## Mathematics

### Domain - Ratios and Proportional Relationships, Grade 6

Understand ratio concepts and use ratio reasoning to solve problems.

Math.6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Activity Page
Warm-Up 53 64
Warm-Up 54 64
Warm-Up 55 65
Warm-Up 56 65
Warm-Up 57 66
Warm-Up 58 66
Warm-Up 60 67
Warm-Up 59 67
Warm-Up 62 68
Warm-Up 61 68
Warm-Up 65 70
Warm-Up 66 70
Warm-Up 77 76
Warm-Up 78 76
Warm-Up 80 77
Warm-Up 79 77
Warm-Up 84 79
Warm-Up 83 79
Warm-Up 86 80
Warm-Up 85 80
Warm-Up 89 82
Warm-Up 90 82
Warm-Up 145 110
Warm-Up 172 123

Understand ratio concepts and use ratio reasoning to solve problems.

Math.6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Activity Page
Warm-Up 82 78
Warm-Up 81 78
Warm-Up 84 79
Warm-Up 83 79
Warm-Up 197 136
Warm-Up 198 136
Warm-Up 200 137
Warm-Up 199 137
Warm-Up 201 138
Warm-Up 202 138
Warm-Up 203 139
Warm-Up 204 139
Warm-Up 205 140
Warm-Up 206 140
Warm-Up 208 141
Warm-Up 207 141
Warm-Up 210 142
Warm-Up 209 142

Understand ratio concepts and use ratio reasoning to solve problems.

Math.6.RP.A.2: Understand 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.”

Activity Page
Warm-Up 81 78
Warm-Up 82 78
Warm-Up 84 79
Warm-Up 83 79
Warm-Up 86 80
Warm-Up 85 80
Warm-Up 138 106
Warm-Up 152 113
Warm-Up 151 113

### Domain - The Number System, Grade 6

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Math.6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

Activity Page
Warm-Up 203 139
Warm-Up 204 139
Warm-Up 205 140
Warm-Up 206 140
Warm-Up 209 142
Warm-Up 232 153
Warm-Up 231 153

Compute fluently with multi-digit numbers and find common factors and multiples.

Math.6.NS.B.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Activity Page
Warm-Up 2 14
Warm-Up 3 15
Warm-Up 32 44
Warm-Up 33 45
Warm-Up 35 47
Warm-Up 36 48
Warm-Up 106 90
Warm-Up 105 90
Warm-Up 108 91
Warm-Up 107 91
Warm-Up 127 101
Warm-Up 128 101
Warm-Up 160 117
Warm-Up 159 117
Warm-Up 162 118
Warm-Up 161 118
Warm-Up 163 119
Warm-Up 164 119

Compute fluently with multi-digit numbers and find common factors and multiples.

Math.6.NS.B.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..

Activity Page
Warm-Up 8 20
Warm-Up 16 28
Warm-Up 17 29
Warm-Up 23 35
Warm-Up 41 53
Warm-Up 46 58
Warm-Up 52 63
Warm-Up 51 63
Warm-Up 64 69
Warm-Up 63 69
Warm-Up 71 73
Warm-Up 73 74
Warm-Up 74 74

Compute fluently with multi-digit numbers and find common factors and multiples.

Math.6.NS.B.2: Fluently divide multi-digit numbers using the standard algorithm.

Activity Page
Warm-Up 46 58
Warm-Up 47 59
Warm-Up 82 78
Warm-Up 81 78
Warm-Up 170 122
Warm-Up 169 122

Apply and extend previous understandings of numbers to the system of rational numbers.

Math.6.NS.C.6: Understand 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.

Activity Page
Warm-Up 70 72
Warm-Up 69 72
Warm-Up 249 162
Warm-Up 250 162

Apply and extend previous understandings of numbers to the system of rational numbers.

Math.6.NS.C.5: Understand 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.

