Common Core State Standards for Math

The Common Core State Standards for Math (CCSSM) are guidelines, not a curriculum. They have been adopted in forty-four states, the District of Columbia, four territories, and the Department of Defense Education Activity (DoDEA).

Texas Essential Knowledge and Skills

The Texas Essential Knowledge and Skills (TEKS) identifies what students should know and be able to do at every grade and in every subject area, including mathematics.

Virginia Public Schools Standards of Learning

The Standards of Learning (SOL) for Virginia Public Schools establish minimum expectations for what students should know and be able to do at the end of each grade or course, including Mathematics Performance Expectations.

The Western and Northern Canadian Protocol (WNCP) is an agreement between Ministers of Education of the four western provinces and three northern territories. It includes the WNCP Mathematics and a Common Curriculum Framework.

Ontario Curriculum

Almost all of Canada’s public schools and most private schools in the second largest province follow the Ontario Curriculum including a math curriculum. It holds specific requirements about knowledge and behaviors to be learned, while allowing flexibility in how the curriculum is to be delivered.

Standards Alignment

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
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
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 functional notation, such as ??(??), to represent such relationships.Grade 8
Minnesota8.2.1.3Understand that a function is linear if it can be expressed in the form ??(??) = ????+?? or if its graph is a straight line.Grade 8
Minnesota8.2.2.1Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.Grade 8
Minnesota8.2.2.2Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the ??-intercept is zero when the function represents a proportional relationship.Grade 8
Minnesota8.2.4.2Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used.Grade 8
Minnesota8.2.4.3Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line.Grade 8
Minnesota8.2.4.7Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically.Grade 8
Minnesota8.2.4.8Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations.Grade 8
Minnesota8.3.1.1Use the Pythagorean Theorem to solve problems involving right triangles.Grade 8
Minnesota8.3.1.2Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system.Grade 8
Minnesota8.4.1.1Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit.Grade 8
MinnesotaK.1.1.2Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes.Kindergarten
MinnesotaK.1.1.3Count, with and without objects, forward and backward to at least 20.Kindergarten
MinnesotaK.1.1.5Compare and order whole numbers, with and without objects, from 0 to 20.Kindergarten
MinnesotaK.1.2.2Compose and decompose numbers up to 10 with objects and pictures.Kindergarten
MissouriA1.CED.A.2Create and graph linear, quadratic and exponential equations in two variables.Algebra
MissouriA1.DS.A.5Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.Algebra
MissouriA1.IF.A.2Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Algebra
MissouriA1.IF.B.3Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.Algebra
MissouriA1.IF.C.7Graph functions expressed symbolically and identify and interpret key features of the graph.Algebra
MissouriA1.LQE.A.3Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.Algebra
MissouriA1.SSE.A.2Analyze the structure of polynomials to create equivalent expressions or equations.Algebra
MissouriA1.SSE.A.3Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.Algebra
MissouriA2.APR.A.5Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.Algebra
Missouri1.DS.A.1Collect, organize and represent data with up to three categories.Grade 1
Missouri1.DS.A.2Draw conclusions from object graphs, picture graphs, T-charts and tallies.Grade 1
Missouri1.GM.C.8Tell and write time in hours and half-hours using analog and digital clocks.Grade 1
Missouri1.NBT.A.1Understand that 10 can be thought of as a bundle of 10 ones called a ten.Grade 1
Missouri1.NBT.A.2Understand two-digit numbers are composed of ten (s) and ones (s).Grade 1
Missouri1.NBT.A.3Compare two two-digit numbers using the symbols >, = or <.Grade 1
Missouri1.NBT.B.6Calculate 10 more or 10 less than a given number mentally without having to count.Grade 1
Missouri1.NBT.B.7Add or subtract a multiple of 10 from another two-digit number, and justify the solution.Grade 1
Missouri1.NS.A.1Count to 120, starting at any number less than 120.Grade 1
Missouri1.NS.A.2Read and write numerals and represent a number of objects with a written numeral.Grade 1
Missouri1.RA.A.3Develop the meaning of the equal sign and determine if equations involving addition and subtraction are true or false.Grade 1
Missouri1.RA.A.4Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.Grade 1
Missouri2.DS.A.1Create a line plot to represent a set of numeric data, given a horizontal scale marked in whole numbers.Grade 2
Missouri2.DS.A.2Generate measurement data to the nearest whole unit, and display the data in a line plot.Grade 2
Missouri2.DS.A.3Draw a picture graph or a bar graph to represent a data set with up to four categories.Grade 2
Missouri2.DS.A.4Solve problems using information presented in line plots, picture graphs and bar graphs.Grade 2
Missouri2.DS.A.5Draw conclusions from line plots, picture graphs and bar graphs.Grade 2
Missouri2.GM.A.1Recognize and draw shapes having specified attributes, such as a given number of angles or sides.Grade 2
Missouri2.GM.D.10Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Grade 2
Missouri2.NBT.A.1Understand three-digit numbers are composed of hundreds, tens and ones.Grade 2
Missouri2.NBT.A.2Understand that 100 can be thought of as 10 tens called a hundred.Grade 2
Missouri2.NBT.A.3Count within 1000 by 1s, 10s and 100s starting with any number.Grade 2
Missouri2.NBT.A.4Read and write numbers to 1000 using number names, base-ten numerals and expanded form.Grade 2
Missouri2.NBT.A.5Compare two three-digit numbers using the symbols >, = or <.Grade 2
Missouri2.NBT.B.10Add or subtract mentally 10 or 100 to or from a given number within 1000.Grade 2
Missouri3.DS.A.1Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories.Grade 3
Missouri3.DS.A.2Solve one- and two-step problems using information presented in bar and/or picture graphs.Grade 3
Missouri3.DS.A.3Create a line plot to represent data.Grade 3
Missouri3.GM.A.1Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category.Grade 3
Missouri3.GM.A.2Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories.Grade 3
Missouri3.GM.B.4Tell and write time to the nearest minute.Grade 3
Missouri3.GM.B.5Estimate time intervals in minutes.Grade 3
Missouri3.GM.C.10Label area measurements with squared units.Grade 3
Missouri3.GM.C.11Demonstrate that tiling a rectangle to find the area and multiplying the side lengths result in the same value.Grade 3
Missouri3.GM.C.12Multiply whole-number side lengths to solve problems involving the area of rectangles.Grade 3
Missouri3.GM.C.13Find rectangular arrangements that can be formed for a given area.Grade 3
Missouri3.GM.C.14Decompose a rectangle into smaller rectangles to find the area of the original rectangle.Grade 3
Missouri3.GM.C.9Calculate area by using unit squares to cover a plane figure with no gaps or overlaps.Grade 3
Missouri3.NBT.A.1Round whole numbers to the nearest 10 or 100.Grade 3
Missouri3.NBT.A.4Multiply whole numbers by multiples of 10 in the range 10-90.Grade 3
Missouri3.NF.A.1Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts.Grade 3
Missouri3.NF.A.2Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole.Grade 3
Missouri3.NF.A.3Represent fractions on a number line.Grade 3
Missouri3.NF.A.4Demonstrate that two fractions are equivalent if they are the same size, or the same point on a number line.Grade 3
Missouri3.NF.A.5Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent.Grade 3
Missouri3.NF.A.6Compare two fractions with the same numerator or denominator using the symbols >, = orGrade 3
Missouri3.NF.A.7Explain why fraction comparisons are only valid when the two fractions refer to the same whole.Grade 3
Missouri3.RA.A.1Interpret products of whole numbers.Grade 3
Missouri3.RA.A.2Interpret quotients of whole numbers.Grade 3
Missouri3.RA.A.3Describe in words or drawings a problem that illustrates a multiplication or division situation.Grade 3
Missouri3.RA.A.4Use multiplication and division within 100 to solve problems.Grade 3
Missouri3.RA.A.5Determine the unknown number in a multiplication or division equation relating three whole numbers.Grade 3
Missouri3.RA.B.6Apply properties of operations as strategies to multiply and divide.Grade 3
Missouri3.RA.C.7Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers.Grade 3
Missouri3.RA.C.8Demonstrate fluency with products within 100.Grade 3
Missouri4.DS.A.1Create a frequency table and/or line plot to display measurement data.Grade 4
Missouri4.DS.A.2Solve problems involving addition and subtraction by using information presented in a data display.Grade 4
Missouri4.GM.A.1Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines.Grade 4
Missouri4.GM.A.2Classify two-dimensional shapes by their sides and/or angles.Grade 4
Missouri4.GM.B.4Identify and estimate angles and their measure.Grade 4
Missouri4.GM.B.5Draw and measure angles in whole-number degrees using a protractor.Grade 4
Missouri4.GM.C.6Know relative sizes of measurement units within one system of units.Grade 4
Missouri4.GM.C.7Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money.Grade 4
Missouri4.NBT.A.1Round multi-digit whole numbers to any place.Grade 4
Missouri4.NBT.A.2Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form.Grade 4
Missouri4.NBT.A.3Compare two multi-digit numbers using the symbols >, = orGrade 4
Missouri4.NBT.A.4Understand that in a multi-digit whole number, a digit represents 10 times what it would represents in the place to its right.Grade 4
Missouri4.NBT.A.6Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution.Grade 4
Missouri4.NBT.A.7Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution.Grade 4
Missouri4.NF.A.1Explain and/or illustrate why two fractions are equivalent.Grade 4
Missouri4.NF.A.2Recognize and generate equivalent fractions.Grade 4
Missouri4.NF.A.3Compare two fractions using the symbols >, = orGrade 4
Missouri4.NF.B.4Understand addition and subtraction of fractions as joining/composing and separating/decomposing parts referring to the same whole.Grade 4
Missouri4.NF.B.5Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification.Grade 4
Missouri4.NF.B.6Solve problems involving adding and subtracting fractions and mixed numbers with like denominators.Grade 4
Missouri4.NF.B.7Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.Grade 4
Missouri4.NF.B.8Solve problems involving multiplication of a fraction by a whole number.Grade 4
Missouri4.NF.C.12Compare two decimals to the hundredths place using the symbols >, = orGrade 4
Missouri4.NF.C.9Use decimal notation for fractions with denominators of 10 or 100.Grade 4
Missouri4.RA.A.1Multiply or divide to solve problems involving a multiplicative comparison.Grade 4
Missouri4.RA.B.4Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number.Grade 4
Missouri4.RA.B.5Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100.Grade 4
Missouri4.RA.C.6Generate a number pattern that follows a given rule.Grade 4
Missouri4.RA.C.7Use words or mathematical symbols to express a rule for a given pattern.Grade 4
Missouri5.DS.A.2Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median.Grade 5
Missouri5.GM.A.1Understand that attributes belonging to a category of figures also belong to all subcategories.Grade 5
Missouri5.GM.A.2Classify figures in a hierarchy based on properties.Grade 5
Missouri5.GM.C.7Plot and interpret points in the first quadrant of the Cartesian coordinate plane.Grade 5
Missouri5.NBT.A.1Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form.Grade 5
Missouri5.NBT.A.2Compare two numbers from billions to thousandths using the symbols >, = orGrade 5
Missouri5.NBT.A.3Understand that in a multi-digit number, a digit represents 1/10 times what it would represents in the place to its left.Grade 5
Missouri5.NBT.A.4Evaluate the value of powers of 10 and understand the relationship to the place value system.Grade 5
Missouri5.NBT.A.5Round numbers from billions to thousandths place.Grade 5
Missouri5.NBT.A.6Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution.Grade 5
Missouri5.NBT.A.7Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution.Grade 5
Missouri5.NBT.A.8Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution.Grade 5
Missouri5.NF.A.2Convert decimals to fractions and fractions to decimals.Grade 5
Missouri5.NF.A.3Compare and order fractions and/or decimals to the thousandths place using the symbols >, = orGrade 5
Missouri5.NF.B.5Justify the reasonableness of a product when multiplying with fractions.Grade 5
Missouri5.NF.B.6Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution.Grade 5
Missouri5.NF.B.7Extend the concept of multiplication to multiply a fraction or whole number by a fraction.Grade 5
Missouri5.NF.B.8Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.Grade 5
Missouri5.RA.A.1Investigate the relationship between two numeric patterns.Grade 5
Missouri5.RA.A.2Write a rule to describe or explain a given numeric pattern.Grade 5
Missouri5.RA.B.3Write, evaluate and interpret numeric expressions using the order of operations.Grade 5
Missouri5.RA.C.5Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals.Grade 5
Missouri6.EEI.A.2Create and evaluate expressions involving variables and whole number exponents.Grade 6
Missouri6.EEI.A.3Identify and generate equivalent algebraic expressions using mathematical properties.Grade 6
Missouri6.EEI.B.4Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true.Grade 6
Missouri6.EEI.B.5Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.Grade 6
Missouri6.EEI.B.7Solve one-step linear equations in one variable involving non-negative rational numbers.Grade 6
Missouri6.EEI.B.8Recognize that inequalities may have infinitely many solutions.Grade 6
Missouri6.GM.A.3Solve problems by graphing points in all four quadrants of the Cartesian coordinate plane.Grade 6
Missouri6.NS.A.1Compute and interpret quotients of positive fractions.Grade 6
Missouri6.NS.B.2Demonstrate fluency with division of multi-digit whole numbers.Grade 6
Missouri6.NS.C.5Use positive and negative numbers to represent quantities.Grade 6
Missouri6.NS.C.6Locate a rational number as a point on the number line.Grade 6
Missouri6.NS.C.7Understand that the absolute value of a rational number is its distance from 0 on the number line.Grade 6
Missouri6.RP.A.1Understand a ratio as a comparison of two quantities and represent these comparisons.Grade 6
Missouri6.RP.A.2Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate.Grade 6
Missouri6.RP.A.3Solve problems involving ratios and rates.Grade 6
Missouri7.EEI.A.1Apply properties of operations to simplify and to factor linear algebraic expressions with rational coefficients.Grade 7
Missouri7.EEI.B.3Solve multi-step problems posed with rational numbers.Grade 7
Missouri7.GM.A.1Solve problems involving scale drawings of real objects and geometric figures, including computing actual lengths and areas from a scale drawing and reproducing the drawing at a different scale.Grade 7
Missouri7.GM.A.2Use a variety of tools to construct geometric shapes.Grade 7
Missouri7.GM.B.5Use angle properties to write and solve equations for an unknown angle.Grade 7
Missouri7.NS.A.1Apply and extend previous understandings of numbers to add and subtract rational numbers.Grade 7
Missouri7.NS.A.2Apply and extend previous understandings of numbers to multiply and divide rational numbers.Grade 7
Missouri7.NS.A.3Solve problems involving the four arithmetic operations with rational numbers.Grade 7
Missouri7.RP.A.1Compute unit rates, including those that involve complex fractions, with like or different units.Grade 7
Missouri7.RP.A.2Recognize and represent proportional relationships between quantities.Grade 7
Missouri7.RP.A.3Solve problems involving ratios, rates, percentages and proportional relationships.Grade 7
Missouri8.DSP.A.1Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities.Grade 8
Missouri8.DSP.A.2Generate and use a trend line for bivariate data, and informally assess the fit of the line.Grade 8
Missouri8.EEI.A.3Express very large and very small quantities in scientific notation and approximate how many times larger one is than the other.Grade 8
Missouri8.EEI.A.4Use scientific notation to solve problems.Grade 8
Missouri8.EEI.B.6Apply concepts of slope and y-intercept to graphs, equations and proportional relationships.Grade 8
Missouri8.EEI.C.7Solve linear equations and inequalities in one variable.Grade 8
Missouri8.EEI.C.8Analyze and solve systems of linear equations.Grade 8
Missouri8.F.A.1Explore the concept of functions. (The use of function notation is not required.)Grade 8
Missouri8.F.A.2Compare characteristics of two functions each represented in a different way.Grade 8
Missouri8.F.A.3Investigate the differences between linear and nonlinear functions.Grade 8
Missouri8.F.B.4Use functions to model linear relationships between quantities.Grade 8
Missouri8.F.B.5Describe the functional relationship between two quantities from a graph or a verbal description.Grade 8
Missouri8.GM.A.1Verify experimentally the congruence properties of rigid transformations.Grade 8
Missouri8.GM.A.2Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image.Grade 8
Missouri8.GM.A.4Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.Grade 8
Missouri8.GM.B.7Use the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two- and three-dimensional contexts.Grade 8
Missouri8.GM.B.8Use the Pythagorean Theorem to find the distance between points in a Cartesian coordinate system.Grade 8
MissouriK.NBT.A.1Compose and decompose numbers from 11 to 19 into sets of tens with additional ones.Kindergarten
MissouriK.NS.A.1Count to 100 by ones and tens.Kindergarten
MissouriK.NS.A.2Count forward beginning from a given number between 1 and 20.Kindergarten
MissouriK.NS.A.4Read and write numerals and represent a number of objects from 0 to 20.Kindergarten
MissouriK.NS.B.5Say the number names when counting objects, in the standard order, pairing each object with one and only one number name and each number name with one and only one object.Kindergarten
MissouriK.NS.B.6Demonstrate that the last number name said tells the number of objects counted and the number of objects is the same regardless of their arrangement or the order in which they were counted.Kindergarten
MissouriK.NS.B.7Demonstrate that each successive number name refers to a quantity that is one larger than the previous number.Kindergarten
MissouriK.NS.B.9Demonstrate that a number can be used to represent how many are in a set.Kindergarten
MissouriK.NS.C.10Compare two or more sets of objects and identify which set is equal to, more than or less than the other.Kindergarten
MissouriK.NS.C.11Compare two numerals, between 1 and 10, and determine which is more than or less than the other.Kindergarten
MissouriK.RA.A.1Represent addition and subtraction within 10.Kindergarten
MissouriK.RA.A.2Demonstrate fluency for addition and subtraction within 5.Kindergarten
MissouriK.RA.A.3Decompose numbers less than or equal to 10 in more than one way.Kindergarten
MissouriK.RA.A.4Make 10 for any number from 1 to 9.Kindergarten
