Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 5

ISBN-13: 9781119358718 / Angielski / Miękka / 2018 / 304 str.

Cathy Williams

Opis

Each volume includes a collection of mathematical tasks focused on the big mathematical ideas in the grade level that create opportunities for students to engage in (1) visual mathematics, (2) play, and (3) investigation. For each big idea the text will introduce and explore the big ideas and address the questions: What is the big idea and why is it important? Activities in the three areas -- visual math, play, and investigation -- will be provided for exploring each big idea along with space for students to write and draw what they are thinking about each concept. The big ideas for Grade 5 are:
1. Thinking in cubes
2. Estimating with fractions
3. Using fraction equivalence
4. Exploring the coordinate plane
5. Seeing and connecting patters across representations
6. Understanding fraction multiplication visually
7. What does it mean to divide with fractions?
8. Thinking in powers of ten
9. Using numbers and symbols flexibly

Spis treści

Introduction 1

Low–Floor, High–Ceiling Tasks 2

Youcubed Summer Camp 3

Memorization versus Conceptual Engagement 4

Mathematical Th inking, Reasoning, and Convincing 5

Big Ideas 9

Structure of the Book 10

Activities for Building Norms 17

Encouraging Good Group Work 17

Paper Folding: Learning to Reason, Convince, and Be a Skeptic 21

Big Idea 1: Thinking in Cubes 23

Visualize: Solids, Inside and Out 25

Play: City of Cubes 33

Investigate: A Box of Boxes 44

Big Idea 2: Estimating with Fractions 53

Visualize: Making Snowfl akes 55

Play: Fraction Blizzard 61

Investigate: Wondering with Fractions 67

Big Idea 3: Using Fraction Equivalence 81

Visualize: Picking Paintings Apart 83

Play: Make a Fake 94

Investigate: Squares with a Diff erence 101

Big Idea 4: Exploring the Coordinate Plane 115

Visualize: Getting around the Plane 118

Play: Ship Shape 124

Investigate: Table Patterns 133

Big Idea 5: Seeing and Connecting Patterns across

Representations 143

Visualize: Two–Pattern Tango 145

Play: Pattern Carnival 153

Investigate: Seeing Growth on a Graph 159

Big Idea 6: Understanding Fraction Multiplication Visually 169

Visualize: Fractions in a Pan 172

Play: Pieces and Parts 180

Investigate: Th e Sum of the Parts 187

Big Idea 7: What Does It Mean to Divide Fractions? 199

Visualize: Creating Cards 201

Play: Cuisenaire Trains 209

Investigate: Fraction Division Conundrum 217

Big Idea 8: Thinking in Powers of 10 223

Visualize: Th e Unit You 225

Play: Filling Small and Large 233

Investigate: Museum of the Very Large and Small 239

Big Idea 9: Using Numbers and Symbols Flexibly 247

Visualize: Seeing Expressions 250

Play: Inside Pascal s Triangle 261

Investigate: Th e 1492 Problem 268

Appendix 279

Centimeter Dot Paper 280

Isometric Dot Paper 281

About the Authors 283

Acknowledgments 285

Index 287

O autorze

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 United States 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.

Blurb

Engage Your Students in Visual, Creative Explorations of the Big Ideas in Mathematics

The Mindset Mathematics series offers a unique, research–based visual approach to exploring the big ideas in mathematics, which is essential to future mathematics success. This hands–on resource is for any teacher who wants to engage their fifth grade students in reasoning and persisting through problems, and provides activities that will engage students′ interest and show them the many ways that mathematics is important in their lives.

During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message: Teachers want to incorporate more brain science into their mathematics instruction, but they need guidance in the techniques that work best to promote learning of mathematics concepts. In this much–needed volume, the authors clearly show what the big ideas are at this grade level, why they are important to know, and how students can best learn those big ideas.

Filled with engaging questions, open–ended tasks, and four–color visuals, Mindset Mathematics is designed to be flexible so that it can be used with any current curriculum. All of the activities and tasks include instructions for launching in the classroom, suggestions for facilitating dynamic discussions, and guidance for what to look for in student thinking as it develops.