Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 6

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 10Note on Materials 16Manipulatives and Materials Used in This Book 17Activities for Building Norms 19Encouraging Good Group Work 19Paper Folding: Learning to Reason, Convince, and Be Skeptical 21Big Idea 1: Taking Apart Prisms and Polygons 24Visualize: How Big Is the Footprint? 26Play: Shards of a Shape 38Investigate: Rising from the Footprint 46Big Idea 2: Folding and Unfolding Objects 57Visualize: Folding Cubes in Your Mind 60Play: Folding Nets in Your Mind 70Investigate: Filling Our Nets 85Big Idea 3: Expanding the Number Line 92Visualize: Folding around Zero 94Play: Bouncing around the Number Line 101Investigate: Going 2-D 107Big Idea 4: Finding and Using Unit Rates 116Visualize: Seeing Unit Rates 118Play: Seeing the Best Deal 128Investigate: How Fast Do You Walk? 136Big Idea 5: Reasoning with Proportions 142Visualize: Jump! Jump! 144Play: Seeing Animals in a New Way 149Investigate: A Seat at the Table 156Big Idea 6: Visualizing the Center and Spread of Data 164Visualize: The Shape of Data 167Play: What Does Mean Mean? 178Investigate: When Does Mean = Median = Mode = Range? 185Big Idea 7: Using Symbols to Describe the World 192Visualize: Cuisenaire Rod Equivalents 195Play: Math Mobiles 204Investigate: Radial Patterns 215Big Idea 8: Generalizing 221Visualize: Generalizing Number Patterns 223Play: Generalizing Strategy 230Investigate: Generalizing Visual Patterns 239Appendix 246Centimeter Grid Paper 247Grid Paper 2481" Grid Paper 249Isometric Dot Paper 250Dot Paper 251About the Authors 252Acknowledgments 254Index 255

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