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: Moving Shapes 27
Visualize: What Does It Mean to Be the Same? 29
Play: Pixel Puzzles 35
Investigate: Slide It, Flip It, Turn It 45
Big Idea 2: Zooming In and Out 53
Visualize: What is Similarity? 55
Play: Find the Fakes 60
Investigate: Growing on a Grid 65
Big Idea 3: Analyzing Proportional Relationships 71
Visualize: Dropping the Altitude 73
Play: Seeing Triangles under the Line 79
Investigate: Stairway to Eleven 85
Big Idea 4: Comparing Patterns of Growth 91
Visualize: Squared Squares 93
Play: Skip-Counting Arrays 100
Investigate: Stacking Pennies 107
Big Idea 5: The Ins and Outs of Functions 117
Visualize: Growing Functions 120
Play: Getting Warmer! 134
Investigate: The Functions of Near Squares 140
Big Idea 6: Finding Patterns in the Clouds 149
Visualize: What’s Going On in This Graph? 151
Play: What’s the Story Here? 158
Investigate: Creating Data Visualizations 166
Big Idea 7: Completing the Real Number System 177
Visualize: Square Sides 179
Play: Between 4 × 4 and 5 × 5 187
Investigate: The Hypotenuse Hypothesis 193
Big Idea 8: Discovering Pythagoras 201
Visualize: Unpacking Pythagoras 204
Play: Pythagorean Triples 209
Investigate: Approximating Square Roots 214
Big Idea 9: Exploring the Geometry of Ice Cream 221
Visualize: Building Intuition about Volume 223
Play: Comparing Cylinders 227
Investigate: Scooping Up Volume 233
Appendix 239
Centimeter Grid Paper 240
Grid Paper 241
Isometric Dot Paper 242
Dot Paper 243
About the Authors 245
Acknowledgments 247
Index 249