Nebraska11.2.1.bAnalyze a relation to determine if it is a function given graphs, tables, or algebraic notation.Algebra
Nebraska11.2.1.cClassify a function given graphs, tables, or algebraic notation, as linear, quadratic, or neither.Algebra
Nebraska11.2.1.eAnalyze and graph linear functions and inequalities (point-slope form, slope-intercept form, standard form, intercepts, rate of change, parallel and perpendicular lines, vertical and horizontal lines, and inequalities).Algebra
Nebraska11.2.1.gAnalyze and graph quadratic functions (standard form, vertex form, finding zeros, symmetry, transformations, determine intercepts, and minimums or maximums).Algebra
Nebraska11.2.2.eEvaluate expressions at specified values of their variables (polynomial, rational, radical, and absolute value).Algebra
Nebraska11.2.2.hAnalyze and solve systems of two linear equations and inequalities in two variables algebraically and graphically.Algebra
Nebraska11.2.2.jFactor polynomials to include factoring out monomial terms and factoring quadratic expressions.Algebra
Nebraska11.2.2.lMake the connection between the factors of a polynomial and the zeros of a polynomial.Algebra
Nebraska11.2.3.aAnalyze, model, and solve real-world problems using various representations (graphs, tables, linear equations and inequalities, systems of linear equations, quadratic, exponential, square root, and absolute value functions).Algebra
Nebraska11.4.2.iUsing scatter plots, analyze patterns and describe relationships in paired data.Algebra
Nebraska1.1.1.aCount to 120 by ones and tens, starting at any given number.Grade 1
Nebraska1.1.1.cWrite numerals to match a representation of a given set of objects for numbers up to 120.Grade 1
Nebraska1.1.1.dDemonstrate that each digit of a two-digit number represents amounts of tens and ones, knowing 10 can be considered as one unit made of ten ones which is called a ten and any two-digit number can be composed of some tens and some ones (e.g., 19 is one ten and nine ones, 83 is eight tens and three ones) and can be recorded as an equation (e.g., 19 = 10 + 9).Grade 1
Nebraska1.1.1.eDemonstrate that decade numbers represent a number of tens and 0 ones (e.g., 50 = 5 tens and 0 ones).Grade 1
Nebraska1.1.1.fCompare two two-digit numbers by using symbols and justify the comparison based on the number of tens and ones.Grade 1
Nebraska1.1.2.cFind the difference between two numbers that are multiples of 10, ranging from 10 - 90 using concrete models, drawings or strategies, and write the corresponding equation (e.g., 90 - 70 = 20).Grade 1
Nebraska1.1.2.dMentally find 10 more or 10 less than a two-digit number without having to count and explain the reasoning used (e.g., 33 is 10 less than 43).Grade 1
Nebraska1.1.2.eAdd within 100, which may include adding a two-digit number and a one-digit number, and adding a twodigit number and a multiple of ten using concrete models, drawings, and strategies which reflect understanding of place value.Grade 1
Nebraska1.2.1.aUse the meaning of the equal sign to determine if equations are true and give examples of equations that are true (e.g., 4 = 4, 6 = 7 - 1, 6 + 3 = 3 + 6, and 7 + 2 = 5 + 4)Grade 1
Nebraska1.2.1.bUse the relationship of addition and subtraction to solve subtraction problems (e.g., find 12 - 9 = ___, using the addition fact 9 + 3 = 12).Grade 1
Nebraska1.2.1.cFind numerical patterns to make connections between counting and addition and subtraction (e.g., adding two is the same as counting on two).Grade 1
Nebraska1.2.1.dDetermine the unknown whole number in an addition or subtraction equation (e.g. 7 + ? = 13).Grade 1
Nebraska1.2.2.aDecompose numbers and use the commutative and associative properties of addition to develop addition and subtraction strategies including (making 10Ís and counting on from the larger number) to add and subtract basic facts within 20 (e.g., decomposing to make 10, 7 + 5 = 7 + 3 + 2 = 10 + 2 = 12; using the commutative property to count on 2 + 6 = 6 + 2; and using the associative property to make 10, 5 + 3 + 7 = 5 + (3 + 7) = 5 + 10).Grade 1
Nebraska1.2.3.aSolve real-world problems involving addition and subtraction within 20 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 objects, drawings, and equations with a symbol for the unknown number to represent the problem).Grade 1
Nebraska1.3.3.bTell and write time to the half hour and hour using analog and digital clocks.Grade 1
Nebraska1.4.1.aOrganize and represent a data set with up to three categories using a picture graph.Grade 1
Nebraska1.4.2.aAsk and answer questions about the total number of data points, how many in each category, and compare categories by identifying how many more or less are in a particular category using a picture graph.Grade 1
Nebraska2.1.1.aCount within 1000, including skip-counting by 5s, 10s, and 100s starting at a variety of multiples of 5, 10 or 100.Grade 2
Nebraska2.1.1.bRead and write numbers within the range of 0 - 1,000 using standard, word, and expanded forms.Grade 2
Nebraska2.1.1.cDemonstrate that each digit of a three-digit number represents amounts of hundreds, tens and ones (e.g., 387 is 3 hundreds, 8 tens, 7 ones).Grade 2
Nebraska2.1.1.eCompare two three-digit numbers by using symbols and justify the comparison based on the meanings of the hundreds, tens, and ones.Grade 2
Nebraska2.1.2.bAdd and subtract within 100 using strategies based on place value, including the standard algorithm, properties of operations, and/or the relationship between addition and subtraction.Grade 2
Nebraska2.1.2.dAdd up to three two-digit numbers using strategies based on place value and understanding of properties.Grade 2
Nebraska2.1.2.eAdd and subtract within 1000, using concrete models, drawings, and strategies, which reflect understanding of place value and properties of operations.Grade 2
Nebraska2.2.3.aSolve real-world problems involving addition and subtraction within 100 in situations of addition and subtraction, including adding to, subtracting from, joining and separating, and comparing situations with unknowns in all positions using objects, models, drawings, verbal explanations, expressions and equations.Grade 2
Nebraska2.2.3.bCreate real-world problems to represent one- and two-step addition and subtraction within 100, with unknowns in all positions.Grade 2
Nebraska2.3.1.aRecognize and draw shapes having a specific number of angles, faces, or other attributes, including triangles, quadrilaterals, pentagons, and hexagons.Grade 2
Nebraska2.3.3.bIdentify and write time to five-minute intervals using analog and digital clocks and both a.m. and p.m.Grade 2
Nebraska2.4.1.aCreate and represent a data set using pictographs and bar graphs to represent a data set with up to four categories.Grade 2
Nebraska2.4.1.bCreate and represent a data set by making a line plot.Grade 2
Nebraska2.4.2.aInterpret data using bar graphs with up to four categories. Solve simple comparison problems using information from the graphs.Grade 2
Nebraska3.1.1.aRead, write and demonstrate multiple equivalent representations for numbers up to 100,000 using objects, visual representations, including standard form, word form, expanded form, and expanded notation.Grade 3
Nebraska3.1.1.cRound a whole number to the tens or hundreds place, using place value understanding or a visual representation.Grade 3
Nebraska3.1.1.dRepresent and understand a fraction as a number on a number line.Grade 3
Nebraska3.1.1.eExpress whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.Grade 3
Nebraska3.1.1.fShow and identify equivalent fractions using visual representations including pictures, manipulatives, and number lines.Grade 3
Nebraska3.1.1.gFind parts of a whole and parts of a set using visual representations.Grade 3
Nebraska3.1.1.iCompare and order fractions having the same numerators or denominators using visual representations, comparison symbols, and verbal reasoning.Grade 3
Nebraska3.1.2.cUse drawings, words, arrays, symbols, repeated addition, equal groups, and number lines to explain the meaning of multiplication.Grade 3
Nebraska3.1.2.eMultiply one digit whole numbers by multiples of 10 in the range of 10 to 90.Grade 3
Nebraska3.1.2.fUse objects, drawings, arrays, words and symbols to explain the relationship between multiplication and division (e.g., if 3 x 4 = 12 then 12  3 = 4).Grade 3
Nebraska3.1.2.gFluently (i.e. automatic recall based on understanding) multiply and divide within 100.Grade 3
Nebraska3.2.1.bInterpret a multiplication equation as equal groups (e.g., interpret 4 _ 6 as the total number of objects in four groups of six objects each). Represent verbal statements of equal groups as multiplication equations.Grade 3
Nebraska3.2.2.aApply the commutative, associative, and distributive properties as strategies to multiply and divide.Grade 3
Nebraska3.2.2.bSolve one-step whole number equations involving addition, subtraction, multiplication, or division, including the use of a letter to represent the unknown quantity.Grade 3
Nebraska3.3.1.aIdentify the number of sides, angles, and vertices of two-dimensional shapes.Grade 3
Nebraska3.3.3.bTell and write time to the minute using both analog and digital clocks.Grade 3
Nebraska3.3.3.eEstimate and measure length to the nearest half inch, quarter inch, and centimeter.Grade 3
Nebraska3.3.3.fUse concrete and pictorial models to measure areas in square units by counting square units.Grade 3
Nebraska3.3.3.gFind 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.Grade 3
Nebraska3.4.1.aCreate scaled pictographs and scaled bar graphs to represent a data setincluding data collected through observations, surveys, and experimentswith several categories.Grade 3
Nebraska3.4.1.bRepresent data using line plots where the horizontal scale is marked off in appropriate unitswhole numbers, halves, or quarters.Grade 3
Nebraska3.4.2.aSolve problems and make simple statements about quantity differences (e.g., how many more and how many less) using information represented in pictographs and bar graphs.Grade 3
Nebraska4.1.1.aRead, write, and demonstrate multiple equivalent representations for whole numbers up to one million and decimals to the hundredths, using objects, visual representations, standard form, word form, and expanded notation.Grade 4
Nebraska4.1.1.bRecognize a digit in one place represents ten times what it represents in the place to its right and 1/10 what it represents in the place to its left.Grade 4
Nebraska4.1.1.dDetermine whether a given whole number up to 100 is a multiple of a given one-digit number.Grade 4
Nebraska4.1.1.fCompare whole numbers up to one million and decimals through the hundredths place using >,Grade 4
Nebraska4.1.1.hUse decimal notation for fractions with denominators of 10 or 100.Grade 4
Nebraska4.1.1.iGenerate and explain equivalent fractions by multiplying by an equivalent fraction of 1.Grade 4
Nebraska4.1.1.jExplain how to change a mixed number to a fraction and how to change a fraction to a mixed number.Grade 4
Nebraska4.1.1.kCompare and order fractions having unlike numerators and unlike denominators using visual representations (number line), comparison symbols and verbal reasoning (e.g., using benchmarks or common numerators or common denominators).Grade 4
Nebraska4.1.1.lDecompose a fraction into a sum of fractions with the same denominator in more than one way and record each decomposition with an equation and a visual representation.Grade 4
Nebraska4.1.2.cMultiply a two-digit whole number by a two-digit whole number using the standard algorithm.Grade 4
Nebraska4.1.2.dDivide up to a four-digit whole number by a one-digit divisor with and without a remainder.Grade 4
Nebraska4.1.2.eUse drawings, words, and symbols to explain the meaning of addition and subtraction of fractions with like denominators.Grade 4
Nebraska4.1.2.hDetermine the reasonableness of whole number products and quotients in real-world problems using estimation, compatible numbers, mental computations, or other strategies.Grade 4
Nebraska4.2.1.bGenerate and analyze a number or shape pattern to follow a given rule, 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.Grade 4
Nebraska4.3.1.aRecognize angles as geometric shapes that are formed where two rays share a common endpoint.Grade 4
Nebraska4.3.1.cIdentify and draw points, lines, line segments, rays, angles, parallel lines, perpendicular lines, and intersecting lines, and recognize them in two-dimensional figures.Grade 4
Nebraska4.3.1.dClassify two-dimensional shapes based on the presence or absence of parallel and perpendicular lines, or the presence or absence of specific angles.Grade 4
Nebraska4.3.3.bIdentify and use the appropriate tools, operations, and units of measurement, both customary and metric, to solve real-world problems involving time, length, weight, mass, capacity, and volume.Grade 4
Nebraska4.3.3.cGenerate simple conversions from a larger unit to a smaller unit within the customary and metric systems of measurement.Grade 4
Nebraska4.4.1.aRepresent data using line plots where the horizontal scale is marked off in appropriate units (e.g., whole numbers, halves, quarters, or eighths).Grade 4
Nebraska5.1.1.bCompare whole numbers, fractions, mixed numbers, and decimals through the thousandths place and represent comparisons using symbols , or =.Grade 5
Nebraska5.1.2.bDivide four-digit whole numbers by a two-digit divisor, with and without remainders using the standard algorithm.Grade 5
Nebraska5.1.2.cMultiply a whole number by a fraction or a fraction by a fraction using models and visual representations.Grade 5
Nebraska5.1.2.dDivide a unit fraction by a whole number and a whole number by a unit fraction.Grade 5
Nebraska5.1.2.eExplain division of a whole number by a fraction using models and visual representations.Grade 5
Nebraska5.1.2.fInterpret a fraction as division of the numerator by the denominator.Grade 5
Nebraska5.1.2.gAdd, subtract, multiply, and divide decimals to the hundredths using concrete models or drawings and strategies based on place value, properties of operations (i.e. Commutative, Associative, Distributive, Identity, Zero), and/or relationships between operations.Grade 5
Nebraska5.2.1.aForm ordered pairs from a rule such as y=2x, and graph the ordered pairs on a coordinate plane.Grade 5
Nebraska5.2.2.aInterpret and evaluate numerical or algebraic expressions using order of operations (excluding exponents).Grade 5
Nebraska5.3.2.aIdentify the origin, x axis, and y axis of the coordinate plane.Grade 5
Nebraska5.3.2.bGraph and name points in the first quadrant of the coordinate plane using ordered pairs of whole numbers.Grade 5
Nebraska6.1.1.cCompare and order rational numbers both on the number line and not on the number line.Grade 6
Nebraska6.1.1.hCompare and order integers and absolute value both on the number line and not on the number line.Grade 6
Nebraska6.2.1.aCreate algebraic expressions (e.g., one operation, one variable as well as multiple operations, one variable) from word phrases.Grade 6
Nebraska6.2.1.bRecognize and generate equivalent algebraic expressions involving distributive property and combining like terms.Grade 6
Nebraska6.2.2.bUse substitution to determine if a given value for a variable makes an equation or inequality true.Grade 6
Nebraska6.2.2.cEvaluate numerical expressions, including absolute value and exponents, with respect to order of operations.Grade 6
Nebraska6.2.2.dGiven the value of the variable, evaluate algebraic expressions (which may include absolute value) with respect to order of operations (non-negative rational numbers).Grade 6
Nebraska6.2.2.fUse equivalent ratios relating quantities with whole numbers to create a table. Find missing values in the table.Grade 6
Nebraska6.2.2.gRepresent inequalities on a number line (e.g., graph x > 3).Grade 6
Nebraska6.2.3.aWrite equations (e.g., one operation, one variable) to represent real-world problems involving nonnegative rational numbers.Grade 6
Nebraska6.3.2.aIdentify the ordered pair of a given point in the coordinate plane.Grade 6
Nebraska6.3.2.bPlot the location of an ordered pair in the coordinate plane.Grade 6
Nebraska6.3.2.dDraw polygons in the coordinate plane given coordinates for the vertices.Grade 6
Nebraska6.3.2.eCalculate vertical and horizontal distances in the coordinate plane to find perimeter and area.Grade 6
Nebraska6.4.1.aRepresent data using line plots, dot plots, box plots, and histograms.Grade 6
Nebraska7.1.2.aSolve problems using proportions and ratios (e.g., cross products, percents, tables, equations, and graphs).Grade 7
Nebraska7.1.2.cApply properties of operations as strategies for problem solving with rational numbers.Grade 7
Nebraska7.2.2.bUse factoring and properties of operations to create equivalent algebraic expressions (e.g., 2x + 6 = 2(x + 3)).Grade 7
Nebraska7.2.2.cGiven the value of the variable(s), evaluate algebraic expressions (including absolute value).Grade 7
Nebraska7.2.3.cSolve real-world problems with equations that involve rational numbers in any form.Grade 7
Nebraska7.2.3.eUse proportional relationships to solve real-world problems, including percent problems, (e.g., % increase, % decrease, mark-up, tip, simple interest).Grade 7
Nebraska7.3.1.aApply and use properties of adjacent, complementary, supplementary, and vertical angles to find missing angle measures.Grade 7
Nebraska7.3.1.bDraw triangles (freehand, using a ruler and a protractor, and using technology) with given conditions of three measures of angles or sides, and notice when the conditions determine a unique triangle, more than one triangle, or no triangle.Grade 7
Nebraska8.1.1.bRepresent numbers with positive and negative exponents and in scientific notation.Grade 8
Nebraska8.2.1.aCreate algebraic expressions, equations, and inequalities (e.g., two-step, one variable) from word phrases, tables, and pictures.Grade 8
Nebraska8.2.1.bDetermine and describe the rate of change for given situations through the use of tables and graphs.Grade 8
Nebraska8.2.1.cDescribe equations and linear graphs as having one solution, no solution, or infinitely many solutions.Grade 8
Nebraska8.2.2.aSolve multi-step equations involving rational numbers with the same variable appearing on both sides of the equal sign.Grade 8
Nebraska8.2.2.bSolve two-step inequalities involving rational numbers and represent solutions on a number line.Grade 8
Nebraska8.3.2.aPerform and describe positions and orientation of shapes under single transformations including rotations (in multiples of 90 degrees about the origin), translations, reflections, and dilations on and off the coordinate plane.Grade 8
Nebraska8.3.2.bFind congruent two-dimensional figures and define congruence in terms of a series of transformations.Grade 8
Nebraska8.3.2.cFind similar two-dimensional figures and define similarity in terms of a series of transformations.Grade 8
Nebraska8.3.3.bApply the Pythagorean Theorem to find side lengths of triangles and to solve real-world problems.Grade 8
Nebraska8.3.3.cFind the distance between any two points on the coordinate plane using the Pythagorean Theorem.Grade 8
Nebraska8.4.2.aSolve problems and make predictions using an approximate line of best fit.Grade 8
Nebraska0.1.1.aPerform the counting sequence by counting forward from any given number to 100, by ones. Count by tens to 100 starting at any decade number.Kindergarten
Nebraska0.1.1.bDemonstrate cardinality (i.e. the last number name said indicates the number of objects counted), regardless of the arrangement or order in which the objects were counted.Kindergarten
