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Common Core State Standards for Math
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
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.

Standards of Learning for Virginia Public Schools
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.

Western and Northern Canadian Protocol
Western and Northern Canadian Protocol

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
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
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.5Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).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 “how many more” and “how many less” 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.MD.C.7Relate area to the operations of multiplication and addition.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.3Read, write, and compare decimals to thousandths.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 “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
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.5Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).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 “how many more” and “how many less” 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.MD.C.7Relate area to the operations of multiplication and addition.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.3Read, write, and compare decimals to thousandths.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 “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
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.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
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
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.3Apply properties of operations as strategies to add and subtract.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.C.5Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).Grade 1
Georgia1.OA.C.6Add 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 “how many more” and “how many less” 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.MD.C.7Relate area to the operations of multiplication and addition.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.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.3Read, write, and compare decimals to thousandths.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 ‘how many?” 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.1Add and subtract fluently within 100.Grade 2
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.1Add and subtract whole numbers fluently within 1000.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.5Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).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 “how many more” and “how many less” 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.MD.C.7Relate area to the operations of multiplication and addition.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.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.3Read, write, and compare decimals to thousandths.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 “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
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
KansasK.OA.A.5Fluently add and subtract within 5.Kindergarten
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
Minnesota1.2.2.2Determine if equations involving addition and subtraction are true.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
Minnesota2.1.2.2Demonstrate fluency with basic addition facts and related subtraction 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
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
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.2.2Determine if equations involving addition and subtraction are true.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.1.1Recognize trapezoids and hexagons.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.3.1Read and write fractions with words and symbols.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.3.1Determine elapsed time.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 1’s and 10’s.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 twodimensional 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 friend’s 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 ˜ 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 o’clock), 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
Ontario3.4.3.2Explain the relationships between different types of quadrilateralsGrade 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 ˜ 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.,““The angle the door makes with the wall is smaller than a right angle but greater than half a right angle.””) (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 180°using 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., “The steep line going upward on this graph represents rapid growth. The steep line going downward on this other graph represents rapid decline.”).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
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.4Understand subtraction as an unknown addend problem.Grade 1
South Carolina1.ATO.5Recognize how counting relates to addition and subtraction.Grade 1
South Carolina1.ATO.6.aDemonstrate: (addition and subtraction through 20)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 one more and each previous number name refers to a quantity that is one less)Kindergarten
South CarolinaK.NS.5Count a given number of objects from 1 - 20 and connect this sequence in a one-to-one manner.Kindergarten
South CarolinaK.NS.7Determine whether the number of up to ten objects in one group is more than, less than, or equal to the number of up to ten objects in another group using matching and counting strategies.Kindergarten
South CarolinaK.NS.8Compare two written numerals up to 10 using more than, less than or equal to.Kindergarten
South CarolinaK.NSBT.1Compose and decompose numbers from 11 - 19 separating ten ones from the remaining ones using objects and drawings.Kindergarten
Virginia1.1.aThe student will count from 0 to 100 and write the corresponding numeralsGrade 1
Virginia1.1.bThe student will group a collection of up to 100 objects into tens and ones and write the corresponding numeral to develop an understanding of place valueGrade 1
Virginia1.14The student will investigate, identify and describe various forms of data collection using tables, picture graphs and object graphs.Grade 1
Virginia1.15The student will interpret information displayed in a picture or object graph, using the vocabulary more, less, fewer, greater than, less than, and equal toGrade 1
Virginia1.2The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30Grade 1
Virginia1.5The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction factsGrade 1
Virginia1.8The student will tell time to the half-hour, using analog and digital clocksGrade 1
Virginia2.1.aThe student will read, write, and identify the place value of each digit in a three-digit numeral, using numeration modelsGrade 2
Virginia2.1.cThe student will compare two whole numbers between 0 and 999, using symbols (>,Grade 2
Virginia2.12The student will tell and write time to the nearest five minutes, using analog and digital clocksGrade 2
Virginia2.17The student will use data from experiments to construct picture graphs, pictographs and bar graphs.Grade 2
Virginia2.19The student will analyze data displayed in picture graphs, pictographs and bar graphs.Grade 2
Virginia2.22The student will demonstrate an understanding of equality by recognizing that the symbol = in an equation indicates equivalent quantities and the symbol ? indicates that quantities are not equivalentGrade 2
Virginia2.3.aThe student will identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenthsGrade 2
Virginia2.4.aThe student will count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5, or 10Grade 2
Virginia2.4.bThe student will count backward by tens from 100Grade 2
