Introduction Low Floor, High Ceiling Tasks Youcubed Summer Camp Memorization vs. 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: Solving Problems with Data Visualize: Tongues, Tails, and In Between Play: Inspector Graph-It Investigate: Data Tells Us About Ourselves Big Idea 2: Thinking Around Shapes Visualize: Get Your Arms Around It Play: Shapes on a Plane Investigate: Shape and Not a Shape Big Idea 3: Thinking in Equal Groups Visualize: Sharing Crackers Play: Dozens of Dice Investigate: Playing with Pairs Big Idea 4: Tiling to Understand Area Visualize: Cover Up Play: A Whole New Alphabet Investigate: Sharing an Area Big Idea 5: Seeing Multiplication as Area Visualize: Rods Around Play: Squares and Near-Squares Investigate: Connecting Area and Perimeter Big Idea 6: Understanding Half Visualize: I Spy 1/2 Play: Spotting 1/2 Investigate: The Many Shapes of 1/2 Big Idea 7: Seeing Fractions, Parts, Wholes, and Forms Visualize: Seeing Parts and Wholes Play: Cover, Cut, and Sort Investigate: Taking a Fractional Walk Big Idea 8: Being Flexible with Numbers Visualize: How Many Do You See? Play: How Close to 100? Investigate: Tile and Table Patterns Appendix Centimeter Dot Paper Isometric Dot Paper Grid Paper Dot Paper Grid Paper
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 postdoctoral fellow at Northwestern University, a professional developer, and a former classroom teacher. She received her PhD in mathematics education from Stanford University. Her research focuses on 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.