoba5.SP.4Compare the likelihood of two possible outcomes occurring, using words such as less likely, equally likely, and more likely.Grade 5
Manitoba6.N.1Demonstrate an understanding of place value for numbers greater than one million and numbers less than one-thousandth.Grade 6
Manitoba6.N.2Solve problems involving large numbers, using technology.Grade 6
Manitoba6.N.3.1Demonstrate an understanding of factors and multiples by determining multiples and factors of numbers less than 100.Grade 6
Manitoba6.N.3.2Demonstrate an understanding of factors and multiples by identifying prime and composite numbers.Grade 6
Manitoba6.N.3.3Demonstrate an understanding of factors and multiples by solving problems involving factors or multiples.Grade 6
Manitoba6.N.4Relate improper fractions to mixed numbers.Grade 6
Manitoba6.N.5Demonstrate an understanding of ratio, concretely, pictorially, and symbolically.Grade 6
Manitoba6.N.6Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially, and symbolically.Grade 6
Manitoba6.N.7Demonstrate an understanding of integers, concretely, pictorially, and symbolically.Grade 6
Manitoba6.N.8.1Demonstrate 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
Manitoba6.N.8.2Demonstrate 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
Manitoba6.N.8.3Demonstrate 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
Manitoba6.N.8.4Demonstrate 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
Manitoba6.N.9Explain and apply the order of operations, excluding exponents (limited to whole numbers).Grade 6
Manitoba6.PR.1Demonstrate an understanding of the relationships within tables of values to solve problems.Grade 6
Manitoba6.PR.2Represent and describe patterns and relationships using graphs and tables.Grade 6
Manitoba6.PR.3Represent generalizations arising from number relationships using equations with letter variables.Grade 6
Manitoba6.PR.4Demonstrate and explain the meaning of preservation of equality, concretely, pictorially, and symbolically.Grade 6
Manitoba6.SS.1.1Demonstrate an understanding of angles by identifying examples of angles in the environment.Grade 6
Manitoba6.SS.1.2Demonstrate an understanding of angles by classifying angles according to their measure.Grade 6
Manitoba6.SS.1.3Demonstrate an understanding of angles by estimating the measure of angles using 45°, 90°, and 180° as reference angles.Grade 6
Manitoba6.SS.1.4Demonstrate an understanding of angles by determining angle measures in degrees.Grade 6
Manitoba6.SS.1.5Demonstrate an understanding of angles by drawing and labelling angles when the measure is specified.Grade 6
Manitoba6.SS.2Demonstrate that the sum of interior angles is 180° in a triangle and 360° in a quadrilateral.Grade 6
Manitoba6.SS.3Develop and apply a formula for determining the perimeter of polygons, area of rectangles, and volume of right rectangular prisms.Grade 6
Manitoba6.SS.4Construct and compare triangles, including scalene, isosceles, equilateral, right, obtuse, and acute in different orientations.Grade 6
Manitoba6.SS.5Describe and compare the sides and angles of regular and irregular polygons.Grade 6
Manitoba6.SS.6Perform a combination of transformations (translations, rotations, or reflections) on a single 2-D shape, and draw and describe the image.Grade 6
Manitoba6.SS.7Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations.Grade 6
Manitoba6.SS.8Identify and plot points in the first quadrant of a Cartesian plane using whole-number ordered pairs.Grade 6
Manitoba6.SS.9Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole-number vertices).Grade 6
Manitoba6.SP.1Create, label, and interpret line graphs to draw conclusions.Grade 6
Manitoba6.SP.2Select, justify, and use appropriate methods of collecting data, including questionnaires, experiments, databases, and electronic media.Grade 6
Manitoba6.SP.3Graph collected data and analyze the graph to solve problems.Grade 6
Manitoba6.SP.4.1Demonstrate an understanding of probability by identifying all possible outcomes of a probability experiment.Grade 6
Manitoba6.SP.4.2Demonstrate an understanding of probability by differentiating between experimental and theoretical probability.Grade 6
Manitoba6.SP.4.3Demonstrate an understanding of probability by determining the theoretical probability of outcomes in a probability experiment.Grade 6
Manitoba6.SP.4.4Demonstrate an understanding of probability by determining the experimental probability of outcomes in a probability experiment.Grade 6
Manitoba6.SP.4.5Demonstrate an understanding of probability by comparing experimental results with the theoretical probability for an experiment.Grade 6
Manitoba7.N.1Determine 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
Manitoba7.N.2Demonstrate 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
Manitoba7.N.3Solve problems involving percents from 1% to 100%.Grade 7
