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Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 6

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Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 6

Jo Boaler, Jen Munson, Cathy Williams

ISBN: 978-1-119-35867-1 January 2019 Jossey-Bass 272 Pages

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Description

Engage students in mathematics using growth mindset techniques

The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the sixth-grade level through visualization, play, and investigation.

During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that:

  • There is no such thing as a math person - anyone can learn mathematics to high levels.
  • Mistakes, struggle and challenge are the most important times for brain growth.
  • Speed is unimportant in mathematics.
  • Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics.

With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

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

Note on Materials 16

Manipulatives and Materials Used in This Book 17

Activities for Building Norms 19

Encouraging Good Group Work 19

Paper Folding: Learning to Reason, Convince, and Be Skeptical 21

Big Idea 1: Taking Apart Prisms and Polygons 24

Visualize: How Big Is the Footprint? 26

Play: Shards of a Shape 38

Investigate: Rising from the Footprint 46

Big Idea 2: Folding and Unfolding Objects 57

Visualize: Folding Cubes in Your Mind 60

Play: Folding Nets in Your Mind 70

Investigate: Filling Our Nets 85

Big Idea 3: Expanding the Number Line 92

Visualize: Folding around Zero 94

Play: Bouncing around the Number Line 101

Investigate: Going 2-D 107

Big Idea 4: Finding and Using Unit Rates 116

Visualize: Seeing Unit Rates 118

Play: Seeing the Best Deal 128

Investigate: How Fast Do You Walk? 136

Big Idea 5: Reasoning with Proportions 142

Visualize: Jump! Jump! 144

Play: Seeing Animals in a New Way 149

Investigate: A Seat at the Table 156

Big Idea 6: Visualizing the Center and Spread of Data 164

Visualize: The Shape of Data 167

Play: What Does Mean Mean? 178

Investigate: When Does Mean = Median = Mode = Range? 185

Big Idea 7: Using Symbols to Describe the World 192

Visualize: Cuisenaire Rod Equivalents 195

Play: Math Mobiles 204

Investigate: Radial Patterns 215

Big Idea 8: Generalizing 221

Visualize: Generalizing Number Patterns 223

Play: Generalizing Strategy 230

Investigate: Generalizing Visual Patterns 239

Appendix 246

Centimeter Grid Paper 247

Grid Paper 248

1" Grid Paper 249

Isometric Dot Paper 250

Dot Paper 251

About the Authors 252

Acknowledgments 254

Index 255