Mindset Mathematics Visualizing and Investigating Big Ideas, Grade 4

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 first-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.

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.

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

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