Manitoba7.N.4Demonstrate an understanding of the relationship between repeating decimals and fractions, and terminating decimals and fractions.Grade 7
Manitoba7.N.5Demonstrate 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
Manitoba7.N.6Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically.Grade 7
Manitoba7.N.7Compare and order fractions, decimals (to thousandths), and integers by using benchmarks, place value and equivalent fractions and/or decimals.Grade 7
Manitoba7.PR.1Demonstrate an understanding of oral and written patterns and their corresponding relations.Grade 7
Manitoba7.PR.2Construct a table of values from a relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.Grade 7
Manitoba7.PR.3Demonstrate 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
Manitoba7.PR.4Explain the difference between an expression and an equation.Grade 7
Manitoba7.PR.5Evaluate an expression given the value of the variable(s).Grade 7
Manitoba7.PR.6Model 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
Manitoba7.PR.7Model 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
Manitoba7.SS.1.1Demonstrate an understanding of circles by describing the relationships among radius, diameter, and circumference of circles.Grade 7
Manitoba7.SS.1.2Demonstrate an understanding of circles by relating circumference to pi.Grade 7
Manitoba7.SS.1.3Demonstrate an understanding of circles by determining the sum of the central angles.Grade 7
Manitoba7.SS.1.4Demonstrate an understanding of circles by constructing circles with a given radius or diameter.Grade 7
Manitoba7.SS.1.5Demonstrate an understanding of circles by solving problems involving the radii, diameters, and circumferences of circles.Grade 7
Manitoba7.SS.2.1Develop and apply a formula for determining the area of triangles.Grade 7
Manitoba7.SS.2.2Develop and apply a formula for determining the area of parallelograms.Grade 7
Manitoba7.SS.2.3Develop and apply a formula for determining the area of circles.Grade 7
Manitoba7.SS.3Perform geometric constructions, including perpendicular line segments, parallel line segments, perpendicular bisectors and angle bisectors.Grade 7
Manitoba7.SS.4Identify and plot points in the four quadrants of a Cartesian plane using ordered pairs.Grade 7
Manitoba7.SS.5Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events.Grade 7
Manitoba7.SP.1.1Demonstrate an understanding of central tendency and range by determining the measures of central tendency (mean, median, mode) and range.Grade 7
Manitoba7.SP.1.2Demonstrate an understanding of central tendency and range by determining the most appropriate measures of central tendency to report findings.Grade 7
Manitoba7.SP.2Determine the effect on the mean, median, and mode when an outlier is included in a data set.Grade 7
Manitoba7.SP.3Construct, label, and interpret circle graphs to solve problems.Grade 7
Manitoba7.SP.4Express probabilities as ratios, fractions, and percents.Grade 7
Manitoba7.SP.5Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events.Grade 7
Manitoba7.SP.6Conduct 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
Manitoba8.N.1Demonstrate an understanding of perfect squares and square roots, concretely, pictorially, and symbolically (limited to whole numbers).Grade 8
Manitoba8.N.2Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers).Grade 8
Manitoba8.N.3Demonstrate an understanding of percents greater than or equalto 0%.Grade 8
Manitoba8.N.4Demonstrate an understanding of ratio and rate.Grade 8
Manitoba8.N.5Solve problems that involve rates, ratios, and proportionalreasoning.Grade 8
Manitoba8.N.6Demonstrate an understanding of multiplying and dividingpositive fractions and mixed numbers, concretely, pictorially,and symbolically.Grade 8
Manitoba8.N.7Demonstrate an understanding of multiplication and division ofintegers, concretely, pictorially, and symbolically.Grade 8
Manitoba8.N.8Solve problems involving positive rational numbers.Grade 8
Manitoba8.PR.1Graph and analyze two-variable linear relations.Grade 8
Manitoba8.PR.2Model and solve problems using linear equations concretely, pictorially, and symbolically, where a, b, and c, are integersGrade 8
Manitoba8.SS.1Develop and apply the Pythagorean theorem to solve problems.Grade 8
Manitoba8.SS.2Draw and construct nets for 3-D objects.Grade 8
Manitoba8.SS.3.1Determine the surface area of right rectangular prisms to solve problems.Grade 8
Manitoba8.SS.3.2Determine the surface area of right triangular prisms to solve problems.Grade 8
Manitoba8.SS.3.3Determine the surface area of right cylinders to solve problems.Grade 8
Manitoba8.SS.4Develop and apply formulas for determining the volume of right prisms and right cylinders.Grade 8
Manitoba8.SS.5Draw and interpret top, front, and side views of 3-D objects composed of right rectangular prisms.Grade 8
Manitoba8.SS.6.1Demonstrate an understanding of tessellation by explaining the properties of shapes that make tessellating possible.Grade 8
