Introduction Low Floor, High Ceiling Tasks Youcubed Summer Camp Memorization versus Conceptual Engagement Mathematical Thinking, Reasoning, and Convincing Big Ideas Structure of the Book Activities for Building Norms Encouraging Good Group Work Paper Folding: Learning to Reason, Convince, and Be Skeptical Big Idea 1: Seeing Patterns inside Numbers Visualize: Visualizing Numbers Play: What Could It Be? Investigate: How Flexible Is a Number? Big Idea 2: Building and Designing with Shapes and Angles Visualize: Tile It! Play: Those Crazy Rep-Tiles Investigate: Polyiamonds Big Idea 3: Making and Naming Number Patterns Visualize: Finding Fibonacci Play: Pattern Carnival Investigate: All Hail! Big Idea 4: Units Are a Relationship Visualize: It's All in the Axes Play: Measure Up Investigate: 10,000 Steps Big Idea 5: Modeling with Unit Fractions Visualize: Perplexing Measures Play: Tangram Designs Investigate: Pixeled Fractions Big Idea 6: Fraction Equivalence Visualize: Painting Pieces Play: Color-Coding Fractions Investigate: Tiling Rectangles Big Idea 7: Illustrating Multiplication and Division Visualize: Visual Proof Play: Cover the Field Investigate: Table Patterns Big Idea 8: Using Operations Flexibly Visualize: How Crowded Is the Crowd? Play: Target 20 Investigate: Supply Parade Big Idea 9: What Is a Decimal? Visualize: Finding the Better Deal Play: Decimals on a Line Investigate: Can You Make It? About the Authors Acknowledgments Index
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 a doctoral candidate at Stanford University, a professional developer, and a former classroom teacher. She works with teachers and school leaders across the U.S. 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.