Nebraska0.1.1.cUse one-to-one correspondence (pairing each object with one and only one spoken number name, and each spoken number name with one and only one object) when counting objects to show the relationship between numbers and quantities of 0 to 20.Kindergarten
Nebraska0.1.1.dDemonstrate the relationship between whole numbers, knowing each sequential number name refers to a quantity that is one larger.Kindergarten
Nebraska0.1.1.eCount 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
Nebraska0.1.1.fWrite numbers 0 to 20 and represent a number of objects with a written numeral 0 to 20.Kindergarten
Nebraska0.1.1.gCompose and decompose numbers from 11 to 19 into ten ones and some more ones by a drawing, model, or equation (e.g., 14 = 10 + 4) to record each composition and decomposition.Kindergarten
Nebraska0.1.1.hCompare the number of objects in two groups by identifying the comparison as greater than, less than, or equal to by using strategies of matching and counting.Kindergarten
Nebraska0.1.1.iCompare the value of two written numerals between 1 and 10.Kindergarten
Nebraska0.1.2.aFluently (i.e. automatic recall based on understanding) add and subtract within 5.Kindergarten
Nebraska0.2.1.aDecompose numbers less than or equal to 10 into pairs in more than one way, showing each decomposition with a model, drawing, or equation (e.g., 7 = 4 + 3 and 7 = 1 + 6).Kindergarten
Nebraska0.2.1.bFor any number from 1 to 9, find the number that makes 10 when added to the given number, showing the answer with a model, drawing, or equation.Kindergarten
Nebraska0.2.3.aSolve real-world problems that involve addition and subtraction within 10 (e.g., by using objects, drawings or equations to represent the problem).Kindergarten
OklahomaA1.A.1.3Analyze and solve real-world and mathematical problems involving systems of linear equations with a maximum of two variables by graphing (may include graphing calculator or other appropriate technology), substitution, and elimination. Interpret the solutions in the original context.Algebra 1
OklahomaA1.A.3.2Simplify polynomial expressions by adding, subtracting, or multiplying.Algebra 1
OklahomaA1.A.3.3Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.Algebra 1
OklahomaA1.A.4.1Calculate and interpret slope and the x- and y-intercepts of a line using a graph, an equation, two points, or a set of data points to solve realworld and mathematical problems.Algebra 1
OklahomaA1.A.4.4Translate between a graph and a situation described qualitatively.Algebra 1
OklahomaA1.D.1.1Describe a data set using data displays, describe and compare data sets using summary statistics, including measures of central tendency, location, and spread. Know how to use calculators, spreadsheets, or other appropriate technology to display data and calculate summary statistics.Algebra 1
OklahomaA1.D.1.2Collect data and use scatterplots to analyze patterns and describe linear relationships between two variables. Using graphing technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.Algebra 1
OklahomaA1.F.1.3Write linear functions, using function notation, to model real-world and mathematical situations.Algebra 1
OklahomaA1.F.3.1Identify and generate equivalent representations of linear equations, graphs, tables, and real-world situations.Algebra 1
OklahomaA1.F.3.2Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of real-world and mathematical problems.Algebra 1
Oklahoma1.D.1.1Collect, sort, and organize data in up to three categories using representations (e.g., tally marks, tables, Venn diagrams).Grade 1
Oklahoma1.D.1.2Use data to create picture and bar-type graphs to demonstrate one-to-one correspondence.Grade 1
Oklahoma1.D.1.3Draw conclusions from picture and bar-type graphs.Grade 1
Oklahoma1.GM.1.1Identify trapezoids and hexagons by pointing to the shape when given the name.Grade 1
Oklahoma1.GM.3.1Tell time to the hour and half-hour (analog and digital).Grade 1
Oklahoma1.N.1.1Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements.Grade 1
Oklahoma1.N.1.2Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones.Grade 1
Oklahoma1.N.1.3Read, write, discuss, and represent whole numbers up to 100. 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
Oklahoma1.N.1.4Count forward, with and without objects, from any given number up to 100 by 1s, 2s, 5s and 10s.Grade 1
Oklahoma1.N.1.5Find a number that is 10 more or 10 less than a given number up to 100.Grade 1
Oklahoma1.N.1.6Compare and order whole numbers from 0 to 100.Grade 1
Oklahoma1.N.1.8Use objects to represent and use words to describe the relative size of numbers, such as more than, less than, and equal to.Grade 1
Oklahoma1.N.2.1Represent and solve real-world and mathematical problems using addition and subtraction up to ten.Grade 1
Oklahoma1.N.2.3Demonstrate fluency with basic addition facts and related subtraction facts up to 10.Grade 1
Oklahoma2.A.2.1Use objects and number lines to represent number sentences.Grade 2
Oklahoma2.A.2.2Generate real-world situations to represent number sentences and vice versa.Grade 2
Oklahoma2.A.2.3Apply commutative and identity properties and number sense to find values for unknowns that make number sentences involving addition and subtraction true or false.Grade 2
Oklahoma2.D.1.1Explain that the length of a bar in a bar graph or the number of objects in a picture graph represents the number of data points for a given category.Grade 2
Oklahoma2.D.1.2Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s or 10s.Grade 2
Oklahoma2.D.1.3Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one.Grade 2
Oklahoma2.GM.1.2Describe, compare, and classify two-dimensional figures according to their geometric attributes.Grade 2
Oklahoma2.GM.3.1Read and write time to the quarter-hour on an analog and digital clock. Distinguish between a.m. and p.m.Grade 2
Oklahoma2.N.1.1Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines and manipulatives.Grade 2
Oklahoma2.N.1.2Use knowledge of number relationships to locate the position of a given whole number on an open number line up to 100.Grade 2
Oklahoma2.N.1.3Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1,000 is 10 hundreds.Grade 2
Oklahoma2.N.1.4Find 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
Oklahoma2.N.1.5Recognize when to round numbers to the nearest 10 and 100.Grade 2
Oklahoma2.N.1.6Use place value to compare and order whole numbers up to 1,000 using comparative language, numbers, and symbols (e.g., 425 > 276, 73 < 107, page 351 comes after page 350, 753 is between 700 and 800).Grade 2
Oklahoma2.N.2.1Use the relationship between addition and subtraction to generate basic facts up to 20.Grade 2
Oklahoma2.N.2.2Demonstrate fluency with basic addition facts and related subtraction facts up to 20.Grade 2
Oklahoma2.N.2.3Estimate sums and differences up to 100.Grade 2
Oklahoma2.N.2.4Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers.Grade 2
Oklahoma2.N.2.5Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits.Grade 2
Oklahoma3.A.2.2Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems.Grade 3
Oklahoma3.D.1.1Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals.Grade 3
Oklahoma3.D.1.2Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals.Grade 3
Oklahoma3.GM.1.3Classify angles as acute, right, obtuse, and straight.Grade 3
Oklahoma3.GM.2.2Develop and use formulas to determine the area of rectangles. 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 3
Oklahoma3.GM.2.3Choose an appropriate measurement instrument and measure the length of objects to the nearest whole centimeter or meter.Grade 3
Oklahoma3.GM.2.4Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch.Grade 3
Oklahoma3.GM.2.8Find the area of two-dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps.Grade 3
Oklahoma3.GM.3.1Read and write time to the nearest 5-minute (analog and digital).Grade 3
Oklahoma3.GM.3.2Determine the solutions to problems involving addition and subtraction of time in intervals of 5 minutes, up to one hour, using pictorial models, number line diagrams, or other tools.Grade 3
Oklahoma3.N.1.1Read, write, discuss, and represent whole numbers up to 10,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives.Grade 3
Oklahoma3.N.1.2Use place value to describe whole numbers between 1,000 and 10,000 in terms of ten thousands, thousands, hundreds, tens and ones, including expanded form.Grade 3
Oklahoma3.N.1.3Find 1,000 more or 1,000 less than a given four- or five-digit number. Find 100 more or 100 less than a given four- or five-digit number.Grade 3
Oklahoma3.N.1.4Use place value to compare and order whole numbers up to 10,000, using comparative language, numbers, and symbols.Grade 3
Oklahoma3.N.2.1Represent 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.Grade 3
Oklahoma3.N.2.2Demonstrate fluency of multiplication facts with factors up to 10.Grade 3
Oklahoma3.N.2.3Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers.Grade 3
Oklahoma3.N.2.4Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences.Grade 3
Oklahoma3.N.2.5Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results.Grade 3
Oklahoma3.N.2.6Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups.Grade 3
Oklahoma3.N.2.7Recognize the relationship between multiplication and division to represent and solve real-world problems.Grade 3
Oklahoma3.N.2.8Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number.Grade 3
Oklahoma3.N.3.2Construct fractions using length, set, and area models.Grade 3
Oklahoma3.N.3.3Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions.Grade 3
Oklahoma3.N.3.4Use models and number lines to order and compare fractions that are related to the same whole.Grade 3
Oklahoma4.A.1.1Create an input/output chart or table to represent or extend a numerical pattern.Grade 4
Oklahoma4.A.1.2Describe the single operation rule for a pattern from an input/output table or function machine involving any operation of a whole number.Grade 4
Oklahoma4.A.1.3Create growth patterns involving geometric shapes and define the single operation rule of the pattern.Grade 4
Oklahoma4.A.2.1Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true.Grade 4
Oklahoma4.D.1.1Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units.Grade 4
Oklahoma4.D.1.2Use tables, bar graphs, timelines, and Venn diagrams to display data sets. The data may include benchmark fractions or decimals.Grade 4
Oklahoma4.D.1.3Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot.Grade 4
Oklahoma4.GM.1.1Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts.Grade 4
Oklahoma4.GM.1.2Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts.Grade 4
Oklahoma4.GM.2.1Measure angles in geometric figures and real-world objects with a protractor or angle ruler.Grade 4
Oklahoma4.GM.2.4Choose an appropriate instrument and measure the length of an object to the nearest whole centimeter or quarter-inch.Grade 4
Oklahoma4.GM.2.5Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric).Grade 4
Oklahoma4.GM.3.2Solve problems involving the conversion of one measure of time to another.Grade 4
Oklahoma4.N.1.1Demonstrate fluency with multiplication and division facts with factors up to 12.Grade 4
Oklahoma4.N.1.2Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000.Grade 4
Oklahoma4.N.1.3Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms.Grade 4
Oklahoma4.N.1.4Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns.Grade 4
Oklahoma4.N.1.6Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties).Grade 4
Oklahoma4.N.1.7Determine the unknown addend or factor in equivalent and non-equivalent expressions (e.g., 5 + 6 = 4 + ? , 3 x 8 < 3 x ?).Grade 4
Oklahoma4.N.2.1Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines).Grade 4
Oklahoma4.N.2.2Use benchmark fractions to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols.Grade 4
Oklahoma4.N.2.3Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations.Grade 4
Oklahoma4.N.2.4Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations.Grade 4
Oklahoma4.N.2.5Represent tenths and hundredths with concrete models, making connections between fractions and decimals.Grade 4
Oklahoma4.N.2.6Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money.Grade 4
Oklahoma4.N.2.7Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.Grade 4
Oklahoma4.N.2.8Compare benchmark fractions and decimals in real-world and mathematical situations.Grade 4
Oklahoma5.A.1.1Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about real-world and mathematical problems.Grade 5
Oklahoma5.A.1.2Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates.Grade 5
Oklahoma5.A.2.1Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents).Grade 5
Oklahoma5.A.2.3Evaluate expressions involving variables when values for the variables are given.Grade 5
Oklahoma5.GM.1.1Describe, classify and construct triangles, including equilateral, right, scalene, and isosceles triangles. Recognize triangles in various contexts.Grade 5
Oklahoma5.GM.3.1Measure and compare angles according to size.Grade 5
Oklahoma5.N.1.1Estimate solutions to division problems in order to assess the reasonableness of results.Grade 5
Oklahoma5.N.1.2Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.Grade 5
Oklahoma5.N.1.3Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution.Grade 5
Oklahoma5.N.2.1Represent decimal fractions using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals.Grade 5
Oklahoma5.N.2.2Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions.Grade 5
Oklahoma5.N.2.3Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line.Grade 5
Oklahoma5.N.2.4Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts.Grade 5
Oklahoma6.A.1.1Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.Grade 6
Oklahoma6.A.1.2Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.Grade 6
Oklahoma6.A.1.3Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.Grade 6
Oklahoma6.A.2.1Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.Grade 6
Oklahoma6.A.3.2Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = q and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.Grade 6
Oklahoma6.GM.2.1Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.Grade 6
Oklahoma6.GM.4.2Recognize that translations, reflections, and rotations preserve congruency and use them to show that two figures are congruent.Grade 6
Oklahoma6.N.1.1Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.Grade 6
Oklahoma6.N.1.2Compare and order positive rational numbers, represented in various forms, or integers using the symbols , and =.Grade 6
Oklahoma6.N.2.3Add and subtract integers; use efficient and generalizable procedures including but not limited to standard algorithms.Grade 6
Oklahoma6.N.3.1Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different.Grade 6
Oklahoma6.N.3.2Determine the unit rate for ratios.Grade 6
Oklahoma6.N.3.3Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.Grade 6
Oklahoma6.N.3.4Use multiplicative reasoning and representations to solve ratio and unit rate problems.Grade 6
Oklahoma6.N.4.1Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.Grade 6
Oklahoma6.N.4.2Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.Grade 6
Oklahoma6.N.4.3Multiply and divide fractions and decimals using efficient and generalizable procedures.Grade 6
Oklahoma6.N.4.4Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.Grade 6
Oklahoma7.A.1.1Describe that the relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx; distinguish proportional relationships from other relationships, including inversely proportional relationships.Grade 7
Oklahoma7.A.1.2Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where both r and the slope are the unit rate (constant of proportionality, k).Grade 7
Oklahoma7.A.2.1Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations.Grade 7
Oklahoma7.A.2.2Solve multi-step problems involving proportional relationships involving distance-time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real-world and mathematical situations.Grade 7
Oklahoma7.A.2.3Use proportional reasoning to solve real-world and mathematical problems involving ratios.Grade 7
Oklahoma7.A.2.4Use proportional reasoning to assess the reasonableness of solutions.Grade 7
Oklahoma7.A.3.1Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers.Grade 7
Oklahoma7.A.3.2Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x + p > q and x + p < q, where p, and q are nonnegative rational numbers.Grade 7
Oklahoma7.A.4.1Use properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.Grade 7
Oklahoma7.A.4.2Apply understanding of order of operations and grouping symbols when using calculators and other technologies.Grade 7
Oklahoma7.GM.4.1Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations.Grade 7
Oklahoma7.GM.4.2Apply proportions, ratios, and scale factors to solve problems involving scale drawings and determine side lengths and areas of similar,triangles and rectangles.Grade 7
Oklahoma7.GM.4.3Graph and describe translations and reflections of figures on a coordinate plane and determine the coordinates of the vertices of the figure after the transformation.Grade 7
Oklahoma7.N.1.2Compare and order rational numbers expressed in various forms using the symbols , and =.Grade 7
Oklahoma7.N.1.3Recognize and generate equivalent representations of rational numbers, including equivalent fractions.Grade 7
Oklahoma7.N.2.1Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results.Grade 7
Oklahoma7.N.2.2Illustrate multiplication and division of integers using a variety of representations.Grade 7
Oklahoma7.N.2.3Solve real-world and mathematical problems involving addition, subtraction, multiplication and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms.Grade 7
Oklahoma7.N.2.5Solve real-world and mathematical problems involving calculations with rational numbers and positive integer exponents.Grade 7
Oklahoma7.N.2.6Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value.Grade 7
OklahomaK.N.1.1Count aloud forward in sequence to 100 by 1Ís and 10Ís.Kindergarten
OklahomaK.N.1.2Recognize that a number can be used to represent how many objects are in a set up to 10.Kindergarten
OklahomaK.N.1.5Count forward, with and without objects, from any given number up to 10.Kindergarten
OklahomaK.N.1.6Read, write, discuss, and represent whole numbers from 0 to at least 10. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives.Kindergarten
OklahomaK.N.1.7Find a number that is 1 more or 1 less than a given number up to 10.Kindergarten
OklahomaK.N.1.8Using the words more than, less than or equal to compare and order whole numbers, with and without objects, from 0 to 10.Kindergarten
OklahomaK.N.2.1Compose and decompose numbers up to 10 with objects and pictures.Kindergarten
OklahomaK.N.3.1Distribute equally a set of objects into at least two smaller equal sets.Kindergarten
OklahomaPA.A.1.1Recognize 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.Pre-Algebra
OklahomaPA.A.1.2Use linear functions to represent and explain real-world and mathematical situations.Pre-Algebra
OklahomaPA.A.1.3Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a straight line.Pre-Algebra
OklahomaPA.A.2.1Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.Pre-Algebra
OklahomaPA.A.2.2Identify, describe, and analyze linear relationships between two variables.Pre-Algebra
OklahomaPA.A.3.1Use substitution to simplify and evaluate algebraic expressions.Pre-Algebra
OklahomaPA.A.3.2Justify steps in generating equivalent expressions by identifying the properties used, including the properties of operations (associative, commutative, and distributive laws) and the order of operations, including grouping symbols.Pre-Algebra
