 ## Common Core State Standards (CCSS) Correlations ## Mathematics

### Domain - Operations and Algebraic Thinking, Grade 4

Use the four operations with whole numbers to solve problems.

Math.4.OA.A.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Activity Page
Doubling and Halving 13
Multiplication with Modeling and Mental Strategies 30
Reasoning with Numbers 31
Multiplication (×2, ×4, and ×8) 32
Multiplication (×5 and ×10) 33
Multiplication (×3, ×6, and ×9) 34
Multiplication (×7, ×8, and ×9) 35
Multiplication 36
Number Lines 51
Multiplication and Division Practice 126

Use the four operations with whole numbers to solve problems.

Math.4.OA.A.3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Activity Page
Subtracting 2-Digit Numbers without Regrouping 23
Subtracting with Regrouping 24
Division with Remainders 47
Division Practice 48
Multiplication and Division 49
Multiplication and Division Practice 126

Use the four operations with whole numbers to solve problems.

Math.4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Activity Page
Multiplication with Modeling and Mental Strategies 30
Multiplication by Tens 41
Extended Multiplication 42
Division 43
Division Problems and Remainders 44
Division with Multiplication Grid 45
Estimation with Division 46
Division with Remainders 47
Division Practice 48
Multiplication and Division 49
Inverse Operations 50

Gain familiarity with factors and multiples.

Math.4.OA.B.4: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Activity Page
Multiples 38
Factors 39
Multiplication Strategies 40
Division with Multiplication Grid 45
Multiplication and Division 49
Inverse Operations 50
Prime and Composite Numbers 52

Generate and analyze patterns.

Math.4.OA.C.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Activity Page
Ordering Numbers 9
Less Than and Greater Than 14
Number Patterns 15
Reasoning with Numbers 31
Multiplication (×2, ×4, and ×8) 32
Multiplication (×5 and ×10) 33
Multiplication (×3, ×6, and ×9) 34
Multiplication (×7, ×8, and ×9) 35
Multiplication 36
Square and Triangular Numbers 37
Multiples 38
1-Step and 2-Step Rules 53

### Domain - Number and Operations in Base Ten, Grade 4

Generalize place value understanding for multi-digit whole numbers.

Math.4.NBT.A.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Activity Page
Numbers to 9,999 7
Place Value 0 – 9,999 8
Ordering Numbers 9
Counting by Thousands 10
Expanding 4-Digit Numbers 11
Less Than and Greater Than 14
Mixed Practice 123
Place Value Practice 124

Generalize place value understanding for multi-digit whole numbers.

Math.4.NBT.A.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Activity Page
Place Value 0 – 9,999 8
Ordering Numbers 9
Counting by Thousands 10
Expanding 4-Digit Numbers 11
Multiplication by Tens 41
Extended Multiplication 42

Generalize place value understanding for multi-digit whole numbers.

Math.4.NBT.A.3: Use place value understanding to round multi-digit whole numbers to any place.

Activity Page
Counting by Thousands 10
Rounding Numbers 22
Rounding Numbers and Estimating 29

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Math.4.NBT.B.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Activity Page
Adding with Regrouping to 999 19
Adding Three or More Numbers 21
Subtracting 2-Digit Numbers without Regrouping 23
Subtracting with Regrouping 24
Subtracting 3-Digit Numbers without Regrouping 25
Subtracting 3-Digit Numbers with Regrouping 26
Subtracting without Regrouping to 9,999 27
Subtracting with Regrouping to 9,999 28
Inverse Operations 50
Number Lines 51
Problem Solving 122
Mixed Practice 123
Place Value Practice 124

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Math.4.NBT.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Activity Page
Multiplication with Modeling and Mental Strategies 30
Reasoning with Numbers 31
Multiplication (×2, ×4, and ×8) 32
Multiplication (×5 and ×10) 33
Multiplication (×3, ×6, and ×9) 34
Multiplication (×7, ×8, and ×9) 35
Multiplication 36
Square and Triangular Numbers 37
Multiples 38
Multiplication and Division 49
Inverse Operations 50
Problem Solving 122
Mixed Practice 123
Multiplication and Division Practice 126

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Math.4.NBT.B.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Activity Page
Reasoning with Numbers 31
Division 43
Division Problems and Remainders 44
Division with Multiplication Grid 45
Estimation with Division 46
Division with Remainders 47
Division Practice 48
Multiplication and Division 49
Multiplication and Division Practice 126

### Domain - Number and Operations-Fractions, Grade 4

Extend understanding of fraction equivalence and ordering.