Virginia2.5The student will recall addition facts with sums to 20 or less and the corresponding subtraction factsGrade 2
Virginia2.6.bThe student will find the sum, using various methods of calculationGrade 2
Virginia2.7.bThe student will find the difference, using various methods of calculationGrade 2
Virginia3.1.aThe student will read and write six-digit numerals and identify the place value and value of each digitGrade 3
Virginia3.1.bThe student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousandGrade 3
Virginia3.1.cThe student will compare two whole numbers between 0 and 9,999, using symbols (>,Grade 3
Virginia3.11.aThe student will tell time to the nearest minute, using analog and digital clocksGrade 3
Virginia3.11.bThe student will determine elapsed time in one-hour increments over a 12-hour periodGrade 3
Virginia3.14The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics, including the number of angles, vertices, and edges, and the number and shape of faces, using concrete modelsGrade 3
Virginia3.15The student will identify and draw representations of points, line segments, rays, angles, and linesGrade 3
Virginia3.17.bThe student will construct a line plot, a picture graph, or a bar graph to represent the dataGrade 3
Virginia3.17.cThe student will read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the dataGrade 3
Virginia3.19The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different formsGrade 3
Virginia3.3.aThe student will name and write fractions (including mixed numbers) represented by a modelGrade 3
Virginia3.3.bThe student will model fractions (including mixed numbers) and write the fraction namesGrade 3
Virginia3.4The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regroupingGrade 3
Virginia3.5The student will recall multiplication facts through the twelves table, and the corresponding division factsGrade 3
Virginia3.6The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or lessGrade 3
Virginia3.7The student will add and subtract proper fractions having like denominators of 12 or lessGrade 3
Virginia3.9.aThe student will estimate and use U.S. Customary and metric units to measure length to the nearest 1/2-inch, inch, foot, yard, centimeter, and meterGrade 3
Virginia4.1.aThe student will identify orally and in writing the place value for each digit in a whole number expressed through millionsGrade 4
Virginia4.10.aThe student will identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and verticesGrade 4
Virginia4.10.bThe student will identify representations of lines that illustrate intersection, parallelism, and perpendicularityGrade 4
Virginia4.12.aThe student will define polygonGrade 4
Virginia4.12.bThe student will identify polygons with 10 or fewer sidesGrade 4
Virginia4.14The student will collect, organize, display, and interpret data from a variety of graphsGrade 4
Virginia4.2.aThe student will compare and order fractions and mixed numbersGrade 4
Virginia4.2.bThe student will represent equivalent fractionsGrade 4
Virginia4.3.aThe student will read, write, represent, and identify decimals expressed through thousandthsGrade 4
Virginia4.3.cThe student will compare and order decimalsGrade 4
Virginia4.4.aThe student will estimate sums, differences, products, and quotients of whole numbersGrade 4
Virginia4.4.bThe student will add, subtract, and multiply whole numbersGrade 4
Virginia4.4.cThe student will divide whole numbers, finding quotients with and without remaindersGrade 4
Virginia4.4.dThe student will solve single-step and multistep addition, subtraction, and multiplication problems with whole numbersGrade 4
Virginia4.5.bThe student will add and subtract fractions having like and unlike denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factorsGrade 4
Virginia4.5.cThe student will add and subtract with decimalsGrade 4
Virginia4.6.bThe student will identify equivalent measurements between units within the U.S. Customary system (ounces, pounds, and tons) and between units within the metric system (grams and kilograms)Grade 4
Virginia4.7.aThe student will estimate and measure length, and describe the result in both metric and U.S. Customary units.Grade 4
Virginia4.7.bThe student will identify equivalent measurements between units within the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters)Grade 4
Virginia4.8.bThe student will identify equivalent measurements between units within the U.S. Customary system (cups, pints, quarts, and gallons)Grade 4
Virginia4.9The student will determine elapsed time in hours and minutes within a 12-hour period.Grade 4
Virginia5.1The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredthGrade 5
Virginia5.1The student will determine an amount of elapsed time in hours and minutes within a 24-hour period.Grade 5
Virginia5.12.aThe student will classify angles as right, acute, obtuse, or straightGrade 5
Virginia5.12.bThe student will classify triangles as right, acute, obtuse, equilateral, scalene, or isoscelesGrade 5
Virginia5.13.aThe student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will develop definitions of these plane figuresGrade 5
Virginia5.17The student will describe the relationship found in a number pattern and express the relationship.Grade 5
Virginia5.18.bThe student will write an open sentence to represent a given mathematical relationship, using a variableGrade 5
Virginia5.19The student will investigate and recognize the distributive property of multiplication over additionGrade 5
Virginia5.2.bThe student will compare and order fractions and decimals in a given set from least to greatest and greatest to leastGrade 5
Virginia5.4The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbersGrade 5
Virginia5.5.aThe student will find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit)Grade 5
Virginia5.7The student will evaluate whole number numerical expressions, using the order of operations limited to parentheses, addition, subtraction, multiplication, and division.Grade 5
Virginia5.8.cThe student will identify equivalent measurements within the metric systemGrade 5
Virginia6.1.aThe student will describe and compare data, using ratios, and will use appropriate notations, such as a/b, a to b, and a:b.Grade 6
Virginia6.11.aThe student will identify the coordinates of a point in a coordinate plane.Grade 6
Virginia6.11.bThe student will graph ordered pairs in a coordinate plane.Grade 6
Virginia6.13The student will describe and identify properties of quadrilateralsGrade 6
Virginia6.18The student will solve one step linear equations in one variable involving whole number coefficients and positive rational solutions.Grade 6
Virginia6.2.aThe student will investigate and describe fractions, decimals, and percents as ratiosGrade 6
Virginia6.2.bThe student will identify a given fraction, decimal, or percent from a representationGrade 6
Virginia6.2.cThe student will demonstrate equivalent relationships among fractions, decimals, and percentsGrade 6
Virginia6.2.dThe student will compare and order fractions, decimals, and percentsGrade 6
Virginia6.2The student will graph inequalities on a number lineGrade 6
Virginia6.3.aThe student will identify and represent integersGrade 6
Virginia6.3.bThe student will order and compare integersGrade 6
Virginia6.3.cThe student will identify and describe absolute value of integers.Grade 6
Virginia6.4The student will demonstrate multiple representations of multiplication and division of fractionsGrade 6
Virginia6.5The student will investigate and describe concepts of positive exponents and perfect squares.Grade 6
Virginia6.6.aThe student will multiply and divide fractions and mixed numbersGrade 6
Virginia6.6.bThe student will estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractionsGrade 6
Virginia6.7The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of decimalsGrade 6
Virginia6.8The student will evaluate whole number numerical expressions, using the order of operations.Grade 6
Virginia7.1.aThe student will investigate and describe the concept of negative exponents for powers of tenGrade 7
Virginia7.1.bThe student will determine scientific notation for numbers greater than zeroGrade 7
