Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Problem Solving: The Great Giants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Number Sense: Now That’s Hot! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Algebra and Functions: At the Aquarium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Measurement: Measure Away . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Geometry: Food and Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 Statistics, Data Analysis, and Probability: How Fast Can You Go? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 3, 5, 7, 9, 11, 13 x Arthur Morris/CORBIS CH APTER 1 Place Value and Number Sense Are You Ready for Chapter 1? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 1-1 Number Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 1-2 Problem-Solving Skill: Use the Four-Step Plan Explore . . . . . . . . . . . . . . . . . . . . . . . . . .20 Math Activity for 1-3: Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 1-3 Place Value through 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 1-4 Place Value through 10,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31 1-5 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . . .32 1-6 Compare Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34 1-7 Order Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 Problem Solving in Geography: The Mighty Mississippi 1-8 . . . . . . . . . . . . . . . . . . .42 Round to the Nearest Ten and Hundred . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44 Game Time: Round Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47 1-9 Round to the Nearest Thousand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 California Standards Practice • 27, 31, 37, 41, 51, 59, 60, 61 Higher Order Thinking 19, 27, 30, 37, 41, 46, 51 19, 21, 23, 27, 30, 31, 33, 37, 41, 46, 51, 59 xi CH APTER 2 Addition Are You Ready for Chapter 2? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 2-1 Addition Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 2-2 Problem-Solving Skill: Estimate or Exact Answer 2-3 Estimate Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 2-4 Two-Digit Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74 . . . . . . . . . . . . . . . . . . . . . . . .68 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77 2-5 Add Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78 Problem Solving in Geography: A Walk in the Park 2-6 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . . .84 Explore 2-7 . . . . . . . . . . . . . . . . . . . . . . .82 Math Activity for 2-7: Add Three-Digit Numbers . . . . . . . . . . . . . . . . . . .86 Three-Digit Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88 Game Time: How Low Can You Go? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91 2-8 Add Greater Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 California Standards Practice • 73, 77, 81, 95, 101, 102, 103 Higher Order Thinking 67, 73, 76, 81, 90, 95 67, 69, 73, 76, 77, 81, 85, 87, 95, 101 xii CORBIS CH APTER 3 Subtraction Are You Ready for Chapter 3? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3-1 Two-Digit Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3-2 Estimate Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 3-3 Subtract Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Problem Solving in Music: The Sounds of the Symphony . . . . . . . . . . . . . . 118 3-4 Problem-Solving Skill: Reasonable Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Explore Math Activity for 3-5: Subtract Three-Digit Numbers with Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . 122 3-5 Three-Digit Subtraction with Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3-6 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 128 3-7 Subtract Greater Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Game Time: Do Not Zero Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 3-8 Subtract Across Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3-9 Algebra: Expressions and Number Sentences . . . . . . . . . . . . . . . . . . . . . . . 138 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 California Standards Practice • 113, 117, 127, 137, 141, 149, 150, 151 Higher Order Thinking 113, 116, 127, 137, 141 109, 113, 116, 117, 121, 123, 127, 129, 132, 137, 141, 149 xiii CH APTER 4 Multiplication Concepts and Facts Are You Ready for Chapter 4? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Explore Math Activity for 4-1: Meaning of Multiplication . . . . . . . . . . . . . . . . . 155 4-1 Multiplication as Repeated Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 4-2 Arrays and Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 4-3 Multiply by 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Mid-Chapter Check. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 4-4 Multiply by 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Game Time: Factor Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 4-5 Problem-Solving Skill: Extra or Missing Information . . . . . . . . . . . . . . . . . . . 172 4-6 Multiply by 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 4-7 Multiply by 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Problem Solving in Science: Lots of Arms and Legs . . . . . . . . . . . . . . . . . . . . 182 4-8 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 184 4-9 Multiply by 0 and 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 California Standards Practice • 163, 137, 181, 188, 195, 196, 197 Higher Order Thinking 159, 163, 166, 170, 176, 181, 188 156, 159, 163, 166, 167, 170, 176, 181, 185, 188, 195 xiv Ellen McKnight/Alamy Images CH APTER 5 More Multiplication Facts Are You Ready for Chapter 5? