4.OA Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 4.OA.1 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.1 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Use drawings and equations with a symbol for the unknown number to represent the problem. 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Use drawings and equations with a symbol for the unknown number to represent the problem. 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Interpret remainders Mixed operations 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Interpret remainders Mixed operations 4.OA.3a: Represent these problems using equations or expressions with a letter standing for the unknown quantity. 4.OA.3a: Represent these problems using equations or expressions with a letter standing for the unknown quantity. 4.OA.3b: Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Rounding Identify reasonable answers 4.OA.3b: Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Rounding Identify reasonable answers Gain familiarity with factors and multiples. 4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Prime or composite Multiples Factors 4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Prime or composite Multiples Factors Generate and analyze patterns. 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify and informally explain apparent features of the pattern that were not explicit in the rule itself. Make patterns Identify features of patterns Analyze patterns 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify and informally explain apparent features of the pattern that were not explicit in the rule itself. Make patterns Identify features of patterns Analyze patterns
 4.NBT Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. 4.NBT.2a Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Expanded form Base-ten numerals Number names 4.NBT.2a Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Expanded form Base-ten numerals Number names 4.NBT.2b Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.2b Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. Rounding Estimate sums Estimate differences Estimate products Estimate quotients Mixed operations 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. Rounding Estimate sums Estimate differences Estimate products Estimate quotients Mixed operations Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.4 Fluently add and subtract multi-digit whole numbers using a standard algorithm. Addition Subtraction Mixed operations 4.NBT.4 Fluently add and subtract multi-digit whole numbers using a standard algorithm. Addition Subtraction Mixed operations 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiplication facts Multiply 1-digit numbers using models Multiply 1-digit numbers Multiply 2-digit numbers using models Multiply 2-digit numbers Place value strategies Properties of multiplication 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiplication facts Multiply 1-digit numbers using models Multiply 1-digit numbers Multiply 2-digit numbers using models Multiply 2-digit numbers Place value strategies Properties of multiplication 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Divide 2-digit numbers Divide larger numbers Place value strategies Properties of division 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Divide 2-digit numbers Divide larger numbers Place value strategies Properties of division
 4.NF Number and Operations—Fractions Extend understanding of fraction equivalence and ordering. 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (a × n)/(b × n) 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. 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (a × n)/(b × n) 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. 4.NF.2 Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions. Models Benchmark fractions Compare fractions 4.NF.2 Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions. Models Benchmark fractions Compare fractions Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Equations Area models Strip models 4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Equations Area models Strip models 4.NF.3b: 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. 4.NF.3b: 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. 4.NF.3c: Add and subtract mixed numbers with like denominators. Fractions Mixed numbers 4.NF.3c: Add and subtract mixed numbers with like denominators. Fractions Mixed numbers 4.NF.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. 4.NF.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. 4.NF.4 Apply and extend previous understandings of multiplication to multiply a whole number by a fraction. 4.NF.4 Apply and extend previous understandings of multiplication to multiply a whole number by a fraction. 4.NF.4a: Understand a fraction a/b as a multiple of 1/b. 4.NF.4a: Understand a fraction a/b as a multiple of 1/b. 4.NF.4b: Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a whole number by a fraction. Multiply with models Multiply without models 4.NF.4b: Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a whole number by a fraction. Multiply with models Multiply without models 4.NF.4c: Solve word problems involving multiplication of a whole number by a fraction. 4.NF.4c: Solve word problems involving multiplication of a whole number by a fraction. Understand decimal notation for fractions, and compare decimal fractions. 4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. 4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions. 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
 4.MD Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 4.MD.1.i Know relative sizes of measurement units: ft., in.; km, m, cm. 4.MD.1.i Know relative sizes of measurement units: ft., in.; km, m, cm. 4.MD.1.ii Know the conversion factor and use it to convert measurements in a larger unit in terms of a smaller unit: ft., in.; km, m, cm; hr., min., sec. Customary units Metric units Time 4.MD.1.ii Know the conversion factor and use it to convert measurements in a larger unit in terms of a smaller unit: ft., in.; km, m, cm; hr., min., sec. Customary units Metric units Time 4.MD.1.iii Given the conversion factor, convert all other measurements within a single system of measurement from a larger unit to a smaller unit. 4.MD.1.iii Given the conversion factor, convert all other measurements within a single system of measurement from a larger unit to a smaller unit. 4.MD.1.iv Record measurement equivalents in a two-column table. 4.MD.1.iv Record measurement equivalents in a two-column table. 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money. 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money. 4.MD.2a: Solve problems involving fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Money Measurement Time 4.MD.2a: Solve problems involving fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Money Measurement Time 4.MD.2b: Represent measurement quantities using diagrams that feature a measurement scale, such as number lines. 4.MD.2b: Represent measurement quantities using diagrams that feature a measurement scale, such as number lines. 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Perimeter Area Area and perimeter 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Perimeter Area Area and perimeter Represent and interpret data. 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. Geometric measurement: understand concepts of angle and measure angles. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. 4.MD.5a: Recognize 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. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. 4.MD.5a: Recognize 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. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. 4.MD.5b: Recognize an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.MD.5b: Recognize an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.
 4.G Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Parallel, perpendicular, and intersecting lines Points, lines, and angles 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Parallel, perpendicular, and intersecting lines Points, lines, and angles 4.G.2a Identify and name triangles based on angle size (right, obtuse, acute). 4.G.2a Identify and name triangles based on angle size (right, obtuse, acute). 4.G.2b Identify and name all quadrilaterals with 2 pairs of parallel sides as parallelograms. 4.G.2b Identify and name all quadrilaterals with 2 pairs of parallel sides as parallelograms. 4.G.2c Identify and name all quadrilaterals with four right angles as rectangles. 4.G.2c Identify and name all quadrilaterals with four right angles as rectangles. 4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. 4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.