Jo Boaler & Jen Munson 
Mindset Mathematics [PDF ebook] 
Visualizing and Investigating Big Ideas, Grade 8

Introduction 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

JO BOALER is a professor of mathematics education at Stanford University and co-founder and faculty director of youcubed. She serves as an advisor to several Silicon Valley companies and is a White House presenter on girls and STEM (Science, Technology, Engineering, and Math). The author of seven books, including Mathematical Mindsets, and numerous research articles, she is a regular contributor to news and radio in the United States and England.
JEN MUNSON is an assistant professor of learning sciences at Northwestern University, a professional developer, and a former classroom teacher. She received her Ph D in teacher education and mathematics education from Stanford University. Her research focuses on responsive, equitable mathematics instruction and coaching.
CATHY WILLIAMS is the co-founder and the executive director of youcubed at Stanford University. Before working at youcubed, she was a high school math teacher and worked in mathematics curriculum and administration at the county and district levels in California.