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Explore Math Activity for 5-1: Multiplication Table . . . . . . . . . . . . . . . . . . . . . . . . 201 5-1 Multiply by 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 5-2 Multiply by 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Game Time: Three in a Row . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 5-3 Problem-Solving Strategy: Look for a Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . 212 5-4 Multiply by 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 5-5 Multiply by 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 5-6 Multiply by 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 5-7 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 226 5-8 Algebra: Associative Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Problem Solving in Art: Not Just a Blanket 5-9 Algebra: Find a Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 California Standards Practice • 209, 217, 221, 231, 237, 245, 246, 247 Higher Order Thinking 205, 208, 216, 221, 224, 231, 237 202, 205, 208, 213, 216, 217, 221, 224, 227, 231, 237, 245 xv CH APTER 6 Division Concepts and Facts Are You Ready for Chapter 6? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 Explore 6-1 Math Activity for 6-1: Understand Division . . . . . . . . . . . . . . . . . . . . . . . 251 Relate Division and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Explore Math Activity for 6-2: Relate Multiplication to Division . . . . . . . . . . . 256 6-2 Relate Multiplication to Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 6-3 Problem-Solving Skill: Choose an Operation 6-4 Divide by 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 6-5 Divide by 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 Problem Solving in Community: Communities within Communities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 6-6 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 274 6-7 Divide by 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Game Time: Number Cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 6-8 Division Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 California Standards Practice • 261, 267, 271, 278, 287, 288, 289 Higher Order Thinking 255, 261, 266, 271, 277, 281 252, 255, 257, 261, 263, 266, 267, 271, 275, 277, 281, 287 xvi Jim West/The Image Works CH APTER 7 More Division Facts Are You Ready for Chapter 7? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 Explore Math Activity for 7-1: Divide Using a Multiplication Table . . . . . . . . 293 7-1 Divide by 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 7-2 Divide by 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 7-3 Problem-Solving Strategy: Make a Table 7-4 Divide by 6 and 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Problem Solving in Civics: Stars and Stripes 7-5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Divide by 8 and 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 Game Time: Facts Roll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 7-6 Determine Unit Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 7-7 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 318 7-8 Algebra: Expressions and Equations 7-9 Algebra: Translate Words to Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 California Standards Practice • 301, 307, 317, 323, 327, 335, 336, 337 Higher Order Thinking 297, 301, 306, 312, 317, 323, 327 294, 297, 301, 303, 306, 307, 312, 317, 319, 323, 327 xvii CH APTER Measurement: Customary System 8 Are You Ready for Chapter 8? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Explore Measurement Activity for 8-1: Length to the Nearest Inch . . . . . . 341 8-1 Length to the Nearest Half Inch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 8-2 Customary Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 8-3 Problem-Solving Strategy: Work Backward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 Explore 8-4 Measurement Activity for 8-4: Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Customary Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Game Time: Capacity Guess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 8-5 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 360 8-6 Customary Units of Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Problem Solving in Science: Lengths, Heights, and Weights, Oh My! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 8-7 Convert Units of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 California Standards Practice • 349, 357, 359, 365, 371, 377, 378, 379 Higher Order Thinking 345, 349, 357, 365, 371 342, 345, 349, 351, 353, 357, 359, 361, 365, 371, 377 xviii CH APTER 9 Measurement: Metric System Are You Ready for Chapter 9? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 Explore 9-1 Measurement Activity for 9-1: Millimeter and Centimeter . . . . . . . 383 Metric Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Game Time: Hit the Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 9-2 Problem-Solving Strategy: Guess and Check . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 9-3 Metric Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 Mid-Chapter Check. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 9-4 Problem-Solving Ivestigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . . 396 9-5 Metric Units of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 Problem Solving in Science: A Visit to the Supermarket 9-6 . . . . . . . . . . . . . . . 