OklahomaPA.A.4.1Illustrate, write, and solve mathematical and real-world problems using linear equations with one variable with one solution, infinitely many solutions, or no solutions. Interpret solutions in the original context.Pre-Algebra
OklahomaPA.D.1.3Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit, make statements about average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels and units.Pre-Algebra
OklahomaPA.GM.1.1Informally justify the Pythagorean Theorem using measurements, diagrams, or dynamic software and use the Pythagorean Theorem to solve problems in two and three dimensions involving right triangles.Pre-Algebra
OklahomaPA.GM.1.2Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.Pre-Algebra
OklahomaPA.N.1.2Express and compare approximations of very large and very small numbers using scientific notation.Pre-Algebra
OklahomaPA.N.1.3Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation.Pre-Algebra
OntarioA.3.2.1Interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant.Algebra
OntarioA.3.3.1Construct tables of values, graphs, and equations, using a variety of tools (e.g., graphing calculators, spreadsheets, graphing software, paper and pencil), to represent linear relations derived from descriptions of realistic situations.Algebra
OntarioA.3.3.2Construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources.Algebra
OntarioA.3.3.3Identify, through investigation, some properties of linear relations (i.e., numerically, the first difference is a constant, which represents a constant rate of change; graphically, a straight line represents the relation), and apply these properties to determine whether a relation is linear or non-linear.Algebra
OntarioA.3.3.4Compare the properties of direct variation and partial variation in applications, and identify the initial value.Algebra
OntarioA.3.3.5Determine the equation of a line of best fit for a scatter plot, using an informal process.Algebra
OntarioA.3.4.1Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation.Algebra
OntarioA.3.4.3Determine other representations of a linear relation, given one representation.Algebra
OntarioA.3.4.4Describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied.Algebra
OntarioA.4.2.1Determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations.Algebra
OntarioA.4.2.2Identify, through investigation, the equation of a line in any of the forms y = mx + b, Ax + By + C = 0, x = a, y = b.Algebra
OntarioA.4.3.1Determine, through investigation, various formulas for the slope of a line segment or a line and use the formulas to determine the slope of a line segment or a line.Algebra
OntarioA.4.3.2Identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b.Algebra
OntarioA.4.3.3Determine, through investigation, connections among the representations of a constant rate of change of a linear relation.Algebra
OntarioA.4.3.4Identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicularity), using graphing technology to facilitate investigations, where appropriate.Algebra
OntarioA.4.4.1Graph lines by hand, using a variety of techniques.Algebra
OntarioA.4.4.2Determine the equation of a line from information about the line.Algebra
Ontario1.2.2.1Represent, compare, and order whole numbers to 50, using a variety of tools (e.g., connecting cubes, ten frames, base ten materials, number lines, hundreds charts) and contexts (e.g., real-life experiences, number stories)Grade 1
Ontario1.2.2.8Compose and decompose numbers up to 20 in a variety of ways, using concrete materials (e.g., 7 can be decomposed using connecting cubes into 6 and 1, or 5 and 2, or 4 and 3)Grade 1
Ontario1.2.2.9Divide whole objects into parts and identify and describe, through investigation, equal-sized parts of the whole, using fractional names (e.g., halves; fourths or quarters).Grade 1
Ontario1.2.3.1Demonstrate, using concrete materials, the concept of one-to-one correspondence between number and objects when countingGrade 1
Ontario1.2.3.2Count forward by 1's, 2's, 5's, and 10's to 100, using a variety of tools and strategies (e.g., move with steps; skip count on a number line; place counters on a hundreds chart; connect cubes to show equal groups; count groups of pennies, nickels, or dimes)Grade 1
Ontario1.2.3.3Count backwards by 1's from 20 and any number less than 20 (e.g., count backwards from 18 to 11), with and without the use of concrete materials and number linesGrade 1
Ontario1.2.4.1Solve a variety of problems involving the addition and subtraction of whole numbers to 20, using concrete materials and drawings (e.g., pictures, number lines) (Sample problem: Miguel has 12 cookies. Seven cookies are chocolate. Use counters to determine how many cookies are not chocolate.)Grade 1
Ontario1.2.4.2Solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of mental strategies (e.g., one more than, one less than, counting on, counting back, doubles)Grade 1
Ontario1.3.2.7Read demonstration digital and analogue clocks, and use them to identify benchmark times (e.g., times for breakfast, lunch, dinner; the start and end of school; bedtime) and to tell and write time to the hourGrade 1
Ontario1.4.2.1identify and describe common two dimensional shapes (e.g., circles, triangles, rectangles, squares) and sort and classify them by their attributes (e.g., colour; size; texture; number of sides), using concrete materials and pictorial representationsGrade 1
Ontario1.5.3.1Create a set in which the number of objects is greater than, less than, or equal to the number of objects in a given setGrade 1
Ontario1.5.3.3Determine, through investigation using a balance model and whole numbers to 10, the number of identical objects that must be added or subtracted to establish equalityGrade 1
Ontario1.6.2.2Collect and organize primary data (e.g., data collected by the class) that is categorical (i.e., that can be organized into categories based on qualities such as colour or hobby), and display the data using one-to-one correspondence, prepared templates of concrete graphs and pictographs (with titles and labels), and a variety of recording methods (e.g., arranging objects, placing stickers, drawing pictures, making tally marks)Grade 1
Ontario2.2.2.1Represent, compare, and order whole numbers to 100, including money amounts to 100¢, using a variety of tools (e.g., ten frames, base ten materials, coin manipulatives, number lines, hundreds charts and hundreds carpets)Grade 2
Ontario2.2.2.3Compose and decompose two-digit numbers in a variety of ways, using concrete materials (e.g., place 42 counters on ten frames to show 4 tens and 2 ones; compose 37¢ using one quarter, one dime, and two pennies) (Sample problem: Use base ten blocks to show 60 in different ways.)Grade 2
Ontario2.2.2.4Determine, using concrete materials, the ten that is nearest to a given two-digit number, and justify the answer (e.g., use counters on ten frames to determine that 47 is closer to 50 than to 40)Grade 2
Ontario2.2.3.1Count forward by 1's, 2's, 5's, 10's, and 25's to 200, using number lines and hundreds charts, starting from multiples of 1, 2, 5, and 10 (e.g., count by 5's from 15; count by 25's from 125)Grade 2
Ontario2.2.3.2Count backwards by 1's from 50 and any number less than 50, and count backwards by 10's from 100 and any number less than 100, using number lines and hundreds charts (Sample problem: Count backwards from 87 on a hundreds carpet, and describe any patterns you see.)Grade 2
Ontario2.2.4.3Represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups (e.g., use counters to show that 3 groups of 2 is equal to 2 + 2 + 2 and to 3 x 2)Grade 2
Ontario2.3.2.2Estimate and measure length, height, and distance, using standard units (i.e., centimetre, metre) and non-standard unitsGrade 2
Ontario2.3.2.3Record and represent measurements of length, height, and distance in a variety of waysGrade 2
Ontario2.3.2.8Tell and write time to the quarter-hour, using demonstration digital and analogue clocks (e.g. My clock shows the time recess will start [10:00], and my friendÍs clock shows the time recess will end [10:15].)Grade 2
Ontario2.4.2.2identify and describe various polygons (i.e., triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons) and sort and classify them by their geometric properties (i.e., number of sides or number of vertices), using concrete materials and pictorial representationsGrade 2
Ontario2.5.2.2Identify, describe, and create, through investigation, growing patterns and shrinking patterns involving addition and subtraction, with and without the use of calculators (e.g., 3 + 1 = 4, 3 + 2 = 5, 3 + 3 = 6)Grade 2
Ontario2.5.3.2Represent, through investigation with concrete materials and pictures, two number expressions that are equal, using the equal sign (e.g., I can break a train of 10 cubes into 4 cubes and 6 cubes. I can also break 10 cubes into 7 cubes and 3 cubes. This means 4 + 6 = 7 + 3)Grade 2
Ontario2.6.2.3Collect and organize primary data (e.g., data collected by the class) that is categorical or discrete (i.e., that can be counted, such as the number of students absent), and display the data using one-to-one correspondence in concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers (e.g., tally charts, diagrams), with appropriate titles and labels and with labels ordered appropriately along horizontal axes, as neededGrade 2
Ontario2.6.3.2Pose and answer questions about class generated data in concrete graphs, pictographs, line plots, simple bar graphs, and tally chartsGrade 2
Ontario3.2.2.1Represent, compare, and order whole numbers to 1000, using a variety of tools (e.g., base ten materials or drawings of them, number lines with increments of 100 or other appropriate amounts)Grade 3
Ontario3.2.2.3Identify and represent the value of a digit in a number according to its position in the number (e.g., use base ten materials to show that the 3 in 324 represents 3 hundreds)Grade 3
Ontario3.2.2.4Compose and decompose three-digit numbers into hundreds, tens, and ones in a variety of ways, using concrete materials (e.g., use base ten materials to decompose 327 into 3 hundreds, 2 tens, and 7 ones, or into 2 hundreds, 12 tens, and 7 ones)Grade 3
Ontario3.2.2.5Round two-digit numbers to the nearest ten, in problems arising from real-life situationsGrade 3
Ontario3.2.2.7Divide whole objects and sets of objects into equal parts, and identify the parts using fractional names (e.g., one half; three thirds; two fourths or two quarters), without using numbers in standard fractional notationGrade 3
Ontario3.2.3.1Count forward by 1's, 2's, 5's, 10's, and 100's to 1000 from various starting points, and by 25's to 1000 starting from multiples of 25, using a variety of tools and strategies (e.g., skip count with and without the aid of a calculator; skip count by 10's using dimes)Grade 3
Ontario3.2.3.2Count backwards by 2's, 5's, and 10's from 100 using multiples of 2, 5, and 10 as starting points, and count backwards by 100's from 1000 and any number less than 1000, using a variety of tools (e.g., number lines, calculators, coins) and strategies.Grade 3
Ontario3.2.4.1Solve problems involving the addition and subtraction of two-digit numbers, using a variety of mental strategies (e.g., to add 37 + 26, add the tens, add the ones, then combine the tens and ones, like this: 30 + 20 = 50, 7 + 6 = 13, 50 + 13 = 63)Grade 3
Ontario3.2.4.2Add and subtract three-digit numbers, using concrete materials, student-generated algorithms, and standard algorithmsGrade 3
Ontario3.2.4.6Multiply to 7 x 7 and divide to 81 Ö 9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting)Grade 3
Ontario3.3.2.2Draw items using a ruler, given specific lengths in centimetresGrade 3
Ontario3.3.2.3Read time using analogue clocks, to the nearest five minutes, and using digital clocks (e.g., 1:23 means twenty-three minutes after one oÍclock), and represent time in 12-hour notationGrade 3
Ontario3.4.2.1Use a reference tool to identify right angles and to describe angles as greater than, equal to, or less than a right angleGrade 3
Ontario3.4.2.2Identify and compare various polygons (i.e., triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons) and sort them by their geometric properties (i.e., number of sides; side lengths; number of interior angles; number of right angles)Grade 3
Ontario3.5.3.2Determine, the missing number in equations involving addition and subtraction of one- and two-digit numbers, using a variety of tools and strategies (e.g., modeling with concrete materials, using guess and check with and without the aid of a calculator) (Sample problem: What is the missing number in the equation 25 - 4 = 15 + ??)Grade 3
Ontario3.6.2.3Collect and organize categorical or discrete primary data and display the data in charts, tables, and graphs (including vertical and horizontal bar graphs), with appropriate titles and labels and with labels ordered appropriately along horizontal axes, as needed, using many-to-one correspondenceGrade 3
Ontario3.6.3.2Interpret and draw conclusions from data presented in charts, tables, and graphsGrade 3
Ontario4.2.2.1Represent, compare, and order whole numbers to 10 000, using a variety of tools (e.g., drawings of base ten materials, number lines with increments of 100 or other appropriate amounts)Grade 4
Ontario4.2.2.2Demonstrate an understanding of place value in whole numbers and decimal numbers from 0.1 to 10 000, using a variety of tools and strategies (e.g., use base ten materials to represent 9307 as 9000 + 300 + 0 + 7) (Sample problem: Use the digits 1, 9, 5, 4 to create the greatest number and the least number possible, and explain your thinking.)Grade 4
Ontario4.2.2.5Represent, compare, and order decimal numbers to tenths, using a variety of tools (e.g., concrete materials such as paper strips divided into tenths and base ten materials, number lines, drawings) and using standard decimal notation (Sample problem: Draw a partial number line that extends from 4.2 to 6.7, and mark the location of 5.6.)Grade 4
Ontario4.2.2.6Represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of fractional parts being consideredGrade 4
Ontario4.2.2.7Compare and order fractions (i.e., halves, thirds, fourths, fifths, tenths) by considering the size and the number of fractional 4/5 is greater than 3/5 because there are more parts in 4/5; 1/4 is greater than 1/5 because the size of the part is larger in 1/4)Grade 4
Ontario4.2.2.9Demonstrate and explain the relationship between equivalent fractions, using concrete materials (e.g., fraction circles, fraction strips, pattern blocks) and drawings (e.g., I can say that 3/6 of my cubes are white, or half of the cubes are white. This means that 3/6 and 1/2 are equal.)Grade 4
Ontario4.2.4.1Add and subtract two-digit numbers, using a variety of mental strategies (e.g., one way to calculate 73 - 39 is to subtract 40 from 73 to get 33, and then add 1 back to get 34)Grade 4
Ontario4.2.4.3Add and subtract decimal numbers to tenths, using concrete materials (e.g., paper strips divided into tenths, base ten materials) and student-generated algorithms (e.g., When I added 6.5 and 5.6, I took five tenths in fraction circles and added six tenths in fraction circles to give me one whole and one tenth. Then I added 6 + 5 + 1.1, which equals 12.1)Grade 4
Ontario4.2.4.5Multiply to 9 x 9 and divide to 81 Ö 9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting)Grade 4
Ontario4.2.4.6Solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x 8)Grade 4
Ontario4.2.4.7Multiply whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule)Grade 4
Ontario4.2.4.8Multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., base ten materials or drawings of them, arrays), student-generated algorithms, and standard algorithmsGrade 4
Ontario4.3.2.1Estimate, measure, and record length, height, and distance, using standard unitsGrade 4
Ontario4.3.2.2Draw items using a ruler, given specific lengths in millimetres or centimetresGrade 4
Ontario4.3.2.3Estimate, measure (i.e., using an analogue clock), and represent time intervals to the nearest minuteGrade 4
Ontario4.3.3.1Describe, through investigation, the relationship between various units of length (i.e., millimetre, centimetre, decimetre, metre, kilometre)Grade 4
Ontario4.4.2.2Identify and compare different types of quadrilaterals (i.e., rectangle, square, trapezoid, parallelogram, rhombus) and sort and classify them by their geometric properties (e.g., sides of equal length; parallel sides; symmetry; number of right angles)Grade 4
Ontario4.4.2.3Identify benchmark angles (i.e., straight angle, right angle, half a right angle), using a reference tool (e.g., paper and fasteners, pattern blocks, straws), and compare other angles to these benchmarks (e.g.,ññThe angle the door makes with the wall is smaller than a right angle but greater than half a right angle.îî) (Sample problem: Use paper folding to create benchmarks for a straight angle, a right angle, and half a right angle, and use these benchmarks to describe angles found in pattern blocks.)Grade 4
Ontario4.4.2.4Relate the names of the benchmark angles to their measures in degrees (e.g., a right angle is 90 degrees)Grade 4
Ontario4.4.4.1Identify and describe the general location of an object using a grid system (e.g.,"The library is located at A3 on the map.").Grade 4
Ontario4.4.4.2Identify, perform, and describe reflections using a variety of tools (e.g., Mira, dot paper, technology).Grade 4
Ontario4.4.4.3Create and analyse symmetrical designs by reflecting a shape, or shapes, using a variety of tools (e.g., pattern blocks, Mira, Geoboard, drawings), and identify the congruent shapes in the designs.Grade 4
Ontario4.5.3.2Determine the missing number in equations involving multiplication of one-and two-digit numbers, using a variety of tools and strategies.Grade 4
Ontario4.5.3.3Identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the commutative property of multiplication to facilitate computation with whole numbers (e.g., I know that 15 x 7 x 2 equals 15 x 2 x 7. This is easier to multiply in my head because I get 30 x 7 = 210.)Grade 4
Ontario4.5.3.4Identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the distributive property of multiplication over addition to facilitate computation with whole numbers (e.g., I know that 9 x 52 equals 9 x 50 + 9 x 2. This is easier to calculate in my head because I get 450 + 18 = 468.)Grade 4
Ontario5.2.2.1Represent, compare, and order whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools (e.g., number lines with appropriate increments, base ten materials for decimals)Grade 5
Ontario5.2.2.2Demonstrate an understanding of place value in whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools and strategies (e.g., use numbers to represent 23 011 as 20 000 + 3000 + 0 + 10 + 1; use base ten materials to represent the relationship between 1, 0.1, and 0.01) (Sample problem: How many thousands cubes would be needed to make a base ten block for 100 000?)Grade 5
Ontario5.2.2.4Round decimal numbers to the nearest tenth, in problems arising from real-life situationsGrade 5
Ontario5.2.2.5Represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using standard fractional notationGrade 5
Ontario5.2.2.6Demonstrate and explain the concept of equivalent fractions, using concrete materials (e.g., use fraction strips to show that 3/4 is equal to 9/12)Grade 5
Ontario5.2.4.1Solve problems involving the addition, subtraction, and multiplication of whole numbers, using a variety of mental strategies (e.g., use the commutative property: 5 x 18 x 2 = 5 x 2 x 18, which gives 10 x 18 = 180)Grade 5