Virginia7.1.dThe student will determine square rootsGrade 7
Virginia7.1.eThe student will identify and describe absolute value for rational numbersGrade 7
Virginia7.12The student will represent relationships with tables, graphs, rules, and words.Grade 7
Virginia7.13.aThe student will write verbal expressions as algebraic expressions and sentences as equations and vice versaGrade 7
Virginia7.13.bThe student will evaluate algebraic expressions for given replacement values of the variablesGrade 7
Virginia7.14.aThe student will solve one and two step linear equations in one variableGrade 7
Virginia7.15.aThe student will solve one step inequalities in one variableGrade 7
Virginia7.15.bThe student will graph solutions to inequalities on the number lineGrade 7
Virginia7.16.bThe student will solve problems using the distributive propertyGrade 7
Virginia7.3.aThe student will model addition, subtraction, multiplication, and division of integersGrade 7
Virginia7.3.bThe student will add, subtract, multiply, and divide integersGrade 7
Virginia7.4The student will solve single-step and multistep practical problems, using proportional reasoningGrade 7
Virginia7.7The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.Grade 7
Virginia7.8The student, given a polygon in the coordinate plane, will represent transformations(reflections, dilations, rotations, and translations) by graphing in the coordinate plane.Grade 7
Virginia8.1.aThe student will simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers.Grade 8
Virginia8.1.bThe student will compare and order decimals, fractions, percents, and numbers written in scientific notation.Grade 8
Virginia8.10.bThe student will apply the Pythagorean Theorem.Grade 8
Virginia8.13.bThe student will construct and analyze scatterplots.Grade 8
Virginia8.14The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship.Grade 8
Virginia8.15.aThe student will solve multistep linear equations in one variable with the variable on one and two sides of the equation.Grade 8
Virginia8.16The student will graph a linear equation in two variables.Grade 8
Virginia8.3.aThe student will solve practical problems involving rational numbers, percents, ratios, and proportions.Grade 8
Virginia8.4The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables.Grade 8
Virginia8.6.aThe student will verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary anglesGrade 8
Virginia8.6.bThe student will measure angles of less than 360°Grade 8
Virginia8.8.aThe student will apply transformations to plane figures.Grade 8
Virginia8.8.bThe student will identify applications of transformations.Grade 8
VirginiaA.11The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions.Grade 9
VirginiaA.2.cThe student will perform operations on polynomials, including factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations.Grade 9
VirginiaA.4.eThe student will solve multistep linear and quadratic equations in two variables, including solving systems of two linear equations in two variables algebraically and graphically.Grade 9
VirginiaA.6.aThe student will graph linear equations and linear inequalities in two variables, including determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined.Grade 9
VirginiaA.6.bThe student will graph linear equations and linear inequalities in two variables, including writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.Grade 9
VirginiaA.7.aThe student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including determining whether a relation is a functionGrade 9
VirginiaA.7.cThe student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including zeros of a function.Grade 9
VirginiaA.7.dThe student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including x- and y-intercepts.Grade 9
VirginiaA.7.eThe student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including finding the values of a function for elements in its domainGrade 9
VirginiaA.7.fThe student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.Grade 9
VirginiaG.4.aThe student will construct and justify the constructions of a line segment congruent to a given line segment.Grade 9
VirginiaG.4.fThe student will construct and justify the constructions of an angle congruent to a given angle.Grade 9
VirginiaG.5.cThe student,given information concerning the lengths of sides and/or measures of angles in triangles, will determine whether a triangle exists.Grade 9
VirginiaK.1The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondenceKindergarten
VirginiaK.2.aThe student will tell how many are in the set by counting the number of objects orallyKindergarten
VirginiaK.2.bThe student will write the numeral to tell how many are in the setKindergarten
VirginiaK.4.aThe student will count forward to 100 and backward from 10Kindergarten
VirginiaK.4.bThe student will identify one more than a number and one less than a numberKindergarten
VirginiaK.4.cThe student will count by fives and tens to 100Kindergarten
VirginiaK.6The student will model adding and subtracting whole numbers, using up to 10 concrete objectsKindergarten
TexasA.10.BMultiply polynomials of degree one and degree two.Algebra
TexasA.10.DRewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.Algebra
TexasA.10.EFactor, if possible, trinomials with real factors in the form ax^2 + bx + c, including perfect square trinomials of degree two.Algebra
TexasA.2.BWrite linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points.Algebra
TexasA.2.CWrite linear equations in two variables given a table of values, a graph, and a verbal description.Algebra
TexasA.2.DWrite and solve equations involving direct variation.Algebra
TexasA.3.ADetermine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1).Algebra
TexasA.3.BCalculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems.Algebra
TexasA.3.CGraph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems.Algebra
TexasA.3.EDetermine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.Algebra
TexasA.3.FGraph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.Algebra
TexasA.4.CWrite, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.Algebra
TexasA.6.BWrite equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)^2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax^2+ bx + c).Algebra
TexasA.7.AGraph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.Algebra
TexasA.7.BDescribe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.Algebra
TexasA.7.CDetermine the effects on the graph of the parent function f(x) = x^2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.Algebra
TexasA.8.BWrite, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.Algebra
TexasA2.4.AWrite the quadratic function given three specified points in the plane.Algebra
TexasA2.6.AAnalyze the effect on the graphs of f(x) = x^3 and f(x) = x^(1/3) when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d.Algebra
Texas1.2.BUse concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones.Grade 1
Texas1.2.CUse objects, pictures, and expanded and standard forms to represent numbers up to 120.Grade 1
Texas1.2.DGenerate a number that is greater than or less than a given whole number up to 120.Grade 1
Texas1.2.EUse place value to compare whole numbers up to 120 using comparative language.Grade 1
Texas1.2.FOrder whole numbers up to 120 using place value and open number lines.Grade 1
Texas1.2.GRepresent the comparison of two numbers to 100 using the symbols >,Grade 1
Texas1.3.AUse concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99.Grade 1
Texas1.3.CCompose 10 with two or more addends with and without concrete objects.Grade 1
Texas1.3.DApply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10.Grade 1
Texas1.3.FGenerate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20.Grade 1
Texas1.5.ARecite numbers forward and backward from any given number between 1 and 120.Grade 1
Texas1.5.BSkip count by twos, fives, and tens to determine the total number of objects up to 120 in a set.Grade 1
Texas1.5.CUse relationships to determine the number that is 10 more and 10 less than a given number up to 120.Grade 1