402 Metric Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 California Standards Practice • 388, 395, 401, 407, 413, 414, 415 Higher Order Thinking 388, 394, 401, 407 384, 388, 391, 394, 395, 397, 401, 407, 413 xix John Cancalosi/Peter Arnold, Inc. CH APTER 10 Measurement and Geometry Are You Ready for Chapter 10? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 10-1 Geometry: Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 10-2 Measurement: Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 Explore Measurement Activity for 10-3: Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 10-3 Measurement: Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 10-4 Problem-Solving Strategy: Solve a Simpler Problem . . . . . . . . . . . . . . . . . . . 432 10-5 Triangles and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 10-6 Geometry: Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 10-7 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 442 10-8 Geometry: Solid Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Game Time: Guess the Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 10-9 Complex Solid Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 Problem Solving in Art: Gardens Under Glass Explore . . . . . . . . . . . . . . . . . . . . . . . . . . 450 Measurement Activity for 10-10: Volume . . . . . . . . . . . . . . . . . . . . . . . 452 10-10 Measurement: Find Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 California Standards Practice • 425, 431, 437, 441, 446, 457, 465, 466, 467 Higher Order Thinking 421, 425, 430, 436, 441, 446, 449, 457 421, 425, 427, 430, 433, 436, 437, 441, 443, 446, 449, 453, 457, 465 xx PETE OXFORD/Minden Pictures CH APTER 11 Statistics: Data, Graphs, and Probability Are You Ready for Chapter 11? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 Explore Graphing Activity for 11-1: Make a Bar Graph . . . . . . . . . . . . . . . . . . . . 471 11-1 Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 11-2 Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 11-3 Problem-Solving Strategy: Make an Organized List . . . . . . . . . . . . . . . . . . . . 480 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 Game Time: Catch Me if You Can! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 11-4 Identify Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 Problem Solving in Science: Eggs! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 11-5 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 490 Explore Probability Activity for 11-6: Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . 492 11-6 Make Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 California Standards Practice • 479, 482, 487, 497, 503, 504, 505 Higher Order Thinking 475, 478, 487, 497 472, 475, 478, 481, 487, 491, 493, 497, 503 xxi CH APTER 12 Fractions Are You Ready for Chapter 12? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 12-1 Parts of a Whole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 12-2 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 512 Explore Math Activity for 12-3: Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . 514 12-3 Find Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 Game Time: Fraction Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 12-4 Problem-Solving Strategy: Draw a Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 12-5 Compare Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 Explore Math Activity for 12-6: Add Like Fractions . . . . . . . . . . . . . . . . . . . . . . . . 526 12-6 Add Like Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528 Problem Solving in Science: The Buzz on Insects Explore . . . . . . . . . . . . . . . . . . . . . . 532 Math Activity for 12-7: Subtract Like Fractions . . . . . . . . . . . . . . . . . . . 534 12-7 Subtract Like Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 California Standards Practice • 518, 525, 531, 539, 545, 546, 547 Higher Order Thinking 511, 518, 524, 531, 538 511, 513, 515, 518, 521, 524, 525, 527, 531, 535, 538, 545 xxii CORBIS CH APTER 13 Fractions and Decimals Are You Ready for Chapter 13? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 Explore Math Activity for 13-1: Fractions and Decimals . . . . . . . . . . . . . . . . . . . 551 13-1 Tenths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 Game Time: Fractoes and Decimoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 13-2 Hundredths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 Problem Solving in Science: Continents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 13-3 Problem-Solving Strategy: Act It Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564 Explore Math Activity for 13-4: Fractions, Decimals, and Money . . . . . . . . . 566 13-4 Decimals and Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 13-5 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 572 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580 California Standards Practice • 556, 561, 571, 579, 580, 581 Higher Order Thinking 556, 560, 571 552, 556, 560, 561, 565, 567, 571, 573, 579 xxiii CH APTER 14 Multiply by One-Digit Numbers Are You Ready for Chapter 14? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 14-1 Multiply Multiples of 10, 100, and 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 14-2 Problem-Solving Strategy: Use Logical Reasoning . . . . . . . . . . . . . . . . . . . . . 588 14-3 Estimate Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 14-4 Multiply by a One-Digit Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 14-5 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 598 Explore Math Activity for 14-6: Multiplication with Rerouping . . . . . . . . . . . . 600 14-6 Multiply Two-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602 14-7 Multiply Greater Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 Game Time: High and Low . