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 10
Activities for Building Norms 17
Encouraging Good Group Work 17
Paper Folding: Learning to Reason, Convince, and Be a Skeptic 21
Big Idea 1: Thinking in Cubes 23
Visualize: Solids, Inside and Out 25
Play: City of Cubes 33
Investigate: A Box of Boxes 44
Big Idea 2: Estimating with Fractions 53
Visualize: Making Snowflakes 55
Play: Fraction Blizzard 61
Investigate: Wondering with Fractions 67
Big Idea 3: Using Fraction Equivalence 81
Visualize: Picking Paintings Apart 83
Play: Make a Fake 94
Investigate: Squares with a Difference 101
Big Idea 4: Exploring the Coordinate Plane 115
Visualize: Getting around the Plane 118
Play: Ship Shape 124
Investigate: Table Patterns 133
Big Idea 5: Seeing and Connecting Patterns across Representations 143
Visualize: Two-Pattern Tango 145
Play: Pattern Carnival 153
Investigate: Seeing Growth on a Graph 159
Big Idea 6: Understanding Fraction Multiplication Visually 169
Visualize: Fractions in a Pan 172
Play: Pieces and Parts 180
Investigate: The Sum of the Parts 187
Big Idea 7: What Does It Mean to Divide Fractions? 199
Visualize: Creating Cards 201
Play: Cuisenaire Trains 209
Investigate: Fraction Division Conundrum 217
Big Idea 8: Thinking in Powers of 10 223
Visualize: The Unit You 225
Play: Filling Small and Large 233
Investigate: Museum of the Very Large and Small 239
Big Idea 9: Using Numbers and Symbols Flexibly 247
Visualize: Seeing Expressions 250
Play: Inside Pascal’s Triangle 261
Investigate: The 1492 Problem 268
Appendix 279
Centimeter Dot Paper 280
Isometric Dot Paper 281
About the Authors 283
Acknowledgments 285
Index 287JO 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 a doctoral candidate at Stanford University, a professional developer, and a former classroom teacher. She works with teachers and school leaders across the United States to develop responsive, equitable mathematics instruction.
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.
![]() |
Ask a Question About this Product More... |
![]() |