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