Manitoba8.SS.6.2Demonstrate an understanding of tessellation by creating tessellations.Grade 8
Manitoba8.SS.6.3Demonstrate an understanding of tessellation by identifying tessellations in the environment.Grade 8
Manitoba8.SP.1Critique ways in which data are presented.Grade 8
Manitoba8.SP.2Solve problems involving the probability of independent events.Grade 8
Manitoba10I.A.3Demonstrate an understanding of powers with integral and rational exponents.Algebra
Manitoba9.PR.2Graph linear relations, analyze the graph, and interpolate or extrapolate to solve problems.Algebra
Manitoba9.PR.4Explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context.Algebra
Manitoba9.PR.5Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2).Algebra
Manitoba9.PR.6Model, 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
Manitoba10I.R.2Demonstrate an understanding of relations and functions.Algebra
Manitoba10I.R.4.4Describe and represent linear relations, using graphs.Algebra
Manitoba10I.R.8Represent a linear function, using function notation.Algebra
Manitoba10I.R.7.5Determine the equation of a linear relation, given a scatterplotAlgebra
Manitoba11P.R.4.5Analyze quadratic functions of the form y = ax2 + bx + c to identify characteristics of the corresponding graph, including x- and y-intercepts.Algebra
Manitoba9.SS.4Draw and interpret scale diagrams of 2-D shapes.Algebra
Minnesota9.2.1.1Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain.Algebra
Minnesota9.2.1.4Obtain information and draw conclusions from graphs of functions and other relations.Algebra
Minnesota9.2.1.6Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.Algebra
Minnesota9.2.1.8Make qualitative statements about the rate of change of a function, based on its graph or table of values.Algebra
Minnesota9.2.2.3Sketch 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
Minnesota9.2.2.4Express 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
Minnesota9.2.2.6Sketch 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
Minnesota9.2.3.2Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.Algebra
Minnesota9.2.3.3Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares.Algebra
Minnesota9.2.3.7Justify 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
Minnesota9.2.4.1Represent 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
Minnesota9.4.1.3Use 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
Minnesota1.1.1.1Use place value to describe whole numbers between 10 and 100 in terms of tens and ones.Grade 1
Minnesota1.1.1.2Read, 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
Minnesota1.1.1.3Count, with and without objects, forward and backward from any given number up to 120.Grade 1
Minnesota1.1.1.4Find a number that is 10 more or 10 less than a given number.Grade 1
Minnesota1.1.1.5Compare and order whole numbers up to 100.Grade 1
Minnesota1.1.1.7Use counting and comparison skills to create and analyze bar graphs and tally charts.Grade 1
Minnesota1.1.2.1Use 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
Minnesota1.1.2.3Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s.Grade 1
Minnesota1.2.2.1Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences.Grade 1
Minnesota1.3.2.2Tell time to the hour and half-hour.Grade 1
Minnesota2.1.1.1Read, 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
Minnesota2.1.1.2Use 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
Minnesota2.1.1.3Find 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
Minnesota2.1.1.5Compare and order whole numbers up to 1000.Grade 2
Minnesota2.1.2.1Use 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
Minnesota2.1.2.4Use 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
Minnesota2.1.2.5Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits.Grade 2
Minnesota2.1.2.6Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts.Grade 2
Minnesota2.2.2.2Use 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
Minnesota2.3.1.2Identify 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
Minnesota2.3.2.1Understand 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
Minnesota3.1.1.2Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones.Grade 3
Minnesota3.1.1.4Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences.Grade 3
Minnesota3.1.2.1Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms.Grade 3
Minnesota3.1.2.3Represent 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
Minnesota3.1.2.4Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems.Grade 3
Minnesota3.1.2.5Use 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
Minnesota3.1.3.1Read 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
Minnesota3.1.3.2Understand that the size of a fractional part is relative to the size of the whole.Grade 3
Minnesota3.1.3.3Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator.Grade 3