Texas1.5.EUnderstand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).Grade 1
Texas1.5.FDetermine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation.Grade 1
Texas1.5.GApply properties of operations to add and subtract two or three numbers.Grade 1
Texas1.7.ETell time to the hour and half hour using analog and digital clocks.Grade 1
Texas1.8.ACollect, sort, and organize data in up to three categories using models/representations such as tally marks or T-chartsGrade 1
Texas1.8.BUse data to create picture and bar-type graphsGrade 1
Texas1.8.CDraw conclusions and generate and answer questions using information from picture and bar-type graphs.Grade 1
Texas2.10.BOrganize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more.Grade 2
Texas2.10.DDraw conclusions and make predictions from information in a graph.Grade 2
Texas2.2.AUse concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones.Grade 2
Texas2.2.CGenerate a number that is greater than or less than a given whole number up to 1,200.Grade 2
Texas2.2.DUse place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>,Grade 2
Texas2.2.ELocate the position of a given whole number on an open number line.Grade 2
Texas2.3.BExplain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part.Grade 2
Texas2.3.CUse concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole.Grade 2
Texas2.4.ARecall basic facts to add and subtract within 20 with automaticity.Grade 2
Texas2.4.BAdd up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations.Grade 2
Texas2.4.CSolve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms.Grade 2
Texas2.4.DGenerate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000.Grade 2
Texas2.8.ACreate two dimensional shpaes based on given attributes including number of sides and vertices.Grade 2
Texas2.9.AFind the length of objects using concrete models for standard units of length.Grade 2
Texas2.9.CRepresent whole numbers as distances from any given location on a number line.Grade 2
Texas2.9.DDetermine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes.Grade 2
Texas2.9.EDetermine a solution to a problem involving length, including estimating lengths.Grade 2
Texas2.9.GRead and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m.Grade 2
Texas3.2.ACompose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate.Grade 3
Texas3.2.DCompare and order whole numbers up to 100,000 and represent comparisons using the symbols >,Grade 3
Texas3.3.ARepresent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines.Grade 3
Texas3.3.BDetermine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line.Grade 3
Texas3.3.DCompose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b.Grade 3
Texas3.3.FRepresent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines.Grade 3
Texas3.3.GExplain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model.Grade 3
Texas3.4.ASolve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.Grade 3
Texas3.4.BRound to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems.Grade 3
Texas3.4.ERepresent 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
Texas3.4.FRecall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts.Grade 3
Texas3.4.GUse strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties.Grade 3
Texas3.4.KSolve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts.Grade 3
Texas3.5.ARepresent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations.Grade 3
Texas3.5.BRepresent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations.Grade 3
Texas3.5.DDetermine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product.Grade 3
Texas3.6.BUse attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories.Grade 3
Texas3.6.CDetermine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row.Grade 3
Texas3.7.ARepresent fractions of halves, fourths, and eighths as distances from zero on a number line.Grade 3
Texas3.7.CDetermine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes.Grade 3
Texas3.8.ASummarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals.Grade 3
Texas3.8.BSolve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals.Grade 3
Texas4.2.AInterpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left.Grade 4
Texas4.2.BRepresent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals.Grade 4
Texas4.2.CCompare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >,Grade 4
Texas4.2.DRound whole numbers to a given place value through the hundred thousands place.Grade 4
Texas4.2.FCompare and order decimals using concrete and visual models to the hundredths.Grade 4
Texas4.2.GRelate decimals to fractions that name tenths and hundredths.Grade 4
Texas4.3.ARepresent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b.Grade 4
Texas4.3.CDetermine if two given fractions are equivalent using a variety of methods.Grade 4
Texas4.3.DCompare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <.Grade 4
Texas4.3.ERepresent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations.Grade 4
Texas4.3.GRepresent fractions and decimals to the tenths or hundredths as distances from zero on a number line.Grade 4
Texas4.4.AAdd and subtract whole numbers and decimals to the hundredths place using the standard algorithm.Grade 4
Texas4.4.BDetermine products of a number and 10 or 100 using properties of operations and place value understandings.Grade 4
Texas4.4.CRepresent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15.Grade 4
Texas4.4.DUse strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties.Grade 4
Texas4.4.ERepresent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations.Grade 4
Texas4.4.FUse strategies and algorithms, including the standard algorithm, to divide up to a four- digit dividend by a one-digit divisor.Grade 4
Texas4.4.GRound to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers.Grade 4
Texas4.4.HSolve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.Grade 4
Texas4.5.BRepresent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequencing and their position in the sequence.Grade 4
Texas4.6.AIdentify points, lines, line segments, rays, angles, and perpendicular and parallel lines.Grade 4
Texas4.6.CApply knowledge of right angles to identify acute, right, and obtuse triangles.Grade 4
Texas4.6.DClassify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of specified size.Grade 4
Texas4.7.AIllustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers.Grade 4
Texas4.7.BIllustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers.Grade 4
Texas4.7.CDetermine the approximate measures of angles in degrees to the nearest whole number using a protractor.Grade 4
Texas4.7.DDraw an angle with a given measure.Grade 4
Texas4.7.EDetermine the measure of an unknown angle formed by two non overlapping adjacent angles given one or both angle measures.Grade 4
Texas4.8.AIdentify relative sizes of measurement units within the customary and metric systems.Grade 4
Texas4.8.BConvert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.Grade 4
Texas4.8.CSolve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.Grade 4
Texas4.9.ARepresent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions.Grade 4
Texas4.9.BSolve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot.Grade 4
Texas5.2.ARepresent the value of the digit in decimals through the thousandths using expanded notation and numerals.Grade 5
Texas5.2.BCompare and order two decimals to thousandths and represent comparisons using the symbols >,Grade 5
Texas5.2.CRound decimals to tenths or hundredths.Grade 5
Texas5.3.AEstimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division.Grade 5
Texas5.3.BMultiply with fluency a three-digit number by a two-digit number using the standard algorithm.Grade 5
Texas5.3.CSolve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm.Grade 5
Texas5.3.DRepresent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models.Grade 5
Texas5.3.ESolve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers.Grade 5
Texas5.3.FRepresent quotients of decimals to the hundredths, up to four-digit dividends and two- digit whole number divisors, using objects and pictorial models, including area models.Grade 5