Activity Page
Warm-Up 70 72
Warm-Up 69 72
Warm-Up 156 115
Warm-Up 158 116

Apply and extend previous understandings of numbers to the system of rational numbers.

Math.6.NS.C.8: Solve 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.

Activity Page
Warm-Up 113 94
Warm-Up 114 94
Warm-Up 115 95
Warm-Up 116 95
Warm-Up 117 96
Warm-Up 118 96
Warm-Up 120 97
Warm-Up 119 97
Warm-Up 250 162
Warm-Up 249 162

Apply and extend previous understandings of numbers to the system of rational numbers.

Math.6.NS.C.7: Understand ordering and absolute value of rational numbers.

Activity Page
Warm-Up 156 115
Warm-Up 158 116

### Domain - Expressions and Equations, Grade 6

Apply and extend previous understandings of arithmetic to algebraic expressions.

Math.6.EE.A.1: Write and evaluate numerical expressions involving whole-number exponents.

Activity Page
Warm-Up 7 19
Warm-Up 18 30
Warm-Up 19 31
Warm-Up 42 54
Warm-Up 67 71
Warm-Up 68 71
Warm-Up 76 75
Warm-Up 75 75
Warm-Up 130 102
Warm-Up 129 102
Warm-Up 235 155
Warm-Up 236 155

Apply and extend previous understandings of arithmetic to algebraic expressions.

Math.6.EE.A.2: Write, read, and evaluate expressions in which letters stand for numbers.

Activity Page
Warm-Up 21 33
Warm-Up 22 34
Warm-Up 24 36
Warm-Up 26 38
Warm-Up 27 39
Warm-Up 28 40
Warm-Up 29 41
Warm-Up 50 62
Warm-Up 222 148
Warm-Up 221 148
Warm-Up 223 149
Warm-Up 224 149
Warm-Up 225 150

Apply and extend previous understandings of arithmetic to algebraic expressions.

Math.6.EE.A.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..

Activity Page
Warm-Up 112 93
Warm-Up 215 145
Warm-Up 238 156
Warm-Up 237 156
Warm-Up 248 161
Warm-Up 247 161

Apply and extend previous understandings of arithmetic to algebraic expressions.

Math.6.EE.A.3: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Activity Page
Warm-Up 222 148
Warm-Up 221 148
Warm-Up 223 149
Warm-Up 224 149
Warm-Up 226 150
Warm-Up 225 150
Warm-Up 227 151
Warm-Up 228 151
Warm-Up 230 152
Warm-Up 229 152
Warm-Up 231 153
Warm-Up 232 153

Reason about and solve one-variable equations and inequalities.

Math.6.EE.B.7: Solve 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.

Activity Page
Warm-Up 22 34
Warm-Up 30 42
Warm-Up 88 81
Warm-Up 87 81
Warm-Up 90 82
Warm-Up 89 82
Warm-Up 216 145
Warm-Up 218 146
Warm-Up 217 146
Warm-Up 220 147
Warm-Up 219 147
Warm-Up 241 158
Warm-Up 242 158
Warm-Up 243 159
Warm-Up 244 159

Reason about and solve one-variable equations and inequalities.

Math.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Activity Page
Warm-Up 88 81
Warm-Up 87 81
Warm-Up 89 82
Warm-Up 90 82
Warm-Up 212 143
Warm-Up 211 143
Warm-Up 216 145
Warm-Up 217 146
Warm-Up 220 147
Warm-Up 219 147
Warm-Up 237 156
Warm-Up 238 156
Warm-Up 240 157
Warm-Up 239 157
Warm-Up 241 158
Warm-Up 242 158
Warm-Up 244 159
Warm-Up 243 159

Reason about and solve one-variable equations and inequalities.

Math.6.EE.B.5: Understand 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.

Activity Page
Warm-Up 212 143
Warm-Up 211 143
Warm-Up 246 160
Warm-Up 245 160
Warm-Up 248 161
Warm-Up 247 161

Represent and analyze quantitative relationships between dependent and independent variables.