Minnesota3.3.1.1Identify 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
Minnesota3.3.3.1Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute.Grade 3
Minnesota3.4.1.1Collect, 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
Minnesota4.1.1.2Use an understanding of place value to multiply a number by 10, 100 and 1000.Grade 4
Minnesota4.1.1.3Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.Grade 4
Minnesota4.1.1.5Solve 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
Minnesota4.1.1.6Use 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
Minnesota4.1.2.1Represent 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
Minnesota4.1.2.2Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions.Grade 4
Minnesota4.1.2.3Use 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
Minnesota4.1.2.5Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.Grade 4
Minnesota4.1.2.6Read 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
Minnesota4.2.1.1Create 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
Minnesota4.2.2.1Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences.Grade 4
Minnesota4.2.2.2Use 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
Minnesota4.3.1.1Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts.Grade 4
Minnesota4.3.1.2Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts.Grade 4
Minnesota4.3.2.1Measure angles in geometric figures and real-world objects with a protractor or angle ruler.Grade 4
Minnesota4.3.2.3Understand 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
Minnesota4.3.2.4Find 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
Minnesota5.1.1.4Solve 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
Minnesota5.1.2.1Read and write decimals using place value to describe decimals in terms of groups from millionths to millions.Grade 5
Minnesota5.1.2.3Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.Grade 5
Minnesota5.1.2.5Round numbers to the nearest 0.1, 0.01 and 0.001.Grade 5
Minnesota5.1.3.1Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.Grade 5
Minnesota5.1.3.4Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data.Grade 5
Minnesota5.2.1.2Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.Grade 5
Minnesota5.2.2.1Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers.Grade 5
Minnesota6.1.1.1Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid.Grade 6
Minnesota6.1.1.2Compare positive rational numbers represented in various forms. Use the symbols .Grade 6
Minnesota6.1.1.3Understand that percent represents parts out of 100 and ratios to 100.Grade 6
Minnesota6.1.1.7Convert between equivalent representations of positive rational numbers.Grade 6
Minnesota6.1.2.1Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction.Grade 6
Minnesota6.1.2.3Determine the rate for ratios of quantities with different units.Grade 6
Minnesota6.1.3.1Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.Grade 6
Minnesota6.1.3.4Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers.Grade 6
Minnesota6.2.1.1Understand 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
Minnesota6.2.3.1Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers.Grade 6
Minnesota6.3.3.1Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units.Grade 6
Minnesota7.1.1.2Understand 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
Minnesota7.1.1.3Locate 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
Minnesota7.1.2.1Add, 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
Minnesota7.1.2.4Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.Grade 7
Minnesota7.1.2.6Demonstrate 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
Minnesota7.2.1.2Understand 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
Minnesota7.2.2.1Represent 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
Minnesota7.2.2.2Solve multi-step problems involving proportional relationships in numerous contexts.Grade 7
Minnesota7.2.2.4Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers.Grade 7
Minnesota7.2.3.1Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws.Grade 7
Minnesota7.2.3.2Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables.Grade 7
Minnesota7.2.3.3Apply understanding of order of operations and grouping symbols when using calculators and other technologies.Grade 7
Minnesota7.2.4.1Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context.Grade 7
Minnesota7.3.2.1Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors.Grade 7
Minnesota7.3.2.3Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units.Grade 7
Minnesota7.3.2.4Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation.Grade 7
Minnesota8.1.1.4Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions.Grade 8
Minnesota8.1.1.5Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved.Grade 8
Minnesota8.2.1.1Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use funct