Ontario5.2.4.2Add and subtract decimal numbers to hundredths, including money amounts, using concrete materials, estimation, and algorithms (e.g., use 10 x 10 grids to add 2.45 and 3.25)Grade 5
Ontario5.2.4.3Multiply two-digit whole numbers by two-digit whole numbers, using estimation, student-generated algorithms, and standard algorithmsGrade 5
Ontario5.2.4.5Multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule)Grade 5
Ontario5.3.3.3Solve problems involving the relationship between a 12-hour clock and a 24-hour clock (e.g., 15:00 is 3 hours after 12 noon, so 15:00 is the same as 3:00 p.m.)Grade 5
Ontario5.4.2.1Distinguish among polygons, regular polygons, and other two-dimensional shapesGrade 5
Ontario5.4.2.3Identify and classify acute, right, obtuse, and straight anglesGrade 5
Ontario5.4.2.4Measure and construct angles up to 90 degrees, using a protractorGrade 5
Ontario5.4.2.5Identify triangles (i.e., acute, right, obtuse, scalene, isosceles, equilateral), and classify them according to angle and side propertiesGrade 5
Ontario5.4.2.6Construct triangles, using a variety of tools (e.g., protractor, compass, dynamic geometry software), given acute or right angles and side measurementsGrade 5
Ontario5.4.3.3Identify, perform, and describe translations, using a variety of tools.Grade 5
Ontario5.4.3.4Create and analyse designs by translating and/or reflecting a shape, or shapes, using a variety of tools.Grade 5
Ontario5.5.2.3Make a table of values for a pattern that is generated by adding or subtracting a number(i.e., a constant) to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence (e.g., 12, 17, 22, 27, 32, ) or the pattern rule in words (e.g., start with 12 and add 5 to each term to get the next term).Grade 5
Ontario6.2.2.1Represent, compare, and order whole numbers and decimal numbers from 0.001 to 1 000 000, using a variety of tools (e.g., number lines with appropriate increments, base ten materials for decimals)Grade 6
Ontario6.2.2.2Demonstrate an understanding of place value in whole numbers and decimal numbers from 0.001 to 1 000 000, using a variety of tools and strategies (e.g. use base ten materials to represent the relationship between 1, 0.1, 0.01, and 0.001) (Sample problem: How many thousands cubes would be needed to make a base ten block for 1 000 000?)Grade 6
Ontario6.2.2.4Represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, number lines, calculators) and using standard fractional notation (Sample problem: Use fraction strips to show that 1 1/2 is greater than 5/4.)Grade 6
Ontario6.2.3.1Use a variety of mental strategies to solve addition, subtraction, multiplication, and division problems involving whole numbers (e.g., use the commutative property: 4 x 16 x 5 = 4 x 5 x 16, which gives 20 x 16 = 320; use the distributive property: (500 + 15) x 5 = 500 x 5 + 15 x 5, which gives 100 + 3 = 103)Grade 6
Ontario6.2.3.2Solve problems involving the multiplication and division of whole numbers (four-digit by two-digit), using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms)Grade 6
Ontario6.2.3.3Add and subtract decimal numbers to thousandths, using concrete materials, estimation, algorithms, and calculatorsGrade 6
Ontario6.2.3.4Multiply and divide decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms, and calculators (e.g., calculate 4 x 1.4 using base ten materials; calculate 5.6 x 4 using base ten materials)Grade 6
Ontario6.2.3.6Multiply and divide decimal numbers by 10, 100, 1000, and 10 000 using mental strategies (e.g., To convert 0.6 m to square centimetres, I calculated in my head 0.6 x 10 000 and got 6000 cm.) (Sample problem: Use a calculator to help you generalize a rule for multiplying numbers by 10 000.)Grade 6
Ontario6.2.4.3Represent relationships using unit rates (Sample problem: If 5 batteries cost \$4.75, what is the cost of 1 battery?).Grade 6
Ontario6.3.3.3Construct a rectangle, a square, a triangle,nd a parallelogram, using a variety of tools.Grade 6
Ontario6.4.2.1Sort and classify quadrilaterals by geometric properties related to symmetry, angles, and sides, through investigation using a variety of tools (e.g., geoboard, dynamic geometry software) and strategies (e.g., using charts, using Venn diagrams).Grade 6
Ontario6.4.2.3Measure and construct angles up to 180Áusing a protractor, and classify them as acute, right, obtuse, or straight angles.Grade 6
Ontario6.4.2.4Construct polygons using a variety of tools, given angle and side measurements.Grade 6
Ontario6.4.4.1Explain how a coordinate system represents location, and plot points in the first quadrant of a Cartesian coordinate plane.Grade 6
Ontario6.4.4.2Identify, perform, and describe , through investigation using a variety of tools, rotations of 180 degreees and clockwise and countercolockwise rotations of 90 degrees, with the centre of rotation indisde or outside the shape.Grade 6
Ontario6.4.4.3Create and analyse designs made by reflecting, translating and or rotating a shape or shapes by 90 degrees or 180 degrees that map congruent shapes, in a given design, onto eachother.Grade 6
Ontario6.5.2.4Determine the solution to a simple equation with one variable, through investigation using a variety of tools and strategies (e.g., modelling with concrete materials, using guess and check with and without the aid of a calculator).Grade 6
Ontario7.2.1.4Represent and order integers, using a variety of tools (e.g., two colour counters, virtual manipulatives, number lines);Grade 7
Ontario7.2.2.6Represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper).Grade 7
Ontario7.2.3.5Use estimation when solving problems involving operations with whole numbers, decimals, and percents, to help judge the reasonableness of a solution (Sample problem: A book costs \$18.49. The salesperson tells you that the total price,including taxes, is \$22.37. How can you tell if the total price is reasonable without using a calculator?)Grade 7
Ontario7.2.3.6Evaluate expressions that involve whole numbers and decimals, including expressions that contain brackets, using order of operations.Grade 7
Ontario7.2.3.7Add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithmsGrade 7
Ontario7.2.3.9Add and subtract integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines).Grade 7
Ontario7.2.4.1Determine, through investigation, the relationships among fractions, decimals, percents, and ratiosGrade 7
Ontario7.2.4.2Solve problems that involve determining whole number percents, using a variety of tools (e.g., base ten materials, paper and pencil, calculators) (Sample problem: If there are 5 blue marbles in a bag of 20 marbles, what percent of the marbles are not blue?)Grade 7
Ontario7.4.3.3Demonstrate an understanding that enlarging or reducing two-dimensional shapes creates similar shapes.Grade 7
Ontario7.4.4.1Plot points using all four quadrants of the Cartesian coordinate plane.Grade 7
Ontario7.4.4.3Create and analyse designs involving translations, reflections, dilatations, and/or simple rotations of two-dimensional shapes, using a variety of tools (e.g., concrete materials, Mira, drawings, dynamic geometry software) and strategies(e.g., paper folding).Grade 7
Ontario7.5.2.1Represent linear growing patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets) and strategies (e.g., make a table of values using the term number and the term; plot the coordinates on a graph; write a pattern rule using words).Grade 7
Ontario7.5.2.3Develop and represent the general term of a linear growing pattern, using algebraic expressions involving one operation (e.g., the general term for the sequence 4, 5, 6, 7,  can be written algebraically as n + 3, where n represents the term number; the general term for the sequence 5, 10, 15, 20,  can be written algebraically as 5n, where n represents the term number).Grade 7
Ontario7.5.2.4Evaluate algebraic expressions by substituting natural numbers for the variables.Grade 7
Ontario7.5.3.6Solve linear equations of the form ax = c or c = ax and ax + b = c or variations such as b + ax = c and c = bx + a (where a, b, and c are natural numbers ) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator.Grade 7
Ontario8.2.2.1Express repeated multiplication using exponential notation (e.g., 2x2x2x2 = 2^4).Grade 8
Ontario8.2.2.7Solve problems involving operations with integers, using a variety of tools (e.g., two colour counters, virtual manipulatives, number lines);Grade 8
Ontario8.2.3.4Represent the multiplication and division of fractions, using a variety of tools and strategies (e.g., use an area model to represent 1/4 multiplied by 1/3)Grade 8
Ontario8.2.3.5Solve problems involving addition, subtraction, multiplication, and division with simple fractionsGrade 8
Ontario8.2.3.6Represent the multiplication and division of integers, using a variety of tools (e.g., if black counters represent positive amounts and red counters represent negative amounts, you can model 3 x (-2) as three groups of two red counts).Grade 8
Ontario8.2.3.7Solve problems involving operations with integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines).Grade 8
Ontario8.2.3.8Evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations.Grade 8
Ontario8.2.3.9Multiply and divide decimal numbers by various powers of ten.Grade 8
Ontario8.4.3.5Solve problems involving right triangles geometrically, using the Pythagorean relationship.Grade 8
Ontario8.4.4.1Graph the image of a point, or set of points, on the Cartesian coordinate plane after applying a transformation to the original point(s) (i.e., translation; reflection in the x-axis, the y-axis, or the angle bisector of the axes that passes through the first and third quadrants; rotation of 90 degrees, 180 degrees, 270 degrees about the origin).Grade 8
Ontario8.5.2.2Represent linear patterns graphically (i.e., make a table of values that shows the term number and the term, and plot the coordinates on a graph), using a variety of tools (e.g., graph paper, calculators, dynamic statistical software).Grade 8
Ontario8.5.2.3Determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation (Sample problem: Given the graph that represents the pattern 1, 3, 5, 7,, find the 10th term. Given the algebraic equation that represents the pattern, t = 2n _ 1, find the 100th term.).Grade 8
Ontario8.5.3.2Model linear relationships using tables of values, graphs, and equations (e.g., the sequence 2, 3, 4, 5, 6, can be represented by the equation t = n + 1, where n represents the term number and t represents the term), through investigation using a variety of tools (e.g., algebra tiles, pattern blocks, connecting cubes, base ten materials)(Sample problem: Leah put \$350 in a bank certificate that pays 4% simple interest each year. Make a table of values to show how much the bank certificate is worth after five years, using base ten materials to help you. Represent the relationship using an equation.).Grade 8
Ontario8.5.3.5Make connections between solving equations and determining the term number in a pattern, using the general term (e.g., for the pattern with the general term 2 n + 1, solving the equation 2 n + 1 = 17 tells you the term number when the term is 17).Grade 8
Ontario8.6.3.5Identify and describe trends, based on the rate of change of data from tables and graphs, using informal language (e.g., ñThe steep line going upward on this graph represents rapid growth. The steep line going downward on this other graph represents rapid decline.î).Grade 8
OntarioK.2.1.1Investigate the idea that quantity is greater when counting forwards and less when counting backwards (e.g., use manipulatives to create a quantity number line; move along a number line; move around on a hundreds carpet; play simple games on number-line game boards; build a structure using blocks, and describe what happens as blocks are added or removed)Kindergarten
OntarioK.2.1.11Begin to make use of one-to-one correspondence in counting objects and matching groups of objects (e.g., one napkin for each of the people at the table)Kindergarten
OntarioK.2.1.12Investigate addition and subtraction in everyday activities through the use of manipulatives (e.g., interlocking cubes), visual models (e.g., a number line, tally marks, a hundreds carpet), or oral exploration (e.g., dramatizing of songs)Kindergarten
OntarioK.2.1.2Investigate some concepts of quantity through identifying and comparing sets with more, fewer, or the same number of objects (e.g., find out which of two cups contains more or fewer beans, using counters; investigate the ideas of more, less, and the same, using five and ten frames; compare two sets of objects that have the same number of items, one set having the items spread out, and recognize that both sets have the same quantity [concept of conservation]; recognize that the last count represents the actual number of objects in the set [concept of cardinality]; compare five beans with five blocks, and recognize that the number 5 represents the same quantity regardless of the different materials [concept of abstraction])Kindergarten
OntarioK.2.1.3Recognize some quantities without having to count, using a variety of tools (e.g., dominoes, dot plates, dice, number of fingers) or strategies (e.g., composing and decomposing numbers, subitizing)Kindergarten
OntarioK.2.1.5Use, read, and represent whole numbers to 10 in a variety of meaningful contexts (e.g., use a hundreds chart; use magnetic and sandpaper numerals; put the house number on a house built at the block centre; find and recognize numbers in the environment; use magnetic numerals to represent the number of objects in a set; write numerals on imaginary bills at the restaurant at the dramatic play centre)Kindergarten
OntarioK.2.1.6Demonstrate awareness of addition and subtraction in everyday activities (e.g., in sharing crayons).Kindergarten
OntarioK.2.1.7Demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation (e.g., initially: show smaller quantities using anchors of five and ten, such as their fingers or manipulatives; eventually: show quantities to 10, using such tools as five and ten frames and manipulatives)Kindergarten
OntarioK.2.1.8Investigate and develop strategies for composing and decomposing quantities to 10 (e.g., use manipulatives or shake and spill activities; initially: to represent the quantity of 8, the child may first count from 1 through to 8 using his or her fingers; later, the child may put up one hand, count from 1 to 5 using each finger, pause, and then continue to count to 8 using three more fingers; eventually: the child may put up all five fingers of one hand at once and simply say Five, then count on, using three more fingers and saying 'Six, seven, eight. There are eight.')Kindergarten
QuebecE1.A.MON.A.1Determines the operation(s) to perform in a given situationGrade 1
QuebecE1.A.MON.A.2Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparingGrade 1
QuebecE1.A.MON.A.3aUses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division): rectangular arrays, repeated addition, Cartesian product, sharing, and number of times x goes into y (using objects and diagrams)Grade 1
QuebecE1.A.MON.A.4Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1)Grade 1
QuebecE1.A.ON.A.2aBuilds a repertoire of memorized addition and subtraction facts: Builds a memory of addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts, using objects, drawings, charts or tablesGrade 1
QuebecE1.A.ON.A.2bBuilds a repertoire of memorized addition and subtraction facts: Develops various strategies that promote mastery of number facts and relates them to the properties of additionGrade 1
QuebecE1.A.ON.A.2cBuilds a repertoire of memorized addition and subtraction facts: Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction factsGrade 1
QuebecE1.A.ON.A.3aDevelops processes for mental computation: Uses his/her own processes to determine the sum or difference of two natural numbersGrade 1
QuebecE1.A.ON.A.4aDevelops processes for written computation (addition and subtraction): Uses his/her own processes as well as objects and drawings to determine the sum or difference of two natural numbers less than 1000Grade 1
QuebecE1.A.ON.A.5Determines the missing term in an equation (relationships between operations): a + b = ?, a + ? = c, ? + b = c, a - b = ?, a - ? = c, ? - b = cGrade 1
QuebecE1.A.ON.A.13Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes numerical patterns (e.g. number rhymes, tables and charts)Grade 1
QuebecE1.A.UWN.A.1aCounts or recites counting rhymes involving natural numbers: counts forward from a given numberGrade 1
QuebecE1.A.UWN.A.1bCounts or recites counting rhymes involving natural numbers: counts forward or backwardGrade 1
QuebecE1.A.UWN.A.1cCounts or recites counting rhymes involving natural numbers: skip counts (e.g. by twos)Grade 1
QuebecE1.A.UWN.A.2aCounts collections (using objects or drawings): matches the gesture to the corresponding number word; recognizes the cardinal aspect of a number and the conservation of number in various combinationsGrade 1
QuebecE1.A.UWN.A.2bCounts collections (using objects or drawings): counts from a given numberGrade 1
QuebecE1.A.UWN.A.2cCounts collections (using objects or drawings): counts a collection by grouping or regroupingGrade 1
QuebecE1.A.UWN.A.5Composes and decomposes a natural number in a variety of waysGrade 1
QuebecE1.A.UWN.A.8Arranges natural numbers in increasing or decreasing orderGrade 1
QuebecE1.A.UWN.A.10Locates natural numbers using different visual aids (e.g. hundreds chart, number strip, number line)Grade 1
QuebecE1.M.G.1Estimates and measures time using conventional unitsGrade 1
QuebecE1.M.G.2Establishes relationships between units of measureGrade 1
QuebecE1.A.UWN.A.13Approximates a collection, using objects or drawings (e.g. estimate, round up/down to a given value)Grade 1
QuebecE1.A.UWN.A.4aRepresents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on apparent, accessible groupings using objects, drawings or unstructured materialsGrade 1
QuebecE2.A.MON.A.1Determines the operation(s) to perform in a given situationGrade 2
QuebecE2.A.MON.A.2Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparingGrade 2
QuebecE2.A.MON.A.3aUses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division): rectangular arrays, repeated addition, Cartesian product, sharing, and number of times x goes into y (using objects and diagrams)Grade 2
QuebecE2.A.MON.A.4Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1)Grade 2
QuebecE2.A.ON.A.2aBuilds a repertoire of memorized addition and subtraction facts: Builds a memory of addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts, using objects, drawings, charts or tablesGrade 2
QuebecE2.A.ON.A.2bBuilds a repertoire of memorized addition and subtraction facts: Develops various strategies that promote mastery of number facts and relates them to the properties of additionGrade 2
QuebecE2.A.ON.A.2cBuilds a repertoire of memorized addition and subtraction facts: Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction factsGrade 2
QuebecE2.A.ON.A.3aDevelops processes for mental computation: Uses his/her own processes to determine the sum or difference of two natural numbersGrade 2
QuebecE2.A.ON.A.4aDevelops processes for written computation (addition and subtraction): Uses his/her own processes as well as objects and drawings to determine the sum or difference of two natural numbers less than 1000Grade 2
QuebecE2.A.ON.A.5Determines the missing term in an equation (relationships between operations): a + b = ?, a + ? = c, ? + b = c, a - b = ?, a - ? = c, ? - b = cGrade 2
QuebecE2.A.ON.A.13Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes numerical patterns (e.g. number rhymes, tables and charts)Grade 2