Math.4.NF.A.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Activity Page
Number Lines 51
Fraction Names 56
Fractions 57
Comparing Fractions 58
Equivalent Fractions 59
Mixed Numbers 60
Hundredths 61
Tenths 62
Percentages 73
Fractions Practice 127

Extend understanding of fraction equivalence and ordering.

Math.4.NF.A.1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Activity Page
Number Lines 51
Fraction Names 56
Fractions 57
Comparing Fractions 58
Equivalent Fractions 59
Mixed Numbers 60
Hundredths 61
Tenths 62
Simple Percentages 72
Percentages 73
Fractions Practice 127

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Math.4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Activity Page
Mixed Numbers 60
Hundredths 61
Fractions Practice 127

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Math.4.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Activity Page
Problem Solving 122

Understand decimal notation for fractions, and compare decimal fractions.

Math.4.NF.C.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Activity Page
Hundredths 61
Tenths 62
Decimals – Place Value 63
Decimals 64
Decimals with Whole Numbers 66
Fractions and Decimals 67
Simple Percentages 72
Percentages 73
Decimals Practice 128

Understand decimal notation for fractions, and compare decimal fractions.

Math.4.NF.C.6: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Activity Page
Hundredths 61
Tenths 62
Decimals – Place Value 63
Decimals 64
Decimals with Whole Numbers 66
Fractions and Decimals 67
Simple Percentages 72
Percentages 73
Fractions, Decimals, and Percentages 74
Decimals Practice 128

Understand decimal notation for fractions, and compare decimal fractions.

Math.4.NF.C.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Activity Page
Tenths 62
Comparing Decimals 65
Decimals with Whole Numbers 66
Fractions and Decimals 67
Simple Percentages 72
Percentages 73
Fractions, Decimals, and Percentages 74
Decimals Practice 128

### Domain - Measurement and Data, Grade 4

Solve problems involving measurement and conversion of measurements.

Math.4.MD.A.2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Activity Page
Use of Money 75
Money Multiplication and Division 77
Money Rounding and Estimation 78
Analog Time 104
Digital and Analog Time 105
Calendars 106
Time Lines and Timetables 107
Weight in Ounces and Pounds 113
Problem Solving 122
Mixed Practice 123
Decimals Practice 128

Solve problems involving measurement and conversion of measurements.

Math.4.MD.A.1: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Activity Page
Length 108
Length with Decimals 109

Solve problems involving measurement and conversion of measurements.

Math.4.MD.A.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Activity Page
Perimeter 110
Area 111
Area and Perimeter 112

Represent and interpret data.

Math.4.MD.B.4: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Activity Page
Picture Graphs 116
Tally Marks and Tables 117
Working with Tables 119
Bar Graphs 120
Surveys and Collecting Data 121
Problem Solving 122

Geometric measurement: understand concepts of angle and measure angles.

Math.4.MD.C.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

Activity Page
Angles in Real Life 83
Comparing Angles 84
Angles – Right, Obtuse, and Acute 85
Drawing Angles 86

Geometric measurement: understand concepts of angle and measure angles.

Math.4.MD.C.7: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Activity Page
Comparing Angles 84
Angles – Right, Obtuse, and Acute 85
Drawing Angles 86

### Domain - Geometry, Grade 4

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Math.4.G.A.3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Activity Page
Symmetry 79
Paper Folding and Shapes 103

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Math.4.G.A.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Activity Page
Shapes 80
Plane Shapes 81
Regular and Irregular Shapes 82
Angles – Right, Obtuse, and Acute 85
Drawing Angles 86
Polygons 91

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Math.4.G.A.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Activity Page
Shapes 80
Plane Shapes 81
Regular and Irregular Shapes 82
Angles in Real Life 83
Comparing Angles 84
Angles – Right, Obtuse, and Acute 85
Drawing Angles 86
Parallel and Perpendicular Lines 87