Texas5.3.GSolve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm.Grade 5
Texas5.3.IRepresent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models.Grade 5
Texas5.3.JRepresent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ? 7 and 7 ? 1/3 using objects and pictorial models, including area models.Grade 5
Texas5.3.LDivide whole numbers by unit fractions and unit fractions by whole numbers.Grade 5
Texas5.4.EDescribe the meaning of parentheses and brackets in a numeric expression.Grade 5
Texas5.4.FSimplify numerical expressions that do not involve exponents, including up to two levels of grouping.Grade 5
Texas5.5.AClassify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties.Grade 5
Texas5.8.ADescribe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin.Grade 5
Texas5.8.BDescribe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane.Grade 5
Texas5.8.CGraph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table.Grade 5
Texas5.9.ARepresent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots.Grade 5
Texas5.9.CSolve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot.Grade 5
Texas6.10.BDetermine if the given value(s) make(s) one-variable, one-step equations or inequalities true.Grade 6
Texas6.11.AGraph points in all four quadrants using ordered pairs of rational numbers.Grade 6
Texas6.2.BIdentify a number, its opposite, and its absolute value.Grade 6
Texas6.2.CLocate, compare, and order integers and rational numbers using a number line.Grade 6
Texas6.2.DOrder a set of rational numbers arising from mathematical and real-world contexts.Grade 6
Texas6.2.EExtend representations for division to include fraction notation such as a/b represents the same number as a ? b where b ? 0.Grade 6
Texas6.3.CRepresent integer operations with concrete models and connect the actions with the models to standardized algorithms.Grade 6
Texas6.3.DAdd, subtract, multiply, and divide integers fluently.Grade 6
Texas6.3.EMultiply and divide positive rational numbers fluently.Grade 6
Texas6.4.ACompare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships.Grade 6
Texas6.4.BApply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates.Grade 6
Texas6.4.CGive examples of ratios as multiplicative comparisons of two quantities describing the same attribute.Grade 6
Texas6.4.ERepresent ratios and percents with concrete models, fractions, and decimals.Grade 6
Texas6.4.FRepresent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers.Grade 6
Texas6.4.HConvert units within a measurement system, including the use of proportions and unit rates.Grade 6
Texas6.5.ARepresent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.Grade 6
Texas6.5.BSolve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models.Grade 6
Texas6.5.CUse equivalent fractions, decimals, and percents to show equal parts of the same whole.Grade 6
Texas6.6.BWrite an equation that represents the relationship between independent and dependent quantities from a table.Grade 6
Texas6.6.CRepresent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.Grade 6
Texas6.7.AGenerate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization.Grade 6
Texas6.7.CDetermine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations.Grade 6
Texas6.7.DGenerate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.Grade 6
Texas6.8.AExtend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle.Grade 6
Texas6.9.AWrite one-variable, one-step equations and inequalities to represent constraints or conditions within problems.Grade 6
Texas6.9.BRepresent solutions for one-variable, one-step equations and inequalities on number lines.Grade 6
Texas7.10.BRepresent solutions for one-variable, two-step equations and inequalities on number lines.Grade 7
Texas7.11.AModel and solve one-variable, two-step equations and inequalities.Grade 7
Texas7.11.BDetermine if the given value(s) make(s) one-variable, two-step equations and inequalities true.Grade 7
Texas7.11.CWrite and solve equations using geometry concepts, including the sum of the angles in a triangle and angle relationships.Grade 7
Texas7.3.AAdd, subtract, multiply, and divide rational numbers fluently.Grade 7
Texas7.3.BApply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers.Grade 7
Texas7.5.AGeneralize the critical attributes of similarity, including ratios within and between similar shapes.Grade 7
Texas7.5.CSolve mathematical and real-world problems involving similar shape and scale drawings.Grade 7
Texas7.7.ARepresent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b.Grade 7
Texas8.10.AGeneralize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane.Grade 8
Texas8.11.AConstruct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data.Grade 8
Texas8.2.CConvert between standard decimal notation and scientific notation.Grade 8
Texas8.4.AUse similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line.Grade 8
Texas8.4.BGraph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship.Grade 8
Texas8.4.CUse data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.Grade 8
Texas8.5.ARepresent linear proportional situations with tables, graphs, and equations in the form of y = kx.Grade 8
Texas8.5.BRepresent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ? 0.Grade 8
Texas8.5.IWrite an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.Grade 8
Texas8.7.CUse the Pythagorean Theorem and its converse to solve problems.Grade 8
Texas8.7.DDetermine the distance between two points on a coordinate plane using the Pythagorean Theorem.Grade 8
Texas8.9.AIdentify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations.Grade 8
TexasK.2.ACount forward and backward to at least 20 with and without objects.Kindergarten
TexasK.2.BRead, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures.Kindergarten
TexasK.2.CCount a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order.Kindergarten
TexasK.2.EGenerate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20.Kindergarten
TexasK.2.FGenerate a number that is one more than or one less than another number up to at least 20.Kindergarten
TexasK.2.GCompare sets of objects up to at least 20 in each set using comparative language.Kindergarten
TexasK.2.HUse comparative language to describe two numbers up to 20 presented as written numerals.Kindergarten
TexasK.2.ICompose and decompose numbers up to 10 with objects and pictures.Kindergarten
TexasK.3.AModel the action of joining to represent addition and the action of separating to represent subtraction.Kindergarten
TexasK.5.ARecite numbers up to at least 100 by ones and tens beginning with any given number.Kindergarten
WNCPA.1.1.7Evaluate powers with integral bases (excluding base 0) and whole number exponents.Algebra
WNCPA.2.1.2Write a linear equation to represent a given context.Algebra
WNCPA.2.1.5Write a linear equation representing the pattern in a given table of values and verify the equation by substituting values from the table.Algebra
WNCPA.2.2.2Graph a given linear relation, including horizontal and vertical lines.Algebra
WNCPA.2.2.3Match given equations of linear relations with their corresponding graphs.Algebra
WNCPA.2.5.2Write the expression for a given model of a polynomial.Algebra
WNCPA.2.5.3Identify the variables, degree, number of terms and coefficients, including the constant term, of a given simplified polynomial expression.Algebra
WNCPA.2.6.3Apply a personal strategy for addition and subtraction of given polynomial expressions, and record the process symbolically.Algebra
WNCPA.2.7.1Model multiplication of a given polynomial expression by a given monomial concretely or pictorially and record the process symbolically.Algebra
WNCPA.2.7.3Apply a personal strategy for multiplication and division of a given polynomial expression by a given monomialAlgebra
WNCP1.1.1.1Recite forward by 1s the number sequence between two given numbers (0 to 100)Grade 1
WNCP1.1.1.4Read a given numeral (0 to 100) when it is presented symbolicallyGrade 1
WNCP1.1.10.1Use and describe a personal strategy for determining a given sumGrade 1