QuebecE2.A.UWN.A.1aCounts or recites counting rhymes involving natural numbers: counts forward from a given numberGrade 2
QuebecE2.A.UWN.A.1bCounts or recites counting rhymes involving natural numbers: counts forward or backwardGrade 2
QuebecE2.A.UWN.A.1cCounts or recites counting rhymes involving natural numbers: skip counts (e.g. by twos)Grade 2
QuebecE2.A.UWN.A.2bCounts collections (using objects or drawings): counts from a given numberGrade 2
QuebecE2.A.UWN.A.2cCounts collections (using objects or drawings): counts a collection by grouping or regroupingGrade 2
QuebecE2.A.UWN.A.4bRepresents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables)Grade 2
QuebecE2.A.UWN.A.5Composes and decomposes a natural number in a variety of waysGrade 2
QuebecE2.A.UWN.A.8Arranges natural numbers in increasing or decreasing orderGrade 2
QuebecE2.A.UWN.A.10Locates natural numbers using different visual aids (e.g. hundreds chart, number strip, number line)Grade 2
QuebecE2.M.G.1Estimates and measures time using conventional unitsGrade 2
QuebecE2.M.G.2Establishes relationships between units of measureGrade 2
QuebecE2.A.UWN.A.13Approximates a collection, using objects or drawings (e.g. estimate, round up/down to a given value)Grade 2
QuebecE2.A.UWN.A.4aRepresents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on apparent, accessible groupings using objects, drawings or unstructured materialsGrade 2
QuebecE3.S.3bInterprets data using a table, a bar graph, a pictograph and a broken-line graphGrade 3
QuebecE3.S.4bDisplays data using table, a bar graph, a pictograph and a broken-line graphGrade 3
QuebecE3.M.A.6Calculates the perimeter of plane figuresGrade 3
QuebecE3.A.MON.A.4Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1)Grade 3
QuebecE3.A.ON.C.3aDevelops processes for written computation: adds and subtracts decimals whose result does not go beyond the second decimal placeGrade 3
QuebecE3.A.ON.B.1Generates a set of equivalent fractionsGrade 3
QuebecE3.A.ON.A.2bBuilds a repertoire of memorized addition and subtraction facts: Develops various strategies that promote mastery of number facts and relates them to the properties of additionGrade 3
QuebecE3.A.ON.A.2cBuilds a repertoire of memorized addition and subtraction facts: Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction factsGrade 3
QuebecE3.A.ON.A.3bDevelops processes for mental computation: Uses his/her own processes to determine the product or quotient of two natural numbersGrade 3
QuebecE3.A.ON.A.4bDevelops processes for written computation (addition and subtraction): Uses conventional processes to determine the sum of two natural numbers of up to four digitsGrade 3
QuebecE3.A.ON.A.4cDevelops processes for written computation (addition and subtraction): Uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0Grade 3
QuebecE3.A.ON.A.6aBuilds a repertoire of memorized multiplication and division facts: Builds a memory of multiplication facts and the corresponding division facts using objects drawings charts or tablesGrade 3
QuebecE3.A.ON.A.6bBuilds a repertoire of memorized multiplication and division facts: Develops various strategies that promote mastery of number facts and relate them to the properties of multiplicationGrade 3
QuebecE3.A.ON.A.6cBuilds a repertoire of memorized multiplication and division facts: Masters all multiplication facts and the corresponding division factsGrade 3
QuebecE3.A.ON.A.7aDevelops processes for written computation (multiplication and division): Uses his/her own processes as well as materials and drawings to determine the product or quotient of a three-digit natural number and a one-digit natural number, expresses the remainder of a division as a fraction, depending on the contextGrade 3
QuebecE3.G.C.6Describes quadrilaterals (e.g. parallel segments, perpendicular segments, right angles, acute angles, obtuse angles)Grade 3
QuebecE3.G.B.5Describes prisms and pyramids in terms of faces, vertices and edgesGrade 3
QuebecE3.G.A.3Locates objects on an axis (based on the types of numbers studied)Grade 3
QuebecE3.M.G.2Establishes relationships between units of measureGrade 3
QuebecE3.A.UWN.C.1Represents decimals in a variety of ways (using objects or drawings)Grade 3
QuebecE3.A.UWN.C.2Identifies equivalent representations (using objects or drawings)Grade 3
QuebecE3.A.UWN.C.4Understands the role of the decimal pointGrade 3
QuebecE3.A.UWN.C.5Composes and decomposes a decimal written in decimal notationGrade 3
QuebecE3.A.UWN.C.7aLocates decimals on a number line between two consecutive natural numbersGrade 3
QuebecE3.A.UWN.C.9Approximates (e.g. estimates, rounds to a given value, truncates decimal places)Grade 3
QuebecE3.A.MON.B.1aUses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparingGrade 3
QuebecE3.A.MON.B.2Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons)Grade 3
QuebecE3.A.UWN.B.2Represents a fraction in a variety of ways, based on a whole or a collection of objectsGrade 3
QuebecE3.A.UWN.B.3Matches a fraction to part of a whole (congruent or equivalent parts) or part of a group of objects, and vice versaGrade 3
QuebecE3.A.UWN.B.4Identifies the different meanings of fractions (sharing, division, ratio)Grade 3
QuebecE3.A.UWN.B.5Distinguishes a numerator from a denominatorGrade 3
QuebecE3.A.UWN.B.8Verifies whether two fractions are equivalentGrade 3
QuebecE3.A.UWN.A.2cCounts collections (using objects or drawings): counts a collection by grouping or regroupingGrade 3
QuebecE3.A.UWN.A.2dCounts collections (using objects or drawings): counts a pre-grouped collectionGrade 3
QuebecE3.A.UWN.A.4bRepresents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables)Grade 3
QuebecE3.A.UWN.A.5Composes and decomposes a natural number in a variety of waysGrade 3
QuebecE3.A.MON.A.3bUses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division): rectangular arrays, repeated addition, Cartesian product, area, volume, repeated subtraction, sharing, number of times x goes into y, and comparisons (using objects, diagrams or equations)Grade 3
QuebecE3.A.MON.A.5bDetermines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication and the associative propertyGrade 3
QuebecE3.A.UWN.A.4cRepresents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on place value in non-apparent, non-accessible groupings, using materials for which groupings are symbolic (e.g. abacus, money)Grade 3
QuebecE3.A.UWN.A.6Identifies equivalent expressions (e.g. 52 = 40 + 12, 25 + 27 = 40 + 12)Grade 3
QuebecE4.S.3bInterprets data using a table, a bar graph, a pictograph and a broken-line graphGrade 4
QuebecE4.S.4bDisplays data using table, a bar graph, a pictograph and a broken-line graphGrade 4
QuebecE4.A.ON.C.3aDevelops processes for written computation: adds and subtracts decimals whose result does not go beyond the second decimal placeGrade 4
QuebecE4.A.ON.B.1Generates a set of equivalent fractionsGrade 4
QuebecE4.A.ON.A.3bDevelops processes for mental computation: Uses his/her own processes to determine the product or quotient of two natural numbersGrade 4
QuebecE4.A.ON.A.4bDevelops processes for written computation (addition and subtraction): Uses conventional processes to determine the sum of two natural numbers of up to four digitsGrade 4
QuebecE4.A.ON.A.4cDevelops processes for written computation (addition and subtraction): Uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0Grade 4
QuebecE4.A.ON.A.6aBuilds a repertoire of memorized multiplication and division facts: Builds a memory of multiplication facts (0 x 0 to 10 x 10) and the corresponding division facts using objects drawings charts or tablesGrade 4
QuebecE4.A.ON.A.6bBuilds a repertoire of memorized multiplication and division facts: Develops various strategies that promote mastery of number facts and relate them to the properties of multiplicationGrade 4
QuebecE4.A.ON.A.6cBuilds a repertoire of memorized multiplication and division facts: Masters all multiplication facts (0 x 0 to 10 x 10) and the corresponding division factsGrade 4
QuebecE4.A.ON.A.7aDevelops processes for written computation (multiplication and division): Uses his/her own processes as well as materials and drawings to determine the product or quotient of a three-digit natural number and a one-digit natural number, expresses the remainder of a division as a fraction, depending on the contextGrade 4
QuebecE4.A.ON.A.9Decomposes a number into prime factorsGrade 4
QuebecE4.A.ON.A.8Determines the missing term in an equation (relationships between operations): a + b = ?, a + ? = c, ? + b = c, a - b = ?, a - ? = c, ? - b = cGrade 4
QuebecE4.G.C.6Describes quadrilaterals (e.g. parallel segments, perpendicular segments, right angles, acute angles, obtuse angles)Grade 4
QuebecE4.G.B.5Describes prisms and pyramids in terms of faces, vertices and edgesGrade 4
QuebecE4.G.A.3Locates objects on an axis (based on the types of numbers studied)Grade 4
QuebecE4.M.G.2Establishes relationships between units of measureGrade 4
QuebecE4.A.UWN.C.1Represents decimals in a variety of ways (using objects or drawings)Grade 4
QuebecE4.A.UWN.C.2Identifies equivalent representations (using objects or drawings)Grade 4
QuebecE4.A.UWN.C.4Understands the role of the decimal pointGrade 4
QuebecE4.A.UWN.C.5Composes and decomposes a decimal written in decimal notationGrade 4
QuebecE4.A.UWN.C.7aLocates decimals on a number line between two consecutive natural numbersGrade 4
QuebecE4.A.UWN.C.7bLocates decimals on a number line between two decimalsGrade 4
QuebecE4.A.UWN.C.9Approximates (e.g. estimates, rounds to a given value, truncates decimal places)Grade 4
QuebecE4.A.MON.B.1aUses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparingGrade 4
QuebecE4.A.MON.B.2Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons)Grade 4
QuebecE4.A.UWN.B.2Represents a fraction in a variety of ways, based on a whole or a collection of objectsGrade 4
QuebecE4.A.UWN.B.3Matches a fraction to part of a whole (congruent or equivalent parts) or part of a group of objects, and vice versaGrade 4
QuebecE4.A.UWN.B.4Identifies the different meanings of fractions (sharing, division, ratio)Grade 4
QuebecE4.A.UWN.B.5Distinguishes a numerator from a denominatorGrade 4
QuebecE4.A.UWN.B.8Verifies whether two fractions are equivalentGrade 4
QuebecE4.A.UWN.B.10Orders fractions with the same denominatorGrade 4
QuebecE4.A.UWN.A.2cCounts collections (using objects or drawings): counts a collection by grouping or regroupingGrade 4
QuebecE4.A.UWN.A.2dCounts collections (using objects or drawings): counts a pre-grouped collectionGrade 4
QuebecE4.A.UWN.A.4bRepresents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables)Grade 4
QuebecE4.A.UWN.A.5Composes and decomposes a natural number in a variety of waysGrade 4
QuebecE4.A.MON.A.3bUses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division): rectangular arrays, repeated addition, Cartesian product, area, volume, repeated subtraction, sharing, number of times x goes into y, and comparisons (using objects, diagrams or equations)Grade 4
QuebecE4.A.MON.A.5bDetermines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication and the associative propertyGrade 4
QuebecE4.A.UWN.A.6Identifies equivalent expressions (e.g. 52 = 40 + 12, 25 + 27 = 40 + 12)Grade 4
QuebecE5.M.D.2Estimates and determines the degree measurement of anglesGrade 5
QuebecE5.S.3cInterprets data using a table, a bar graph, a pictograph, a broken-line graph and a circle graphGrade 5
QuebecE5.A.ON.C.1bApproximates the result of a multiplication or divisionGrade 5
QuebecE5.A.ON.C.2bDevelops processes for mental computation: performs operations involving decimals (multiplication, division by a natural number)Grade 5
QuebecE5.A.ON.C.3bDevelops processes for written computation: multiplies decimals whose product does not go beyond the second decimal placeGrade 5
QuebecE5.A.ON.C.3cDevelops processes for written computation: divides a decimal by a natural number less than 11Grade 5
QuebecE5.A.ON.B.1Generates a set of equivalent fractionsGrade 5
QuebecE5.A.ON.B.3Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction(s)Grade 5
QuebecE5.A.ON.B.4Multiplies a natural number by a fractionGrade 5
QuebecE5.A.ON.A.3bDevelops processes for mental computation: Uses his/her own processes to determine the product or quotient of two natural numbersGrade 5
QuebecE5.A.ON.A.6bBuilds a repertoire of memorized multiplication and division facts: Develops various strategies that promote mastery of number facts and relate them to the properties of multiplicationGrade 5
QuebecE5.A.ON.A.6cBuilds a repertoire of memorized multiplication and division facts: Masters all multiplication facts (0 x 0 to 10 x 10) and the corresponding division factsGrade 5
QuebecE5.A.ON.A.7bDevelops processes for written computation (multiplication and division): Uses conventional processes to determine the product of a three-digit natural number and a two-digit natural numberGrade 5
QuebecE5.A.ON.A.7cDevelops processes for written computation (multiplication and division): Uses conventional processes to determine the quotient of a four-digit natural number and a two-digit natural number, expresses the remainder of a division as a decimal that does not go beyond the second decimal placeGrade 5
QuebecE5.A.ON.A.9Decomposes a number into prime factorsGrade 5
QuebecE5.A.ON.A.10Calculates the power of a numberGrade 5
QuebecE5.A.ON.A.12Performs a series of operations in accordance with the order of operationsGrade 5
QuebecE5.A.ON.A.8Determines the missing term in an equation (relationships between operations): a + b = ?, a + ? = c, ? + b = c, a - b = ?, a - ? = c, ? - b = cGrade 5
QuebecE5.G.C.8Describes triangles: scalene triangles, right triangles, isosceles triangles, equilateral trianglesGrade 5
QuebecE5.G.A.3Locates objects on an axis (based on the types of numbers studied)Grade 5
QuebecE5.M.G.2Establishes relationships between units of measureGrade 5
QuebecE5.A.UWN.C.1Represents decimals in a variety of ways (using objects or drawings)Grade 5
QuebecE5.A.UWN.C.2Identifies equivalent representations (using objects or drawings)Grade 5
QuebecE5.A.UWN.C.5Composes and decomposes a decimal written in decimal notationGrade 5
QuebecE5.A.UWN.C.7aLocates decimals on a number line between two consecutive natural numbersGrade 5
QuebecE5.A.UWN.C.7bLocates decimals on a number line between two decimalsGrade 5
QuebecE5.A.MON.B.1aUses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparingGrade 5
QuebecE5.A.MON.B.2Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons)Grade 5
QuebecE5.A.UWN.B.2Represents a fraction in a variety of ways, based on a whole or a collection of objectsGrade 5
QuebecE5.A.UWN.B.8Verifies whether two fractions are equivalentGrade 5
QuebecE5.A.UWN.B.10Orders fractions with the same denominatorGrade 5
QuebecE5.A.UWN.B.12Orders fractions with the same numeratorGrade 5
QuebecE5.A.UWN.B.13Locates fractions on a number lineGrade 5
QuebecE5.A.UWN.D.3Locates integers on a number line or Cartesian planeGrade 5
QuebecE5.A.UWN.D.5Arranges integers in increasing or decreasing orderGrade 5
QuebecE5.A.UWN.A.14Represents the power of a natural numberGrade 5
QuebecE5.A.MON.A.5cDetermines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtractionGrade 5
QuebecE5.A.MON.A.6Translates a situation using a series of operations in accordance with the order of operationsGrade 5
QuebecE6.M.D.2Estimates and determines the degree measurement of anglesGrade 6
QuebecE6.S.1Formulates questions for a survey (based on age-appropriate topics, students' language level, etc.)Grade 6
QuebecE6.A.ON.C.1bApproximates the result of a multiplication or divisionGrade 6
QuebecE6.A.ON.C.2bDevelops processes for mental computation: performs operations involving decimals (multiplication, division by a natural number)Grade 6
QuebecE6.A.ON.C.3bDevelops processes for written computation: multiplies decimals whose product does not go beyond the second decimal placeGrade 6
QuebecE6.A.ON.C.3cDevelops processes for written computation: divides a decimal by a natural number less than 11Grade 6
QuebecE6.A.ON.B.1Generates a set of equivalent fractionsGrade 6
QuebecE6.A.ON.B.3Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction(s)Grade 6
QuebecE6.A.ON.B.4Multiplies a natural number by a fractionGrade 6
QuebecE6.A.ON.A.3bDevelops processes for mental computation: Uses his/her own processes to determine the product or quotient of two natural numbersGrade 6
QuebecE6.A.ON.A.7bDevelops processes for written computation (multiplication and division): Uses conventional processes to determine the product of a three-digit natural number and a two-digit natural numberGrade 6
QuebecE6.A.ON.A.7cDevelops processes for written computation (multiplication and division): Uses conventional processes to determine the quotient of a four-digit natural number and a two-digit natural number, expresses the remainder of a division as a decimal that does not go beyond the second decimal placeGrade 6
QuebecE6.A.ON.A.9Decomposes a number into prime factorsGrade 6
QuebecE6.A.ON.A.10Calculates the power of a numberGrade 6
QuebecE6.A.ON.A.12Performs a series of operations in accordance with the order of operationsGrade 6
QuebecE6.G.C.8Describes triangles: scalene triangles, right triangles, isosceles triangles, equilateral trianglesGrade 6
QuebecE6.G.A.3Locates objects on an axis (based on the types of numbers studied)Grade 6
QuebecE6.M.G.2Establishes relationships between units of measureGrade 6
QuebecE6.A.UWN.C.1Represents decimals in a variety of ways (using objects or drawings)Grade 6
QuebecE6.A.UWN.C.2Identifies equivalent representations (using objects or drawings)Grade 6
QuebecE6.A.UWN.C.5Composes and decomposes a decimal written in decimal notationGrade 6
QuebecE6.A.UWN.C.7aLocates decimals on a number line between two consecutive natural numbersGrade 6
QuebecE6.A.UWN.C.7bLocates decimals on a number line between two decimalsGrade 6
QuebecE6.A.MON.B.1aUses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparingGrade 6
QuebecE6.A.MON.B.2Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons)Grade 6
QuebecE6.A.UWN.B.2Represents a fraction in a variety of ways, based on a whole or a collection of objectsGrade 6
QuebecE6.A.UWN.B.8Verifies whether two fractions are equivalentGrade 6
QuebecE6.A.UWN.B.12Orders fractions with the same numeratorGrade 6
QuebecE6.A.UWN.B.13Locates fractions on a number lineGrade 6
QuebecE6.A.UWN.D.3Locates integers on a number line or Cartesian planeGrade 6
QuebecE6.A.UWN.D.5Arranges integers in increasing or decreasing orderGrade 6
QuebecE6.A.UWN.A.14Represents the power of a natural numberGrade 6
QuebecE6.A.MON.A.5cDetermines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtractionGrade 6
QuebecE6.A.MON.A.6Translates a situation using a series of operations in accordance with the order of operationsGrade 6
QuebecS1.AG.ASAG.A.2Locates points in a Cartesian plane, based on the types of numbers studied (x- and y-coordinates of a point)Grade 7
QuebecS1.A.ORN.7aComputes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: numbers written in decimal notation, using rules of signsGrade 7
QuebecS1.A.ORN.6Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operationsGrade 7
QuebecS1.A.ORN.7bComputes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: positive numbers written in fractional notation, with or without the use of objects or diagramsGrade 7
QuebecS2.A.ORN.5Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operationsGrade 7
QuebecS2.A.ORN.7bComputes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: positive numbers written in fractional notation, with or without the use of objects or diagramsGrade 7
