## 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
Warm-Up 15 27
Warm-Up 75 75
Warm-Up 76 75
Warm-Up 116 95
Warm-Up 115 95

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
Warm-Up 23 35
Warm-Up 35 47
Warm-Up 39 51
Warm-Up 62 68
Warm-Up 61 68
Warm-Up 74 74
Warm-Up 165 120
Warm-Up 166 120
Warm-Up 211 143
Warm-Up 212 143
Warm-Up 224 149
Warm-Up 223 149
Warm-Up 225 150
Warm-Up 228 151
Warm-Up 227 151
Warm-Up 229 152
Warm-Up 230 152
Warm-Up 232 153
Warm-Up 231 153
Warm-Up 234 154
Warm-Up 233 154
Warm-Up 235 155
Warm-Up 236 155
Warm-Up 237 156
Warm-Up 238 156
Warm-Up 241 158
Warm-Up 242 158
Warm-Up 243 159
Warm-Up 244 159
Warm-Up 246 160
Warm-Up 245 160
Warm-Up 247 161

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
Warm-Up 60 67
Warm-Up 59 67
Warm-Up 62 68
Warm-Up 73 74
Warm-Up 89 82
Warm-Up 90 82
Warm-Up 112 93
Warm-Up 128 101
Warm-Up 215 145
Warm-Up 217 146
Warm-Up 218 146
Warm-Up 227 151
Warm-Up 228 151

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
Warm-Up 124 99
Warm-Up 123 99

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
Warm-Up 11 23
Warm-Up 14 26
Warm-Up 24 36
Warm-Up 30 42
Warm-Up 41 53
Warm-Up 42 54
Warm-Up 43 55
Warm-Up 44 56
Warm-Up 45 57
Warm-Up 46 58
Warm-Up 47 59
Warm-Up 48 60
Warm-Up 49 61
Warm-Up 50 62
Warm-Up 222 148
Warm-Up 221 148
Warm-Up 249 162
Warm-Up 250 162

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

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
Warm-Up 17 29
Warm-Up 88 81
Warm-Up 87 81

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
Warm-Up 85 80
Warm-Up 86 80
Warm-Up 88 81
Warm-Up 87 81

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
Warm-Up 213 144
Warm-Up 214 144
Warm-Up 240 157
Warm-Up 239 157
Warm-Up 241 158
Warm-Up 242 158

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
Warm-Up 1 13
Warm-Up 2 14
Warm-Up 3 15
Warm-Up 5 17
Warm-Up 6 18
Warm-Up 8 20
Warm-Up 10 22
Warm-Up 24 36
Warm-Up 25 37
Warm-Up 26 38
Warm-Up 33 45
Warm-Up 36 48
Warm-Up 39 51
Warm-Up 84 79
Warm-Up 83 79
Warm-Up 163 119
Warm-Up 164 119
Warm-Up 165 120
Warm-Up 223 149
Warm-Up 224 149
Warm-Up 225 150
Warm-Up 226 150

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
Warm-Up 5 17
Warm-Up 51 63
Warm-Up 61 68
Warm-Up 76 75
Warm-Up 75 75
Warm-Up 101 88
Warm-Up 102 88
Warm-Up 103 89
Warm-Up 104 89
Warm-Up 106 90
Warm-Up 105 90
Warm-Up 110 92
Warm-Up 116 95
Warm-Up 127 101
Warm-Up 128 101
Warm-Up 130 102
Warm-Up 220 147
Warm-Up 219 147
Warm-Up 228 151
Warm-Up 227 151
Warm-Up 231 153
Warm-Up 232 153

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
Warm-Up 54 64
Warm-Up 53 64
Warm-Up 56 65
Warm-Up 55 65
Warm-Up 59 67
Warm-Up 60 67
Warm-Up 62 68
Warm-Up 74 74
Warm-Up 90 82
Warm-Up 89 82
Warm-Up 150 112
Warm-Up 149 112
Warm-Up 181 128
Warm-Up 182 128
Warm-Up 218 146
Warm-Up 217 146

### 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
Warm-Up 9 21
Warm-Up 63 69
Warm-Up 64 69
Warm-Up 65 70
Warm-Up 66 70
Warm-Up 180 127
Warm-Up 179 127
Warm-Up 207 141
Warm-Up 208 141