WNCP1.1.10.2Use and describe a personal strategy for determining a given differenceGrade 1
WNCP1.1.10.3Write the related subtraction fact for a given addition factGrade 1
WNCP1.1.2.1Look briefly at a given familiar arrangement of objects or dots and identify the number represented without countingGrade 1
WNCP1.1.3.5Determine the total number of objects in a given set, starting from a known quantity and counting onGrade 1
WNCP1.1.3.6Count quantity using groups of 2s, 5s or 10s and counting onGrade 1
WNCP1.1.4.1Represent a given number up to 20 using a variety of manipulatives, including ten frames and base ten materialsGrade 1
WNCP1.1.4.3Partition any given quantity up to 20 into 2 parts and identify the number of objects in each partGrade 1
WNCP1.1.5.4Compare two given sets using one-to-one correspondence and describe them using comparative words, such as more, fewer or as manyGrade 1
WNCP1.1.5.5Compare a set to a given referent using comparative languageGrade 1
WNCP1.1.7.1Represent a given number in a variety of equal groups with and without singlesGrade 1
WNCP1.1.7.2Recognize that for a given number of counters, no matter how they are grouped, the total number of counters does not changeGrade 1
WNCP1.1.8.1Name the number that is one more, two more, one less or two less than a given number, up to 20Grade 1
WNCP1.1.8.2Represent a number on a ten frame that is one more, two more, one less or two less than a given numberGrade 1
WNCP1.2.3.3Determine if two given concrete sets are equal or unequal and explain the process usedGrade 1
WNCP2.1.1.1Extend a given skip counting sequence (by 2s, 5s or 10s) forward and backwardGrade 2
WNCP2.1.1.2Skip count by 10s, given any number from 1 to 9 as a starting pointGrade 2
WNCP2.1.1.5Count quantity using groups of 2s, 5s or 10s and counting onGrade 2
WNCP2.1.10.1Explain the mental mathematics strategy that could be used to determine a basic fact, such as doublesGrade 2
WNCP2.1.10.2Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles plus oneGrade 2
WNCP2.1.10.3Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles take away oneGrade 2
WNCP2.1.10.4Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles plus twoGrade 2
WNCP2.1.10.5Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles take away twoGrade 2
WNCP2.1.10.6Explain the mental mathematics strategy that could be used to determine a basic fact, such as making 10Grade 2
WNCP2.1.10.7Explain the mental mathematics strategy that could be used to determine a basic fact, such as building on a known doubleGrade 2
WNCP2.1.4.1Represent a given number using concrete materials, such as ten frames and base ten materialsGrade 2
WNCP2.1.5.1Order a given set of numbers in ascending or descending order and verify the result using a hundred chart, number line, ten frames or by making references to place valueGrade 2
WNCP2.1.5.3Identify missing numbers in a given hundred chartGrade 2
WNCP2.1.7.2Count the number of objects in a given set using groups of 10s and 1s, and record the result as a 2-digit numeral under the headings of 10s and 1sGrade 2
WNCP2.1.7.3Describe a given 2-digit numeral in at least two waysGrade 2
WNCP2.1.7.4Illustrate using ten frames and diagrams that a given numeral consists of a certain number of groups of ten and a certain number of onesGrade 2
WNCP2.1.8.1Add zero to a given number and explain why the sum is the same as the addendGrade 2
WNCP2.1.8.2Subtract zero from a given number and explain why the difference is the same as the given numberGrade 2
WNCP2.1.9.1Model addition and subtraction using concrete materials or visual representations and record the process symbolicallyGrade 2
WNCP2.1.9.3Solve a given problem involving a missing addend and describe the strategy usedGrade 2
WNCP2.1.9.7Add a given set of numbers in two different ways, and explain why the sum is the sameGrade 2
WNCP2.2.3.1Determine whether two given quantities of the same object (same shape and mass) are equal by using a balance scaleGrade 2
WNCP2.3.8.2Identify common attributes of triangles, squares, rectangles and circles from given sets of the same type of 2-D shapes.Grade 2
WNCP2.3.8.3Identify given 2-D shapes with different dimensions.Grade 2
WNCP2.3.8.4Identify given 2-D shapes with different orientations.Grade 2
WNCP2.3.8.5Create a model to represent a given 2-D shape.Grade 2
WNCP2.3.8.6Create a pictorial representation of a given 2-D shape.Grade 2
WNCP2.4.1.2Organize data as it is collected using concrete objects, tallies, checkmarks, charts or lists.Grade 2
WNCP2.4.1.3Answer questions using collected data.Grade 2
WNCP2.4.2.3Answer questions pertaining to a given concrete graph or pictograph.Grade 2
WNCP2.4.2.4Create a concrete graph to display a given set of data and draw conclusions.Grade 2
WNCP2.4.2.5Create a pictograph to represent a given set of data using one-to-one correspondence.Grade 2
WNCP2.4.2.6Solve a given problem by constructing and interpreting a concrete graph or pictograph.Grade 2
WNCP3.1.1.1Extend a given skip counting sequence by 5s, 10s or 100s, forward and backward, using a given starting pointGrade 3
WNCP3.1.1.2Extend a given skip counting sequence by 3s, forward and backward, starting at a given multiple of 3Grade 3
WNCP3.1.1.3Extend a given skip counting sequence by 4s, forward and backward, starting at a given multiple of 4Grade 3
WNCP3.1.10.1Describe a mental mathematics strategy that could be used to determine a given basic fact, such as doublesGrade 3
WNCP3.1.10.6Describe a mental mathematics strategy that could be used to determine a given basic fact, such as making 10Grade 3
WNCP3.1.11.3Represent a given multiplication expression as repeated additionGrade 3
WNCP3.1.11.6Represent, concretely or pictorially, equal groups for a given number sentenceGrade 3
WNCP3.1.11.7Represent a given multiplication expression using an arrayGrade 3
WNCP3.1.11.9Relate multiplication to division by using arrays and writing related number sentencesGrade 3
WNCP3.1.12.10Solve a given problem involving divisionGrade 3
WNCP3.1.13.3Cut or fold a whole into equal parts, or draw a whole in equal parts; demonstrate that the parts are equal and name the partsGrade 3
WNCP3.1.13.5Represent a given fraction concretely or pictoriallyGrade 3
WNCP3.1.2.4Represent a given number using manipulatives, such as base ten materialsGrade 3
WNCP3.1.3.1Place a given set of numbers in ascending or descending order and verify the result by using a hundred chartGrade 3
WNCP3.1.4.3Estimate a given quantity by comparing it to a referentGrade 3
WNCP3.1.5.1Record, in more than one way, the number represented by given proportional and nonproportional concrete materialsGrade 3
WNCP3.1.5.2Represent a given number in different ways using proportional and non-proportional concrete materials and explain how they are equivalentGrade 3
WNCP3.1.6.1Add two given 2-digit numerals using a mental mathematics strategy and explain or illustrate the strategyGrade 3
WNCP3.1.7.1Subtract two given 2-digit numerals using a mental mathematics strategy and explain or model the strategy usedGrade 3
WNCP3.1.9.1Model the addition of two or more given numbers using concrete or visual representations and record the process symbolicallyGrade 3
WNCP3.1.9.2Model the subtraction of two given numbers using concrete or visual representations and record the process symbolicallyGrade 3
WNCP3.1.9.6Solve a given problem involving the sum or difference of two given numbersGrade 3
WNCP3.2.3.5Solve a given addition or subtraction equation with one unknown using a variety of strategies including guess and testGrade 3
WNCP3.3.3.6Determine and record the length and width of a given 2-D shapeGrade 3
WNCP3.3.3.8Draw a line segment of a given length using a rulerGrade 3
WNCP3.3.3.9Sketch a line segment of a given length without using a rulerGrade 3
WNCP3.3.7.1Classify a given set of regular and irregular polygons according to the number of sideGrade 3
WNCP3.4.1.1Record the number of objects in a given set using tally marksGrade 3
WNCP3.4.1.3Organize a given set of data using tally marks, line plots, charts or listsGrade 3