QuebecS1.A.ORN.8Computes, in writing, sequences of operations (numbers written in decimal notation) in accordance with the order of operations, using equivalent ways of writing numbers and the properties of operations (with no more than two levels of parentheses)Grade 7
QuebecS1.G.SSAS.A.5Recognizes and names regular convex polygonsGrade 7
QuebecS1.G.SSAS.C.3Identifies congruence (translation, rotation and reflection) between two figuresGrade 7
QuebecS1.G.SSAS.C.4Constructs the image of a figure under a translation, rotation and reflectionGrade 7
QuebecS1.G.SSAS.C.5Recognizes dilatation with a positive scale factorGrade 7
QuebecS1.G.SSAS.C.6Constructs the image of a figure under a dilatation with a positive scale factorGrade 7
QuebecS1.A.UAPS.1aCalculates a certain percentage of a numberGrade 7
QuebecS1.A.UAPS.1bCalculates the value corresponding to 100 per centGrade 7
QuebecS1.A.UAPS.4Describes the effect of changing a term in a ratio or rateGrade 7
QuebecS1.A.UAPS.8Represents or interprets a proportional situation using a graph, a table of values or a proportionGrade 7
QuebecS1.A.UAPS.9Solves proportional situations (direct or inverse variation) by using different strategies (e.g. unit-rate method, factor of change, proportionality ratio, additive procedure, constant product [inverse variation])Grade 7
QuebecS1.AL.UMAE.B.1Calculates the numeric value of an algebraic expressionGrade 7
QuebecS1.AL.UMAE.B.2Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of first-degree monomialsGrade 7
QuebecS1.AL.UMAE.B.3Factors out the common factor in numerical expressions (distributive property of multiplication over addition or subtraction)Grade 7
QuebecS1.AL.UMAE.C.9Uses different methods to solve first-degree equations with one unknown of the form ax + b = cx + d : trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms)Grade 7
QuebecS1.A.UORN.6Translates (mathematizes) a situation using a sequence of operations (no more than two levels of parentheses)Grade 7
QuebecS1.A.URN.10Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)Grade 7
QuebecS1.A.URN.11cRepresents and writes numbers in exponential notation (integral exponent)Grade 7
QuebecS1.A.URN.15aCompares and arranges in order numbers written in fractional or decimal notationGrade 7
QuebecS1.A.URN.15bCompares and arranges in order numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)Grade 7
QuebecS2.A.ORN.7aComputes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: numbers written in decimal notation, using rules of signsGrade 8
QuebecS2.A.ORN.6Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operationsGrade 8
QuebecS2.G.SSAS.C.4Constructs the image of a figure under a translation, rotation and reflectionGrade 8
QuebecS2.A.UAPS.1bCalculates the value corresponding to 100 per centGrade 8
QuebecS2.AL.UMAE.C.9Uses different methods to solve first-degree equations with one unknown of the form ax + b = cx + d : trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms)Grade 8
QuebecS2.AL.UMAE.D.4bSolves a system involving various functional models (mostly graphical solutions)Grade 8
QuebecS2.AL.UMAE.D.2aTranslates a situation algebraically or graphically using a system of equationsGrade 8
QuebecS2.AL.UMAE.B.1Calculates the numeric value of an algebraic expressionGrade 8
QuebecS2.AL.UMAE.B.2Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of first-degree monomialsGrade 8
QuebecS2.AL.UMAE.B.6bFactors polynomials by factoring by grouping (polynomials including decomposable second-degree trinomials)Grade 8
QuebecS2.AL.UMAE.B.6cFactors polynomials by completing the square (factoring and switching from one type of notation to another)Grade 8
QuebecS2.A.URN.10Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)Grade 8
QuebecS2.G.SSAS.C.3Identifies congruence (translation, rotation and reflection) between two figuresGrade 8
QuebecS2.G.SSAS.C.5Recognizes dilatation with a positive scale factorGrade 8
QuebecS2.G.SSAS.C.6Constructs the image of a figure under a dilatation with a positive scale factorGrade 8
South CarolinaAAPR.3Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior. Write a polynomial function of least degree corresponding to a given graph.Algebra
South CarolinaACE.2Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales.Algebra
South CarolinaASE.2Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.Algebra
South CarolinaASE.3.aChoose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression (Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation)Algebra
South CarolinaASE.3.bChoose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression (Determine the maximum or minimum value of a quadratic function by completing the square)Algebra
South CarolinaASE.3.cChoose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression (Use the properties of exponents to transform expressions for exponential functions)Algebra
South CarolinaFBF.1.aWrite a function that describes a relationship between two quantities (Write a function that models a relationship between two quantities using both explicit expressions and a recursive process and by combining standard forms using addition, subtraction, multiplication and division to build new functions)Algebra
South CarolinaFBF.1.bWrite a function that describes a relationship between two quantities (Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations)Algebra
South CarolinaFIF.2Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation.Algebra
South CarolinaFIF.4Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.Algebra
South CarolinaFIF.7.aGraph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases (Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior)Algebra
South CarolinaFIF.7.cGraph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases (Graph exponential and logarithmic functions, showing intercepts and end behavior)Algebra
South CarolinaFIF.7.dGraph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases (Graph trigonometric functions, showing period, midline, and amplitude)Algebra
South CarolinaSPID.6Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data.Algebra
South CarolinaSPID.7Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem.Algebra
South Carolina1.ATO.3Apply Commutative and Associative Properties of Addition to find the sum (through 20) of two or three addends.Grade 1
South Carolina1.ATO.6.bDemonstrate: (fluency with addition and related subtraction facts through 10)Grade 1
South Carolina1.ATO.7Understand the meaning of the equal sign as a relationship between two quantities (sameness) and determine if equations involving addition and subtraction are true.Grade 1
South Carolina1.ATO.8Determine the missing number in addition and subtraction equations within 20.Grade 1
South Carolina1.MDA.3Use analog and digital clocks to tell and record time to the hour and half hour.Grade 1
South Carolina1.MDA.4Collect, organize, and represent data with up to 3 categories using object graphs, picture graphs, t-charts and tallies.Grade 1
South Carolina1.NSBT.1.aExtend the number sequence to: (count forward by ones to 120 starting at any number)Grade 1
South Carolina1.NSBT.2.aUnderstand place value through 99 by demonstrating that: (ten ones can be thought of as a bundle (group) called a 'ten')Grade 1
South Carolina1.NSBT.3Compare two two-digit numbers based on the meanings of the tens and ones digits, using the words greater than, equal to, or less than.Grade 1
South Carolina1.NSBT.4.aAdd through 99 using concrete models, drawings, and strategies based on place value to: (add a two-digit number and a one-digit number, understanding that sometimes it is necessary to compose a ten (regroup))Grade 1
South Carolina1.NSBT.4.bAdd through 99 using concrete models, drawings, and strategies based on place value to: (add a two-digit number and a multiple of 10)Grade 1
South Carolina1.NSBT.5Determine the number that is 10 more or 10 less than a given number through 99 and explain the reasoning verbally and with multiple representations, including concrete models.Grade 1
South Carolina1.NSBT.6Subtract a multiple of 10 from a larger multiple of 10, both in the range 10 to 90, using concrete models, drawings, and strategies based on place value.Grade 1
South Carolina2.ATO.1Solve one- and two-step real-world/story problems using addition (as a joining action and as a part-part-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 99 with unknowns in all positions.Grade 2
South Carolina2.ATO.2Demonstrate fluency with addition and related subtraction facts through 20.Grade 2
South Carolina2.G.1Identify triangles, quadrilaterals, hexagons, and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.Grade 2
South Carolina2.MDA.6Use analog and digital clocks to tell and record time to the nearest five-minute interval using a.m. and p.m.Grade 2
South Carolina2.MDA.8Generate data by measuring objects in whole unit lengths and organize the data in a line plot using a horizontal scale marked in whole number units.Grade 2
South Carolina2.MDA.9Collect, organize, and represent data with up to four categories using picture graphs and bar graphs with a single-unit scale.Grade 2
South Carolina2.NSBT.1.aUnderstand place value through 999 by demonstrating that: (100 can be thought of as a bundle (group) of 10 tens called a 'hundred')Grade 2
South Carolina2.NSBT.2Count by tens and hundreds to 1,000 starting with any number.Grade 2
South Carolina2.NSBT.3Read, write and represent numbers through 999 using concrete models, standard form, and equations in expanded form.Grade 2
South Carolina2.NSBT.4Compare two numbers with up to three digits using words and symbols (i.e., >, =, or <).Grade 2
South Carolina2.NSBT.5Add and subtract fluently through 99 using knowledge of place value and properties of operations.Grade 2
South Carolina2.NSBT.6Add up to four two-digit numbers using strategies based on knowledge of place value and properties of operations.Grade 2
South Carolina2.NSBT.7Add and subtract through 999 using concrete models, drawings, and symbols which convey strategies connected to place value understanding.Grade 2
South Carolina2.NSBT.8Determine the number that is 10 or 100 more or less than a given number through 1,000 and explain the reasoning verbally and in writing.Grade 2
South Carolina3.ATO.1Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers and explain the relationship between the factors (i.e., 0 - 10) and the product.Grade 3
South Carolina3.ATO.2Use concrete objects, drawings and symbols to represent division without remainders and explain the relationship among the whole number quotient (i.e., 0 - 10), divisor (i.e., 0 - 10), and dividend.Grade 3
South Carolina3.ATO.3Solve real-world problems involving equal groups, area/array, and number line models using basic multiplication and related division facts. Represent the problem situation using an equation with a symbol for the unknown.Grade 3
South Carolina3.ATO.4Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient.Grade 3
South Carolina3.ATO.5Apply properties of operations (i.e., Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply and divide and explain the reasoning.Grade 3
South Carolina3.ATO.6Understand division as a missing factor problem.Grade 3
South Carolina3.ATO.7Demonstrate fluency with basic multiplication and related division facts of products and dividends through 100.Grade 3
South Carolina3.G.1Understand that shapes in different categories (e.g., rhombus, rectangle, square, and other 4-sided shapes) may share attributes (e.g., 4-sided figures) and the shared attributes can define a larger category (e.g., quadrilateral). 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
South Carolina3.MDA.1Use analog and digital clocks to determine and record time to the nearest minute, using a.m. and p.m.; measure time intervals in minutes; and solve problems involving addition and subtraction of time intervals within 60 minutes.Grade 3
South Carolina3.MDA.3Collect, organize, classify, and interpret data with multiple categories and draw a scaled picture graph and a scaled bar graph to represent the data.Grade 3
South Carolina3.MDA.4Generate data by measuring length to the nearest inch, half-inch and quarter-inch and organize the data in a line plot using a horizontal scale marked off in appropriate units.Grade 3
South Carolina3.MDA.5.aUnderstand the concept of area measurement (Recognize area as an attribute of plane figures)Grade 3
South Carolina3.MDA.5.bUnderstand the concept of area measurement (Measure area by building arrays and counting standard unit squares)Grade 3
South Carolina3.MDA.5.cUnderstand the concept of area measurement (Determine the area of a rectilinear polygon and relate to multiplication and addition)Grade 3
South Carolina3.NSBT.1Use place value understanding to round whole numbers to the nearest 10 or 100.Grade 3
South Carolina3.NSBT.2Add and subtract whole numbers fluently to 1,000 using knowledge of place value and properties of operations.Grade 3
South Carolina3.NSBT.3Multiply one-digit whole numbers by multiples of 10 in the range 10 - 90, using knowledge of place value and properties of operations.Grade 3
South Carolina3.NSF.1.aDevelop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers (A fraction 1/b (called a unit fraction) is the quantity formed by one part when a whole is partitioned into b equal parts)Grade 3
South Carolina3.NSF.1.bDevelop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers (A fraction a/b is the quantity formed by ?? parts of size 1/b)Grade 3
South Carolina3.NSF.1.cDevelop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers (A fraction is a number that can be represented on a number line based on counts of a unit fraction)Grade 3
South Carolina3.NSF.2.aExplain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: (two fractions are equal if they are the same size, based on the same whole, or at the same point on a number line)Grade 3
South Carolina3.NSF.2.bExplain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: (fraction equivalence can be represented using set, area, and linear models)Grade 3
South Carolina3.NSF.2.cExplain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: (whole numbers can be written as fractions (e.g., 4 = 4/1 and 1 = 4/4))Grade 3
South Carolina3.NSF.2.dExplain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: (fractions with the same numerator or same denominator can be compared by reasoning about their size based on the same whole)Grade 3
South Carolina4.ATO.1Interpret a multiplication equation as a comparison (e.g. interpret 35 = 5x7 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
South Carolina4.ATO.2Solve real-world problems using multiplication (product unknown) and division (group size unknown, number of groups unknown).Grade 4
South Carolina4.ATO.4Recognize that a whole number is a multiple of each of its factors. Find all factors for a whole number in the range 1 - 100 and determine whether the whole number is prime or composite.Grade 4
South Carolina4.ATO.5Generate a number or shape pattern that follows a given rule and determine a term that appears later in the sequence.Grade 4
South Carolina4.G.1Draw points, lines, line segments, rays, angles (i.e., right, acute, obtuse), and parallel and perpendicular lines. Identify these in two-dimensional figures.Grade 4
South Carolina4.G.2Classify quadrilaterals based on the presence or absence of parallel or perpendicular lines.Grade 4
South Carolina4.MDA.1Convert measurements within a single system of measurement, customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., cm, m, km, g, kg, mL, L) from a larger to a smaller unit.Grade 4
South Carolina4.MDA.2Solve real-world problems involving distance/length, intervals of time within 12 hours, liquid volume, mass, and money using the four operations.Grade 4
South Carolina4.MDA.4Create a line plot to display a data set (i.e., generated by measuring length to the nearest quarter-inch and eighth-inch) and interpret the line plot.Grade 4
South Carolina4.MDA.5Understand the relationship of an angle measurement to a circle.Grade 4
South Carolina4.MDA.6Measure and draw angles in whole number degrees using a protractor.Grade 4
South Carolina4.MDA.7Solve addition and subtraction problems to find unknown angles in real-world and mathematical problems.Grade 4
South Carolina4.NSBT.1Understand that, in a multi-digit whole number, a digit represents ten times what the same digit represents in the place to its right.Grade 4
South Carolina4.NSBT.3Use rounding as one form of estimation and round whole numbers to any given place value.Grade 4
South Carolina4.NSBT.4Fluently add and subtract multi-digit whole numbers using strategies to include a standard algorithm.Grade 4
South Carolina4.NSBT.5Multiply up to a four-digit number by a one-digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using rectangular arrays, area models and/or equations.Grade 4
South Carolina4.NSBT.6Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.Grade 4
South Carolina4.NSF.1Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), 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
South Carolina4.NSF.2Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2 and represent the comparison using the symbols >, =, or <.Grade 4
South Carolina4.NSF.3Develop an understanding of addition and subtraction of fractions based on unit fractions.Grade 4
South Carolina4.NSF.4Apply and extend an understanding of multiplication by multiplying a whole number and a fraction.Grade 4
South Carolina4.NSF.5Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100.Grade 4
South Carolina4.NSF.6Write a fraction with a denominator of 10 or 100 using decimal notation, and read and write a decimal number as a fraction.Grade 4
South Carolina4.NSF.7Compare and order decimal numbers to hundredths, and justify using concrete and visual models.Grade 4
South Carolina5.ATO.1Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces).Grade 5
South Carolina5.ATO.3.aInvestigate the relationship between two numerical patterns (Generate two numerical patterns given two rules and organize in tables)Grade 5
South Carolina5.ATO.3.bInvestigate the relationship between two numerical patterns (Translate the two numerical patterns into two sets of ordered pairs)Grade 5
South Carolina5.ATO.3.cInvestigate the relationship between two numerical patterns (Graph the two sets of ordered pairs on the same coordinate plane)Grade 5
South Carolina5.ATO.3.dInvestigate the relationship between two numerical patterns (Identify the relationship between the two numerical patterns)Grade 5
South Carolina5.G.1.aDefine a coordinate system (The x- and y- axes are perpendicular number lines that intersect at 0 (the origin))Grade 5
South Carolina5.G.1.bDefine a coordinate system (Any point on the coordinate plane can be represented by its coordinates)Grade 5
South Carolina5.G.1.cDefine a coordinate system (The first number in an ordered pair is the x-coordinate and represents the horizontal distance from the origin)Grade 5
South Carolina5.G.1.dDefine a coordinate system (The second number in an ordered pair is the y-coordinate and represents the vertical distance from the origin)Grade 5
South Carolina5.G.2Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical situations.Grade 5
South Carolina5.G.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Grade 5
South Carolina5.G.4Classify two-dimensional figures in a hierarchy based on their attributes.Grade 5
South Carolina5.MDA.2Create a line plot consisting of unit fractions and use operations on fractions to solve problems related to the line plot.Grade 5