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
Warm-Up 12 24
Warm-Up 15 27
Warm-Up 16 28
Warm-Up 17 29
Warm-Up 18 30
Warm-Up 19 31
Warm-Up 64 69
Warm-Up 63 69
Warm-Up 65 70
Warm-Up 66 70
Warm-Up 70 72

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
Warm-Up 9 21
Warm-Up 58 66
Warm-Up 57 66
Warm-Up 215 145

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
Warm-Up 15 27
Warm-Up 57 66
Warm-Up 58 66
Warm-Up 129 102
Warm-Up 130 102

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
Warm-Up 18 30
Warm-Up 37 49
Warm-Up 38 50
Warm-Up 53 64
Warm-Up 54 64
Warm-Up 56 65
Warm-Up 55 65
Warm-Up 68 71
Warm-Up 67 71
Warm-Up 69 72
Warm-Up 72 73
Warm-Up 82 78
Warm-Up 81 78

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
Warm-Up 19 31
Warm-Up 67 71
Warm-Up 68 71
Warm-Up 69 72
Warm-Up 81 78
Warm-Up 180 127
Warm-Up 179 127
Warm-Up 185 130
Warm-Up 186 130
Warm-Up 193 134
Warm-Up 194 134

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
Warm-Up 67 71
Warm-Up 68 71
Warm-Up 69 72
Warm-Up 71 73
Warm-Up 72 73
Warm-Up 82 78
Warm-Up 81 78
Warm-Up 179 127
Warm-Up 180 127

### 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
Warm-Up 22 34
Warm-Up 32 44
Warm-Up 35 47
Warm-Up 37 49
Warm-Up 38 50
Warm-Up 52 63
Warm-Up 54 64
Warm-Up 53 64
Warm-Up 56 65
Warm-Up 55 65
Warm-Up 78 76
Warm-Up 77 76
Warm-Up 80 77
Warm-Up 79 77
Warm-Up 143 109
Warm-Up 144 109
Warm-Up 158 116
Warm-Up 157 116
Warm-Up 166 120
Warm-Up 165 120
Warm-Up 167 121
Warm-Up 168 121
Warm-Up 169 122
Warm-Up 170 122

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
Warm-Up 31 43
Warm-Up 93 84
Warm-Up 94 84
Warm-Up 102 88
Warm-Up 101 88
Warm-Up 104 89
Warm-Up 103 89
Warm-Up 106 90
Warm-Up 105 90
Warm-Up 108 91
Warm-Up 107 91
Warm-Up 110 92
Warm-Up 109 92
Warm-Up 120 97
Warm-Up 119 97
Warm-Up 121 98
Warm-Up 122 98
Warm-Up 123 99
Warm-Up 124 99
Warm-Up 128 101
Warm-Up 127 101
Warm-Up 130 102
Warm-Up 145 110
Warm-Up 146 110
Warm-Up 147 111
Warm-Up 148 111
Warm-Up 150 112
Warm-Up 149 112

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
Warm-Up 34 46
Warm-Up 40 52
Warm-Up 132 103
Warm-Up 131 103
Warm-Up 133 104
Warm-Up 134 104
Warm-Up 136 105
Warm-Up 135 105
Warm-Up 137 106
Warm-Up 138 106
Warm-Up 139 107
Warm-Up 140 107
Warm-Up 142 108
Warm-Up 141 108
Warm-Up 143 109
Warm-Up 144 109
Warm-Up 146 110
Warm-Up 145 110

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
Warm-Up 162 118
Warm-Up 161 118
Warm-Up 176 125
Warm-Up 175 125
Warm-Up 198 136
Warm-Up 197 136
Warm-Up 199 137
Warm-Up 200 137

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
Warm-Up 153 114
Warm-Up 154 114
Warm-Up 155 115
Warm-Up 156 115

### Domain - Geometry, Grade 4

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
Warm-Up 7 19
Warm-Up 29 41
Warm-Up 92 83
Warm-Up 91 83
Warm-Up 96 85
Warm-Up 97 86
Warm-Up 113 94
Warm-Up 114 94
Warm-Up 117 96
Warm-Up 118 96
Warm-Up 130 102
Warm-Up 129 102

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
Warm-Up 92 83
Warm-Up 91 83
Warm-Up 95 85
Warm-Up 96 85
Warm-Up 98 86
Warm-Up 97 86
Warm-Up 117 96
Warm-Up 118 96
Warm-Up 122 98
Warm-Up 121 98