WNCP3.4.1.4Collect and organize data using tally marks, line plots, charts and listsGrade 3
WNCP3.4.1.5Answer questions arising from a given line plot, chart or listGrade 3
WNCP3.4.1.6Answer questions using collected dataGrade 3
WNCP3.4.2.2Create bar graphs from a given set of data including labelling the title and axesGrade 3
WNCP3.4.2.3Draw conclusions from a given bar graph to solve problemsGrade 3
WNCP3.4.2.4Solve problems by constructing and interpreting a bar graphGrade 3
WNCP4.1.10.4Express a given pictorial or concrete representation as a fraction or decimalGrade 4
WNCP4.1.11.1Predict sums and differences of decimals using estimation strategiesGrade 4
WNCP4.1.2.1Order a given set of numbers in ascending or descending order and explain the order by making references to place valueGrade 4
WNCP4.1.3.4Estimate sums and differences using different strategies, e.g., front-end estimation and compensationGrade 4
WNCP4.1.5.1Provide examples for applying mental mathematics strategies: doublingGrade 4
WNCP4.1.5.2Provide examples for applying mental mathematics strategies: doubling and adding one more groupGrade 4
WNCP4.1.5.4Provide examples for applying mental mathematics strategies: halvingGrade 4
WNCP4.1.6.1Model a given multiplication problem using the distributive propertyGrade 4
WNCP4.1.6.2Use concrete materials, such as base ten blocks or their pictorial representations, to represent multiplication and record the process symbolicallyGrade 4
WNCP4.1.6.5Model and solve a given multiplication problem using an array and record the processGrade 4
WNCP4.1.7.3Solve a given division problem using a personal strategy and record the processGrade 4
WNCP4.1.8.11Name fractions between two given benchmarks on a number lineGrade 4
WNCP4.1.8.6Represent a given fraction pictorially by shading parts of a given wholeGrade 4
WNCP4.1.8.8Order a given set of fractions that have the same numerator and explain the orderingGrade 4
WNCP4.1.8.9Order a given set of fractions that have the same denominator and explain the orderingGrade 4
WNCP4.1.9.2Represent a given decimal using concrete materials or a pictorial representationGrade 4
WNCP4.1.9.3Explain the meaning of each digit in a given decimal with all digits the sameGrade 4
WNCP4.2.5.3Identify the unknown in a story problem, represent the problem with an equation and solve the problem concretely, pictorially or symbolicallyGrade 4
WNCP4.3.1.2Express the time orally and numerically from a 12-hour analog clockGrade 4
WNCP4.3.1.3Express the time orally and numerically from a 24-hour analog clockGrade 4
WNCP4.3.1.4Express the time orally and numerically from a 12-hour digital clockGrade 4
WNCP4.3.5.3Complete a symmetrical 2-D shape given half the shape and its line of symmetry.Grade 4
WNCP4.4.2.1Identify an interval and correspondence for displaying a given set of data in a graph and justify the choiceGrade 4
WNCP4.4.2.2Create and label (with categories, title and legend) a pictograph to display a given set of data using many-to-one correspondence, and justify the choice of correspondence usedGrade 4
WNCP4.4.2.3Create and label (with axes and title) a bar graph to display a given set of data using many-to one correspondence, and justify the choice of interval usedGrade 4
WNCP4.4.2.4Answer a given question using a given graph in which data is displayed using many-to-one correspondenceGrade 4
WNCP5.1.10.1Order a given set of decimals by placing them on a number line that contains benchmarksGrade 5
WNCP5.1.10.2Order a given set of decimals including only tenths using place valueGrade 5
WNCP5.1.10.3Order a given set of decimals including only hundredths using place valueGrade 5
WNCP5.1.11.5Solve a given problem that involves addition and subtraction of decimals, limited to thousandthsGrade 5
WNCP5.1.3.1Describe the mental mathematics strategy used to determine a given basic fact, such as skip count up by one or two groups from a known factGrade 5
WNCP5.1.3.3Describe the mental mathematics strategy used to determine a given basic fact, such as doublingGrade 5
WNCP5.1.3.5Describe the mental mathematics strategy used to determine a given basic fact, such as repeated doublingGrade 5
WNCP5.1.4.1Determine the products when one factor is a multiple of 10, 100 or 1000 by annexing zero or adding zerosGrade 5
WNCP5.1.4.2Apply halving and doubling when determining a given productGrade 5
WNCP5.1.4.3Apply the distributive property to determine a given product involving multiplying factors that are close to multiples of 10Grade 5
WNCP5.1.6.2Explain that the interpretation of a remainder depends on the context: ignore the remainderGrade 5
WNCP5.1.6.3Explain that the interpretation of a remainder depends on the context: round up the quotientGrade 5
WNCP5.1.6.4Explain that the interpretation of a remainder depends on the context: express remainders as fractionsGrade 5
WNCP5.1.7.1Create a set of equivalent fractions and explain why there are many equivalent fractions for any given fraction using concrete materialsGrade 5
WNCP5.1.8.2Represent a given decimal using concrete materials or a pictorial representationGrade 5
WNCP5.3.6.2Sort a given set of quadrilaterals and explain the sorting rule.Grade 5
WNCP5.3.6.4Sort a given set of quadrilaterals according to whether or not opposite sides are parallel.Grade 5
WNCP5.3.7.1Translate a given 2-D shape horizontally, vertically or diagonally, and descrive the position and orientation of the image.Grade 5
WNCP5.3.7.2Rotate a given 2-D shape about a point, and describe the position and orientation of the image.Grade 5
WNCP5.3.7.3Reflect a given 2-D shape in a line of reflection, and describe the position and orientation of the image.Grade 5
WNCP5.3.7.4Perform a transformation ofa given 2-D shape by following instructions.Grade 5
WNCP5.3.7.7Draw a 2-D shape, reflect the shape, and identify the line of reflection and the distance of the image from the line of reflection.Grade 5
WNCP5.3.8.1Provide an example of a translation, a rotation and a reflection.Grade 5
WNCP5.3.8.2Identify a given single transformation as a translation, rotation or reflection.Grade 5
WNCP5.3.8.3Describe a given rotation by the direction of the turn (clockwise or counterclockwise).Grade 5
WNCP6.1.3.1Identify multiples for a given number and explain the strategy used to identify themGrade 6
WNCP6.1.3.3Identify the factors for a given number and explain the strategy usedGrade 6
WNCP6.1.6.3Use concrete materials and pictorial representations to illustrate a given percentGrade 6
WNCP6.1.6.5Express a given percent as a fraction and a decimalGrade 6
WNCP6.1.6.7Solve a given problem involving percentsGrade 6
WNCP6.1.7.2Place given integers on a number line and explain how integers are orderedGrade 6
WNCP6.1.7.4Compare two integers, represent their relationship using the symbols and =, and verify using a number line.Grade 6
WNCP6.1.8.5Solve a given problem that involves multiplication and division of decimals using multipliers from 0 to 9 and divisors from 1 to 9Grade 6
WNCP6.1.9.1Demonstrate and explain with examples why there is a need to have a standardized order of operations.Grade 6
WNCP6.1.9.2Apply the order of operations to solve multi-step problems with or without technology, e.g., computer, calculator.Grade 6
WNCP6.2.1.1Generate values in one column of a table of values, given values in the other column and pattern rule.Grade 6
WNCP6.2.1.2State, using mathematical language, the relationship in a given table of values.Grade 6
WNCP6.2.1.3Create a concrete or pictorial representation of the relationship shown in a table of values.Grade 6
WNCP6.2.1.5Formulate a rule to describe the relationship between two columns of numbers in a table of values.Grade 6
WNCP6.2.1.6Identify missing elements in a given table of values.Grade 6
WNCP6.2.2.1Translate a pattern to a table of values and graph the table of values (limit to linear graphs with discrete elements).Grade 6
WNCP6.2.2.2Create a table of values from a given pattern or a given graph.Grade 6
WNCP6.3.1.4Estimate the measure of an angle using 45°, 90° and 180° as reference anglesGrade 6
