Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 3

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.

• Introduction 1Low-Floor, High-Ceiling Tasks 2Youcubed Summer Camp 3Memorization versus Conceptual Engagement 4Mathematical Thinking, Reasoning, and Convincing 5Big Ideas 9Structure of the Book 10Activities for Building Norms 17Encouraging Good Group Work 17Paper Folding: Learning to Reason, Convince, and Be a Skeptic 21Big Idea 1: Solving Problems with Data 23Visualize: Tongues, Tails, and in Between 25Play: Inspector Graph-It 36Investigate: Data Tells Us about Ourselves 41Big Idea 2: Thinking around Shapes 51Visualize: Get Your Arms around It 53Play: 36-Unit Walk 59Investigate: Shapes on a Plane 65Big Idea 3: Thinking in Equal Groups 75Visualize: Sharing Crackers 78Play: Dozens of Dice 85Investigate: Playing with Pairs 91Big Idea 4: Tiling to Understand Area 99Visualize: Cover Up 101Play: A Whole New Alphabet 111Investigate: Sharing an Area 119Big Idea 5: Seeing Multiplication as Area 125Visualize: Rods Around 127Play: Squares and Near-Squares 132Investigate: Connecting Area and Perimeter 142Big Idea 6: Understanding 1 2 149Visualize: I Spy 1 2 151Play: Spotting 1 2 160Investigate: The Many Shapes of 1 2 171Big Idea 7: Seeing Fractions: The Parts and the Wholes 183Visualize: Seeing Parts and Wholes 185Play: Cover, Cut, and Sort 191Investigate: Taking a Fractional Walk 202Big Idea 8: Being Flexible with Numbers 209Visualize: How Many Do You See? 211Play: How Close to 100? 217Investigate: Tile and Table Patterns 222Appendix 231¼˝ Grid Paper 232Grid Paper 2331˝ Grid Paper 234¼˝ Dot Paper 235Centimeter Dot Paper 236Isometric Dot Paper 237Hundred Grids 238About the Authors 239Acknowledgments 241Index 243

Select Guide Rating