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609 14-8 Multiply Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610 Problem Solving in Art: Stamp Collecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622 California Standards Practice • 593, 597, 605, 613, 621, 622, 623 Higher Order Thinking 587, 592, 597, 605, 608, 613 587, 589, 592, 593, 597, 599, 601, 605, 608, 613, 621 xxiv Bill Ross/CORBIS CH APTER 15 Divide by One-Digit Numbers Are You Ready for Chapter 15? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626 15-1 Divide Multiples of 10, 100, and 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627 15-2 Estimate Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630 Explore Math Activity for 15-3: Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 15-3 Two-Digit Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639 15-4 Problem-Solving Strategy: Work Backward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640 15-5 Three-Digit Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642 Game Time: That’s Close! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645 Problem Solving in Science: Roller Coaster Physics . . . . . . . . . . . . . . . . . . . . 646 15-6 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 648 15-7 Divide Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650 ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660 California Standards Practice • 633, 639, 653, 659, 660, 661 Higher Order Thinking 629, 633, 638, 644, 653 629, 633, 635, 638, 639, 641, 644, 649, 653, 659 xxv California Standards Review Tips for Success . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CA1 Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CA2 Practice by Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CA4 to Grade 4 Algebra: Function Tables (+/-) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 Algebra: Function Tables (×/÷) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668 Ordered Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672 Geometry: Congruent Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676 Geometry: Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678 Higher Order Thinking 667, 671, 675, 677, 679 667, 671, 675, 677, 679 xxvi Stockbyte Student Handbook Built-In Workbooks Extra Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R2 Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R41 Reference English-Spanish Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R49 Photo Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R69 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R70 xxvii California Standards for Mathematics Grade 3 denotes Key standards Standard Text of Standard Primary Citations Supporting Citations Number Sense 1.0 Students understand the place value of whole numbers: 1.1 Count, read, and write whole numbers to 10,000 17–19 24–30 1.2 Compare and order whole numbers to 10,000. 34–43 17–19 1.3 Identify the place value for each digit in numbers to 10,000. 22–30 34–41, 44–46, 48–51 1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand. 44–51, 70–76, 110–113 1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6). 24–30 2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division: 2.1 Find the sum or difference of two whole numbers between 0 and 10,000. 32–33, 65–67, 74–77, 82–83, 86–87, 107–116, 120–127, 490–491, 640–641 20–21, 68–73, 78–81, 84–85, 88–95, 128–137, 512–513, 588–589 2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10. 157–159, 164–181, 184–185, 201–202, 210, 214–216, 218–225 155–156, 226–227 2.3 Use the inverse relationship of multiplication and division to compute and check results. 114–116, 256–261, 264–271, 274–281, 293–301, 304–312, 642–644, 636–638 318–319, 251–255, 262–263, 272–273 2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 × 3 = ̲ ). 585–587, 590–597, 600– 608 442–443, 598–599, 614–615 2.5 Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ÷ 5 = ̲ ). 627–638, 642–644, 648–649 2.6 Understand the special properties of 0 and 1 in multiplication and division. 186–188, 280–281 2.7 Determine the unit cost when given the total cost and number of units. 314–317, 360–361, 650–653 350–351 2.8 Solve problems that require two or more of the skills mentioned above. 8–3; 8–5; 396–397, 432–433, 648–649 3.0 Students understand the relationship between whole numbers, simple fractions, and decimals: 514–518, 522–524 509–511, 526–531, 534–539 3.1 xxviii Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g.,1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4). Standard Text of Standard Primary Citations Supporting Citations 3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2). 526–539 3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors. 78–81, 88–95, 610–613, 650–653 512–513, 572–573 3.4 Know and understand that fractions are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar). 548–560, 566–571 564–565 182–183, 600–601 Algebra and Functions 1.0 Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve number relationships: 1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities. 65–67, 138–141, 320–327 1.2 Solve problems involving numeric equations or inequalities. 320–323 1.3 Select appropriate operational and relational symbols to make an expression true (e.g., if 4 ̲ 3 = 12, what operation symbol goes in the blank?). 138–141, 320–323 1.4 Express simple unit coversions in symbolic form (e.g., ̲ inches = ̲ feet × 12). 404–407 1.5 Recognize and use the commutative and associative properties of multiplication (e.g., if 5 × 7 = 35, then what is 7 × 5? And if 5 × 7 × 3 = 105, then what is 7 × 3 × 5?). 