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 10
Note on Materials 16
Manipulatives and Materials Used in This Book 17
Activities for Building Norms 19
Encouraging Good Group Work 19
Paper Folding: Learning to Reason, Convince, and Be Skeptical 21
Big Idea 1: Taking Apart Prisms and Polygons 24
Visualize: How Big Is the Footprint? 26
Play: Shards of a Shape 38
Investigate: Rising from the Footprint 46
Big Idea 2: Folding and Unfolding Objects 57
Visualize: Folding Cubes in Your Mind 60
Play: Folding Nets in Your Mind 70
Investigate: Filling Our Nets 85
Big Idea 3: Expanding the Number Line 92
Visualize: Folding around Zero 94
Play: Bouncing around the Number Line 101
Investigate: Going 2-D 107
Big Idea 4: Finding and Using Unit Rates 116
Visualize: Seeing Unit Rates 118
Play: Seeing the Best Deal 128
Investigate: How Fast Do You Walk? 136
Big Idea 5: Reasoning with Proportions 142
Visualize: Jump! Jump! 144
Play: Seeing Animals in a New Way 149
Investigate: A Seat at the Table 156
Big Idea 6: Visualizing the Center and Spread of Data 164
Visualize: The Shape of Data 167
Play: What Does Mean Mean? 178
Investigate: When Does Mean = Median = Mode = Range? 185
Big Idea 7: Using Symbols to Describe the World 192
Visualize: Cuisenaire Rod Equivalents 195
Play: Math Mobiles 204
Investigate: Radial Patterns 215
Big Idea 8: Generalizing 221
Visualize: Generalizing Number Patterns 223
Play: Generalizing Strategy 230
Investigate: Generalizing Visual Patterns 239
Appendix 246
Centimeter Grid Paper 247
Grid Paper 248
1" Grid Paper 249
Isometric Dot Paper 250
Dot Paper 251
About the Authors 252
Acknowledgments 254
Index 255