Math.6.EE.C.9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Activity Page
Warm-Up 9 21
Warm-Up 25 37
Warm-Up 40 52
Warm-Up 43 55
Warm-Up 48 60
Warm-Up 88 81
Warm-Up 87 81
Warm-Up 90 82
Warm-Up 89 82
Warm-Up 182 128
Warm-Up 213 144
Warm-Up 214 144
Warm-Up 233 154
Warm-Up 234 154
Warm-Up 235 155
Warm-Up 236 155
Warm-Up 239 157
Warm-Up 240 157
Warm-Up 244 159
Warm-Up 243 159

### Domain - Geometry, Grade 6

Solve real-world and mathematical problems involving area, surface area, and volume.

Math.6.G.A.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Activity Page
Warm-Up 45 57
Warm-Up 95 85
Warm-Up 96 85
Warm-Up 103 89
Warm-Up 104 89
Warm-Up 111 93
Warm-Up 149 112
Warm-Up 150 112
Warm-Up 166 120
Warm-Up 165 120
Warm-Up 168 121
Warm-Up 167 121

Solve real-world and mathematical problems involving area, surface area, and volume.

Math.6.G.A.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these technique in the context of solving real-world and mathematical problems.

Activity Page
Warm-Up 92 83
Warm-Up 91 83
Warm-Up 93 84
Warm-Up 94 84
Warm-Up 100 87
Warm-Up 99 87
Warm-Up 101 88
Warm-Up 102 88
Warm-Up 109 92
Warm-Up 110 92
Warm-Up 112 93
Warm-Up 133 104
Warm-Up 134 104
Warm-Up 137 106
Warm-Up 140 107
Warm-Up 139 107
Warm-Up 141 108
Warm-Up 142 108

### Domain - Statistics and Probability, Grade 6

Develop understanding of statistical variability.

Math.6.SP.A.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Activity Page
Warm-Up 82 78
Warm-Up 81 78
Warm-Up 83 79
Warm-Up 84 79
Warm-Up 176 125
Warm-Up 175 125
Warm-Up 177 126
Warm-Up 180 127
Warm-Up 179 127
Warm-Up 181 128
Warm-Up 182 128
Warm-Up 185 130

Develop understanding of statistical variability.

Math.6.SP.A.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

Activity Page
Warm-Up 125 100
Warm-Up 126 100
Warm-Up 176 125
Warm-Up 175 125
Warm-Up 177 126
Warm-Up 179 127
Warm-Up 185 130

Develop understanding of statistical variability.

Math.6.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Activity Page
Warm-Up 175 125
Warm-Up 176 125
Warm-Up 177 126
Warm-Up 180 127
Warm-Up 179 127
Warm-Up 181 128
Warm-Up 183 129
Warm-Up 184 129
Warm-Up 185 130

Summarize and describe distributions.

Math.6.SP.B.5: Summarize numerical data sets in relation to their context, such as by:

Activity Page
Warm-Up 1 13
Warm-Up 2 14
Warm-Up 3 15
Warm-Up 4 16
Warm-Up 5 17
Warm-Up 6 18
Warm-Up 10 22
Warm-Up 11 23
Warm-Up 12 24
Warm-Up 13 25
Warm-Up 14 26
Warm-Up 15 27
Warm-Up 18 30
Warm-Up 20 32
Warm-Up 31 43
Warm-Up 37 49
Warm-Up 38 50
Warm-Up 39 51
Warm-Up 44 56
Warm-Up 144 109
Warm-Up 143 109
Warm-Up 172 123
Warm-Up 171 123
Warm-Up 174 124
Warm-Up 173 124
Warm-Up 187 131
Warm-Up 188 131
Warm-Up 189 132
Warm-Up 190 132
Warm-Up 192 133
Warm-Up 191 133
Warm-Up 194 134
Warm-Up 193 134
Warm-Up 196 135
Warm-Up 195 135