160–163, 228–230 2.0 Students represent simple functional relationships: 2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit). 14–8 2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4). 212–213, 234–237, 302–303 368–371 314–317 Measurement and Geometry 1.0 Students choose and use appropriate units and measurement tools to quantify the properties of objects 1.1 Choose the appropriate tools and units (metric and U.S.) and estimate and measure length, liquid volume, and weight/mass. 341–349, 352–357, 362–365, 383–388, 392–394, 398–401, 404–407, EX 8–1; 8–1; 8–2; EX 8–4; 8–4; 8–6; 8–7; CC 385–388, 390–391, 398–401 1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. 426–431, 442–443, 452–457, 480–481 1.3 Find the perimeter of a polygon with integer sides. 422–425, 432–433, xxix Standard Text of Standard Primary Citations 1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes). 2.0 Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems: 2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons). 419–421, 450–451 2.2 Identify attributes of triangles (e.g. two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle). 434–436 2.3 Identify attributes of quadrilaterals (e.g. parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square). 438–441 2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle. 434–441 2.5 Identify, describe, and classify common three–dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, and cylinder). 444–446 2.6 Identify common solid objects that are the components needed to make a more complex solid object. 448–449 346–349, 9–6 Supporting Citations 352–357, 362–365, 368–371 Statistics, Data Analysis, and Probability 1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions: 1.1 Identify whether common events are certain, likely, unlikely, or improbable. 484–487 1.2 Record the possible outcomes for a simple event (e.g., tossing a coin) and systematically keep track of the outcomes when the event is repeated many times. 492–493 1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot). 476–479 1.4 Use the results of probability experiments to predict future events (e.g., use a line plot to predict the temperature forecast for the next day). 494–497 Preparation for 471–475, 492–493 Mathematical Reasoning xxx 1.0 Students make decisions about how to approach problems: 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing, prioritizing information, and observing patterns 20–21, 32–33, 84–85, 128–129, 172–173, 184–185, 212–213, 226–227, 262–263, 274–275, 302–303, 318–319, 350–351, 390–391,396–397, 442–443, 480–481, 490–491, 520–521, 598–599, 648–649 360–361, 366–367, 426–427, 432–433, 512–513, 640–641 Standard Text of Standard 1.2 Determine when and how to break a problem into simpler parts. 2.0 Students use strategies, skills, and concepts in finding solutions: 2.1 Primary Citations Supporting Citations 350–351, 432–433, 572–573, 640–641 360–361, 448–453, 585– 587, 627–629, 634–635 Use estimation to verify the reasonableness of calculated results. 74–81, 88–95, 426–427, 590–592, 602–605, 630–633 110–116,120–121, 343– 349, 354–357, 362–365, 428–431, 442–443, 452–457, 594–597, 606–608, 650–653 2.2 Apply strategies and results from simpler problems to more complex problems. 585–587, 600–601, 86–87, 155–159,177, 189, 210,225, 253–255, 264– 271, 324–327, 343–345, 432–441, 444–453, 452– 453, 492–493, 528–531, 536–539, 627–629 2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. 20–21, 68–69, 155–159, 203–209, 214–216, 218– 224, 251–255, 341–342, 352–353, 396–397, 512– 513, 526–527, 564–565, 588–589, 634–635 22–23, 32–33, 84–85, 107–109, 120–127, 160– 181, 184–185, 256–261, 274–281, 302–303, 419– 421, 426–431, 434–443, 471–479, 490–491, 494– 497, 509–511, 514–524, 558–560, 566–567, 636–641 2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work. 2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. 2.6 Make precise calculations and check the validity of the results from the context of the problem. 3.0 Students move beyond a particular problem by generalizing to other situations: 3.1 Evaluate the reasonableness of the solution in the context of the original situation. 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. 3.3 Develop generalizations of the results obtained and apply them in other circumstances. 65–67, 324–327, 568– 571, 642–644 68–73, 383–388 590–592, 630–633 78–81, 128–132, 134– 137, 512–513, 642–644 588–589 74–81, 341–342, 602–604 86–95, 138–141, 295– 301–306, 310–312, 320– 323, 341–342, 404–407, 422–427, 426–427, 448–449, 452–453, 512–513, 551–556 494–497 201–202, 293–294, 426– 427, 484–487, 610–613 xxxi Let’s Get Started Use the Scavenger Hunt below to learn where things are located in each chapter. 1 What is the title of Chapter 1? 2 What is the Main Idea of Lesson 1-1? 3 How do you know which words are vocabulary words? 4 What are the vocabulary words for Lesson 1-3? 5 What is the key concept shown in Lesson 1-9? 6 How many Examples are presented in Lesson 1-4? 7 What is the web address where you could find extra examples? 8 On page 29, there is a Remember tip box. How does the Remember tip help you? 9 How many exercises are there in Lesson 1-5? 10 Suppose you need more practice on a concept. Where can you go for Extra Practice? 11 Suppose you’re doing your homework on page 36 and you get stuck on Exercise 18. Where could you find help? 12 What is the web address that would allow you to take a self-check quiz to be sure you understand the lesson? 13 On what pages will you find the Chapter 1 Study Guide and Review? 14 Suppose you can’t figure out how to do Exercise 7 in the Study Guide and Review on page 53. Where could you find help? xxxii