South Carolina5.NSBT.1Understand that, in a multi-digit whole number, a digit in one place represents 10 times what the same digit represents in the place to its right, and represents 1/10 times what the same digit represents in the place to its left.Grade 5
South Carolina5.NSBT.2.aUse whole number exponents to explain: (patterns in the number of zeroes of the product when multiplying a number by powers of 10)Grade 5
South Carolina5.NSBT.2.bUse whole number exponents to explain: (patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10)Grade 5
South Carolina5.NSBT.3Read and write decimals in standard and expanded form. Compare two decimal numbers to the thousandths using the symbols >, =, or <.Grade 5
South Carolina5.NSBT.4Round decimals to any given place value within thousandths.Grade 5
South Carolina5.NSBT.5Fluently multiply multi-digit whole numbers using strategies to include a standard algorithm.Grade 5
South Carolina5.NSBT.6Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication and division.Grade 5
South Carolina5.NSBT.7Add, subtract, multiply, and divide decimal numbers to hundredths using concrete area models and drawings.Grade 5
South Carolina5.NSF.3Understand the relationship between fractions and division of whole numbers by interpreting a fraction as the numerator divided by the denominator (i.e., a/b = a divided by b).Grade 5
South Carolina5.NSF.4.aExtend the concept of multiplication to multiply a fraction or whole number by a fraction (Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths)Grade 5
South Carolina5.NSF.4.bExtend the concept of multiplication to multiply a fraction or whole number by a fraction (Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product)Grade 5
South Carolina5.NSF.5.aJustify the reasonableness of a product when multiplying with fractions (Estimate the size of the product based on the size of the two factors)Grade 5
South Carolina5.NSF.5.bJustify the reasonableness of a product when multiplying with fractions (Explain why multiplying a given number by a number greater than 1 (e.g., improper fractions, mixed numbers, whole numbers) results in a product larger than the given number)Grade 5
South Carolina5.NSF.5.cJustify the reasonableness of a product when multiplying with fractions (Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number)Grade 5
South Carolina5.NSF.5.dJustify the reasonableness of a product when multiplying with fractions (Explain why multiplying the numerator and denominator by the same number has the same effect as multiplying the fraction by 1)Grade 5
South Carolina5.NSF.6Solve real-world problems involving multiplication of a fraction by a fraction, improper fraction and a mixed number.Grade 5
South Carolina5.NSF.7.aExtend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations (Interpret division of a unit fraction by a non-zero whole number and compute the quotient)Grade 5
South Carolina5.NSF.7.bExtend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations (Interpret division of a whole number by a unit fraction and compute the quotient)Grade 5
South Carolina5.NSF.8Solve real-world problems involving division of unit fractions and whole numbers, using visual fraction models and equations.Grade 5
South Carolina6.EEI.1Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of Operations.Grade 6
South Carolina6.EEI.2.aExtend the concepts of numerical expressions to algebraic expressions involving positive rational numbers (Translate between algebraic expressions and verbal phrases that include variables)Grade 6
South Carolina6.EEI.2.bExtend the concepts of numerical expressions to algebraic expressions involving positive rational numbers (Investigate and identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and factor)Grade 6
South Carolina6.EEI.2.cExtend the concepts of numerical expressions to algebraic expressions involving positive rational numbers (Evaluate real-world and algebraic expressions for specific values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to whole-numbers)Grade 6
South Carolina6.EEI.3Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions.Grade 6
South Carolina6.EEI.5Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.Grade 6
South Carolina6.EEI.7Write and solve one-step linear equations in one variable involving nonnegative rational numbers for real-world and mathematical situations.Grade 6
South Carolina6.EEI.8.aExtend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations (Write an inequality of the form x > c or x < c and graph the solution set on a number line)Grade 6
South Carolina6.EEI.8.bExtend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations (Recognize that inequalities have infinitely many solutions)Grade 6
South Carolina6.GM.3.aApply the concepts of polygons and the coordinate plane to real-world and mathematical situations (Given coordinates of the vertices, draw a polygon in the coordinate plane)Grade 6
South Carolina6.GM.3.bApply the concepts of polygons and the coordinate plane to real-world and mathematical situations (Find the length of an edge if the vertices have the same x-coordinates or same y-coordinates)Grade 6
South Carolina6.NS.1Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations).Grade 6
South Carolina6.NS.2Fluently divide multi-digit whole numbers using a standard algorithmic approach.Grade 6
South Carolina6.NS.3Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach.Grade 6
South Carolina6.NS.5Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation.Grade 6
South Carolina6.NS.6.aExtend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane (Understand the concept of opposite numbers, including zero, and their relative locations on the number line)Grade 6
South Carolina6.NS.6.bExtend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane (Understand that the signs of the coordinates in ordered pairs indicate their location on an axis or in a quadrant on the coordinate plane)Grade 6
South Carolina6.NS.7.bUnderstand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers (Interpret statements using less than (), and equal to (=) as relative locations on the number line)Grade 6
South Carolina6.NS.7.cUnderstand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers (Use concepts of equality and inequality to write and to explain real-world and mathematical situations)Grade 6
South Carolina6.NS.7.dUnderstand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers (Understand that absolute value represents a number's distance from zero on the number line and use the absolute value of a rational number to represent real-world situations)Grade 6
South Carolina6.NS.7.eUnderstand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers (Recognize the difference between comparing absolute values and ordering rational numbers. For negative rational numbers, understand that as the absolute value increases, the value of the negative number decreases)Grade 6
South Carolina6.NS.8.aExtend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers (Plot points in all four quadrants to represent the problem)Grade 6
South Carolina6.NS.8.bExtend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers (Find the distance between two points when ordered pairs have the same x-coordinates or same y-coordinates)Grade 6
South Carolina6.RP.1Interpret the concept of a ratio as the relationship between two quantities, including part to part and part to whole.Grade 6
South Carolina6.RP.2.bInvestigate relationships between ratios and rates (Recognize that a rate is a type of ratio involving two different units)Grade 6
South Carolina6.RP.3.aApply the concepts of ratios and rates to solve real-world and mathematical problems (Create a table consisting of equivalent ratios and plot the results on the coordinate plane)Grade 6
South Carolina6.RP.3.cApply the concepts of ratios and rates to solve real-world and mathematical problems (Use two tables to compare related ratios)Grade 6
South Carolina6.RP.3.dApply the concepts of ratios and rates to solve real-world and mathematical problems (Apply concepts of unit rate to solve problems, including unit pricing and constant speed)Grade 6
South Carolina6.RP.3.eApply the concepts of ratios and rates to solve real-world and mathematical problems (Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages)Grade 6
South Carolina7.EEI.1Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic expressions with rational coefficients.Grade 7
South Carolina7.EEI.3Extend previous understanding of Order of Operations to solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol.Grade 7
South Carolina7.GM.1Determine the scale factor and translate between scale models and actual measurements (e.g., lengths, area) of real-world objects and geometric figures using proportional reasoning.Grade 7
South Carolina7.GM.2.aConstruct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology) (Construct triangles given all measurements of either angles or sides)Grade 7
South Carolina7.GM.2.bConstruct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology) (Decide if the measurements determine a unique triangle, more than one triangle, or no triangle)Grade 7
South Carolina7.GM.5Write equations to solve problems involving the relationships between angles formed by two intersecting lines, including supplementary, complementary, vertical, and adjacent.Grade 7
South Carolina7.NS.1.aExtend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Understand that the additive inverse of a number is its opposite and their sum is equal to zero)Grade 7
South Carolina7.NS.1.bExtend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Understand that the sum of two rational numbers (p + q) represents a distance from p on the number line equal to |q| where the direction is indicated by the sign of q)Grade 7
South Carolina7.NS.1.cExtend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Translate between the subtraction of rational numbers and addition using the additive inverse, p ? q = p + (?q))Grade 7
South Carolina7.NS.1.dExtend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference)Grade 7
South Carolina7.NS.1.eExtend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers)Grade 7
South Carolina7.NS.2.bExtend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers (Understand sign rules for multiplying rational numbers)Grade 7
South Carolina7.NS.2.cExtend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers (Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number)Grade 7
South Carolina7.NS.2.dExtend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers (Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide rational numbers)Grade 7
South Carolina7.NS.2.eExtend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers (Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or decimal numbers that terminate or repeat)Grade 7
South Carolina7.NS.3Apply the concepts of all four operations with rational numbers to solve real-world and mathematical problems.Grade 7
South Carolina7.RP.1Compute unit rates, including those involving complex fractions, with like or different units.Grade 7
South Carolina7.RP.2.aIdentify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Determine when two quantities are in a proportional relationship)Grade 7
South Carolina7.RP.2.bIdentify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Recognize or compute the constant of proportionality)Grade 7
South Carolina7.RP.2.cIdentify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Understand that the constant of proportionality is the unit rate)Grade 7
South Carolina7.RP.2.dIdentify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Use equations to model proportional relationships)Grade 7
South Carolina7.RP.2.eIdentify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Investigate the graph of a proportional relationship and explain the meaning of specific points (e.g., origin, unit rate) in the context of the situation)Grade 7
South Carolina7.RP.3Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis, percent increase/decrease, tax).Grade 7
South Carolina8.DSP.1.aInvestigate bivariate data (Collect bivariate data)Grade 8
South Carolina8.DSP.1.bInvestigate bivariate data (Graph the bivariate data on a scatter plot)Grade 8
South Carolina8.DSP.1.cInvestigate bivariate data (Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear))Grade 8
South Carolina8.DSP.2Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points.Grade 8
South Carolina8.EEI.3.aExplore the relationship between quantities in decimal and scientific notation (Express very large and very small quantities in scientific notation in the form a x 10 to the b power = p where 1 ? a < 10 and b is an integer)Grade 8
South Carolina8.EEI.4.aApply the concepts of decimal and scientific notation to solve real-world and mathematical problems (Multiply and divide numbers expressed in both decimal and scientific notation)Grade 8
South Carolina8.EEI.4.bApply the concepts of decimal and scientific notation to solve real-world and mathematical problems (Select appropriate units of measure when representing answers in scientific notation)Grade 8
South Carolina8.EEI.5.aApply concepts of proportional relationships to real-world and mathematical situations (Graph proportional relationships)Grade 8
South Carolina8.EEI.5.bApply concepts of proportional relationships to real-world and mathematical situations (Interpret unit rate as the slope of the graph)Grade 8
South Carolina8.EEI.5.cApply concepts of proportional relationships to real-world and mathematical situations (Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions)Grade 8
South Carolina8.EEI.6.aApply concepts of slope and y - intercept to graphs, equations, and proportional relationships (Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles)Grade 8
South Carolina8.EEI.6.bApply concepts of slope and y - intercept to graphs, equations, and proportional relationships (Derive the slope-intercept form (y = mx + b) for a non-vertical line)Grade 8
South Carolina8.EEI.7.aExtend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations (Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides)Grade 8
South Carolina8.EEI.7.bExtend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations (Recognize the three types of solutions to linear equations: one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b))Grade 8
South Carolina8.EEI.7.cExtend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations (Generate linear equations with the three types of solutions)Grade 8
South Carolina8.EEI.7.dExtend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations (Justify why linear equations have a specific type of solution)Grade 8
South Carolina8.EEI.8.aInvestigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions (Graph systems of linear equations and estimate their point of intersection)Grade 8
South Carolina8.EEI.8.bInvestigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions (Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines)Grade 8
South Carolina8.EEI.8.cInvestigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions (Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection)Grade 8
South Carolina8.F.1.aExplore the concept of functions (Understand that a function assigns to each input exactly one output)Grade 8
South Carolina8.F.2Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions.Grade 8
South Carolina8.F.3.aInvestigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions) (Define an equation in slope-intercept form (y = mx + b) as being a linear function)Grade 8
South Carolina8.F.3.cInvestigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions) (Provide examples of nonlinear functions)Grade 8
South Carolina8.F.4.bApply the concepts of linear functions to real-world and mathematical situations (Determine the slope and the ??-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions)Grade 8
South Carolina8.F.4.cApply the concepts of linear functions to real-world and mathematical situations (Construct a function in slope-intercept form that models a linear relationship between two quantities)Grade 8
South Carolina8.F.4.dApply the concepts of linear functions to real-world and mathematical situations (Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation)Grade 8
South Carolina8.F.5.aApply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations (Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous))Grade 8
South Carolina8.F.5.bApply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations (Sketch the graph of a function from a verbal description)Grade 8
South Carolina8.GM.1.aInvestigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology) (Verify that lines are mapped to lines, including parallel lines)Grade 8
South Carolina8.GM.1.bInvestigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology) (Verify that corresponding angles are congruent)Grade 8
South Carolina8.GM.1.cInvestigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology) (Verify that corresponding line segments are congruent)Grade 8
South Carolina8.GM.2.dApply the properties of rigid transformations (rotations, reflections, translations) (Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image)Grade 8
South Carolina8.GM.2.eApply the properties of rigid transformations (rotations, reflections, translations) (Given two congruent figures, describe the series of rigid transformations that justifies this congruence)Grade 8
South Carolina8.GM.4.bApply the properties of transformations (rotations, reflections, translations, dilations) (Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image)Grade 8
South Carolina8.GM.4.cApply the properties of transformations (rotations, reflections, translations, dilations) (Given two similar figures, describe the series of transformations that justifies this similarity)Grade 8
South Carolina8.GM.7Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.Grade 8
South Carolina8.GM.8Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.Grade 8
South CarolinaK.ATO.1Model situations that involve addition and subtraction within 10 using objects, fingers, mental images, drawings, acting out situations, verbal explanations, expressions, and equations.Kindergarten
South CarolinaK.ATO.2Solve real-world/story problems using objects and drawings to find sums up to 10 and differences within 10.Kindergarten
South CarolinaK.ATO.3Compose and decompose numbers up to 10 using objects, drawings, and equations.Kindergarten
South CarolinaK.ATO.4Create a sum of 10 using objects and drawings when given one of two addends 1 - 9.Kindergarten
South CarolinaK.ATO.5Add and subtract fluently within 5.Kindergarten
South CarolinaK.NS.1Count forward by ones and tens to 100.Kindergarten
South CarolinaK.NS.2Count forward by ones beginning from any number less than 100.Kindergarten
South CarolinaK.NS.3Read numbers from 0 - 20 and represent a number of objects 0 - 20 with a written numeral.Kindergarten
South CarolinaK.NS.4.aUnderstand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that: (the last number said tells the number of objects in the set (cardinality))Kindergarten
South CarolinaK.NS.4.bUnderstand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that: (the number of objects is the same regardless of their arrangement or the order in which they are counted (conservation of number))Kindergarten
South CarolinaK.NS.4.cUnderstand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that: (each successive number name refers to a quantity that is