WNCP6.3.1.5Measure, using a protractor, given angles in various orientations.Grade 6
WNCP6.3.1.6Draw and label a specified angle in various orientations using a protractorGrade 6
WNCP6.3.1.7Describe the measure of an angle as the measure of rotation of one of its sidesGrade 6
WNCP6.3.1.8Describe the measure of angles as the measure of an interior angle of a polygon.Grade 6
WNCP6.3.2.1Explain, using models, that the sum of the interior angles of a triangle is the same for all triangles.Grade 6
WNCP6.3.2.2Explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals.Grade 6
WNCP6.3.4.2Sort a given set of triangles according to the measures of the interior angles.Grade 6
WNCP6.3.4.3Identify the characteristics of a given set of triangles according to their sides and/or their interior angles.Grade 6
WNCP6.3.4.4Sort a given set of triangles and explain the sorting rule.Grade 6
WNCP6.3.4.5Draw a specified triangle, e.g. scalene.Grade 6
WNCP6.3.4.6Replicate a given triangle in a different orientation and show that the two are congruent.Grade 6
WNCP6.3.5.1Sort a given set of 2-D shapes into polygons and non-polygonsGrade 6
WNCP6.3.5.3Demonstrate congruence (sides to sides and angles to angles) in a regular polygon by measuring.Grade 6
WNCP6.3.5.4Demonstrate that the sides of a regular polygon are of the same length and that the angles of a regular polygon are of the same measure.Grade 6
WNCP6.3.6.7Perform and record one or more transformations of a 2-D shape that will result in a given image.Grade 6
WNCP6.3.8.2Plot a point in the first quadrant of a Cartesian plane given its ordered pair.Grade 6
WNCP6.3.8.3Match points in the first quadrant of a Cartesian plane with their corresponding ordered pair.Grade 6
WNCP6.3.8.4Plot points in the first quadrant of a Cartesian plane with intervals of 1, 2, 5 or 10 on its axes, given whole number ordered pairs.Grade 6
WNCP6.3.8.5Draw shapes or designs, given ordered pairs in the first quadrant of a Cartesian plane.Grade 6
WNCP6.3.8.6Determine the distance between points along horizontal and vertical lines in the first quadrant of a Cartesian plane.Grade 6
WNCP7.1.2.1Solve a given problem involving the addition of two or more decimal numbersGrade 7
WNCP7.1.2.3Solve a given problem involving the multiplication of decimal numbersGrade 7
WNCP7.1.2.4Solve a given problem involving the multiplication or division of decimal numbers with 2- digit multipliers or 1-digit divisors (whole numbers or decimals)Grade 7
WNCP7.1.3.2Solve a given problem that involves finding a percentGrade 7
WNCP7.1.5.1Model addition and subtraction of a given positive fraction or a given mixed number using concrete representations, and record symbolicallyGrade 7
WNCP7.1.5.2Determine the sum of two given positive fractions or mixed numbers with like denominatorsGrade 7
WNCP7.1.5.3Determine the difference of two given positive fractions or mixed numbers with like denominatorsGrade 7
WNCP7.1.6.1Explain, using concrete materials such as integer tiles and diagrams, that the sum of opposite integers is zero.Grade 7
WNCP7.1.6.2Illustrate, using a number line, the results of adding or subtracting negative and positive integersGrade 7
WNCP7.1.6.3Add two given integers using concrete materials or pictorial representations and record the process symbolically.Grade 7
WNCP7.1.6.4Subtract two given integers using concrete materials or pictorial representations and record the process symbolically.Grade 7
WNCP7.1.6.5Solve a given problem involving the addition and subtraction of integers.Grade 7
WNCP7.1.7.2Identify a number that would be between two given numbers in an ordered sequence or on a number line.Grade 7
WNCP7.2.2.1Create a table of values for a given linear relation by substituting values for the variable.Grade 7
WNCP7.2.2.2Create a table of values using a linear relation and graph the table of values (limited to discrete elements).Grade 7
WNCP7.2.2.3Sketch the graph from a table of values created for a given linear relation and describe the patterns found in the graph to draw conclusions, e.g., graph the relationship between n and 2n + 3.Grade 7
WNCP7.2.5.1Substitute a value for an unknown in a given expression and evaluate the expression.Grade 7
WNCP7.2.6.3Solve a given problem using a linear equation.Grade 7
WNCP7.2.7.3Solve a given problem using a linear equation and record the process.Grade 7
WNCP7.3.4.2Identify the location of a given point in any quadrant of a Cartesian plane using an integral ordered pair.Grade 7
WNCP7.3.4.3Plot the point corresponding to a given integral ordered pair on a Cartesian plane with units of 1, 2, 5 or 10 on its axes.Grade 7
WNCP7.3.4.4Draw shapes and designs, using given integral ordered pairs, in a Cartesian plane.Grade 7
WNCP7.3.4.5Create shapes and designs, and identify the points used to produce the shapes and designs in any quadrant of a Cartesian plane.Grade 7
WNCP7.3.5.1Identify the coordinates of the vertices of a given 2-D shape on a Cartesian plane.Grade 7
WNCP7.3.5.3Describe the positional change of the vertices of a given 2-D shape to the corresponding vertices of its image as a result of a transformation or successive transformations on a Cartesian plane.Grade 7
WNCP8.1.1.1Represent a given perfect square as a square region using materials, such as grid paper or square shapes.Grade 8
WNCP8.1.1.4Determine the square root of a given perfect square and record it symbolically.Grade 8
WNCP8.1.1.5Determine the square of a given number.Grade 8
WNCP8.1.6.10Model division of a positive proper fraction by a positive proper fraction pictorially and record the processGrade 8
WNCP8.1.6.11Generalize and apply rules for multiplying and dividing positive fractions, including mixed numbersGrade 8
WNCP8.1.6.8Model multiplication of a positive fraction by a positive fraction concretely or pictorially using an area model and record the processGrade 8
WNCP8.1.6.9Model division of a positive proper fraction by a whole number concretely or pictorially and record the processGrade 8
WNCP8.1.7.4Model the process of multiplying two integers using concrete materials or pictorial representations and record the processGrade 8
WNCP8.1.7.5Model the process of dividing an integer by an integer using concrete materials or pictorial representations and record the process.Grade 8
WNCP8.1.7.8Generalize and apply a rule for determining the sign of the product and quotient of integers.Grade 8
WNCP8.1.7.9Solve a given problem involving integers taking into consideration order of operations.Grade 8
WNCP8.2.1.1Determine the missing value in an ordered pair for a given equation.Grade 8
WNCP8.2.1.2Create a table of values by substituting values for a variable in the equation of a given linear relation.Grade 8
WNCP8.2.1.3Construct a graph from the equation of a given linear relation (limited to discrete data).Grade 8
WNCP8.2.1.4Describe the relationship between the variables of a given graph.Grade 8
WNCP8.2.2.4Solve a given linear equation symbolically.Grade 8
WNCP8.3.1.4Determine the measure of the third side of a right triangle, given the measures of the other two sides, to solve a given problem.Grade 8
WNCP8.3.1.5Solve a given problem that involves Pythagorean triples, e.g., 3, 4, 5 or 5, 12, 13.Grade 8
WNCPK.1.1.1Name the number that comes after a given number, one to nineKindergarten
WNCPK.1.2.1Look briefly at a given familiar arrangement of 1 to 5 objects or dots and identify the number represented without countingKindergarten
WNCPK.1.4.1Show a given number as two parts, using fingers, counters or other objects, and name the number of objects in each partKindergarten
WNCPK.1.5.2Compare two given sets through direct comparison and describe the sets using words, such as more, fewer, as many as or the same numberKindergarten

DreamBox has been very instrumental in helping my school meet State of Delaware Goals and AYP by decreasing the educational gap. After using it with our Hispanic English Language Learners for just 5 months last year, they met our AYP in math for the first time ever—on the first attempt.

— Marilyn Dollard, Principal, Oberle Elementary School, Bear, Delaware