Introduction |
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1 | (26) |
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Low-Floor, High-Ceiling Tasks |
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2 | (1) |
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3 | (1) |
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Memorization versus Conceptual Engagement |
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4 | (1) |
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Mathematical Thinking, Reasoning, and Convincing |
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5 | (4) |
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9 | (1) |
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9 | (8) |
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17 | (1) |
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Manipulatives and Materials Used in This Book |
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18 | (3) |
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Activities for Building Norms |
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21 | (1) |
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Encouraging Good Group Work |
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21 | (1) |
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Paper Folding: Learning to Reason, Convince, and Be a Skeptic |
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22 | (5) |
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Big Idea 1 Connecting 2D and 3D Worlds |
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27 | (20) |
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29 | (5) |
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34 | (6) |
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Investigate: The Area of Slices |
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40 | (7) |
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Big Idea 2 Constructing Figures to Scale |
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47 | (22) |
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Visualize: What Is Scale? |
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50 | (5) |
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55 | (6) |
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Investigate: Magnifying Solids |
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61 | (8) |
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Big Idea 3 Seeing Proportional Relationships |
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69 | (24) |
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72 | (8) |
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Play: Is It Proportional? |
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80 | (6) |
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Investigate: Sizing Up Proportions |
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86 | (7) |
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Big Idea 4 Understanding Percents in the World |
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93 | (26) |
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Visualize: Painting Percents |
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95 | (8) |
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Play: Building Benchmarks |
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103 | (6) |
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Investigate: What's It Going to Cost? |
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109 | (10) |
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Big Idea 5 Building Intuition about Probability |
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119 | (26) |
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121 | (10) |
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131 | (5) |
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Investigate: What's in the Bag? |
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136 | (9) |
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Big Idea 6 Modeling Probabilities |
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145 | (26) |
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Visualize: What's the Chance of That? |
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147 | (8) |
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Play: Probability Carnival |
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155 | (8) |
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Investigate: Go, Go Galton Board! |
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163 | (8) |
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Big Idea 7 Sampling to Understand Populations |
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171 | (26) |
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Visualize: Sampling Dots and Beads |
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173 | (7) |
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180 | (6) |
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Investigate: Wildlife Populations |
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186 | (11) |
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Big Idea 8 Operating with Opposites |
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197 | (28) |
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199 | (8) |
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Play: Integer Tic-Tac-Toe |
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207 | (9) |
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Investigate: Coordinating Multiplication |
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216 | (9) |
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Big Idea 9 Using Algebra as a Problem-Solving Tool |
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225 | (26) |
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228 | (9) |
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Play: (Non) Linear Pattern Puzzles |
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237 | (8) |
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Investigate: Linear Letters |
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245 | (6) |
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Big Idea 10 Exploring Circles |
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251 | (22) |
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Visualize: Building Hunches about Circumference |
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253 | (7) |
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Play: Dissecting Circle Area |
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260 | (7) |
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Investigate: Unraveling Circles |
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267 | (6) |
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273 | (6) |
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274 | (1) |
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275 | (1) |
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276 | (1) |
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277 | (1) |
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278 | (1) |
About the Authors |
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279 | (2) |
Acknowledgments |
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281 | (2) |
Index |
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283 | |