Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom

by SMALL

Overview

Now in its Third Edition—expanded with over 100 new tasks and questions—this bestselling resource helps experienced and novice teachers to effectively and efficiently differentiate mathematics instruction in grades K–8. Math education expert Marian Small shows teachers how to get started and become expert at using two powerful and universal strategies: Open Questions and Parallel Tasks. This volume includes key changes that will make it easier for teachers to use in all quality state standards environments, including direct links to Common Core content standards and standards for mathematical practice. Classroom examples, many new for this edition, are provided at each grade band: K–2, 3–5 and 6–8. Along with each example, the text describes how teachers can evoke productive conversations that meet the needs of a broad range of learners.

Book Features:

• Chapters organized around Common Core headings.
• Continued attention to big ideas in math.
• Many new questions that teachers can adapt or use as is.
• Teaching tips and task variations.
• A template to help users build new tasks.
• Guidance for using follow-up questions to create a rich math classroom.

PROFESSIONAL DEVELOPMENT: Visit Marian Small’s website

for in-person and online professional development.

Praise for Previous Editions!

“A must for an educator who is serious about reaching more students more often and achieving more positive results.”

—Resources for the Mathematics Educator

"This is a valuable book for mathematics teachers, teacher educators, and faculty involved in differentiated instruction."

—Choice

"This book is a great resource, with realistic applications to current instruction and tips for creating solid math discourse with your students."

—Mathematics: Teaching in the Middle School

"The glossary is a great resource for math language, and the index of big ideas provides a snapshot of focus points. . . . I highly recommend this user-friendly resource for all mathematics teachers."

—Teaching Children Mathematics

Product Details

ISBN-13:	9780807758540
Publisher:	Teachers College Press
Publication date:	04/28/2017
Edition description:	3
Pages:	304
Product dimensions:	5.90(w) x 9.10(h) x 0.50(d)

About the Author

Marian Small is an international professional developer and conference speaker. A former dean of education and professor of mathematics education, she is widely known for her bestselling books and her in-district work with educators. Visit her website at www.onetwoinfinity.ca for in-person and online professional development.

Table of Contents

Foreword Carol Ann Tomlinson ix

Preface xi

Organization of the Book xi

Mathematical Practice Standards xii

Changes in the Fourth Edition xiii

Acknowledgments xiv

Introduction: Why and How to Differentiate Math Instruction 1

The Challenge in Math Classrooms 1

What It Means to Meet Student Needs 3

Assessing Students' Needs 4

Principles and Approaches to Differentiating Instruction 4

Two Core Strategies for Differentiating Mathematics Instruction: Open Questions and Parallel Tasks 6

Creating a Math Talk Community 13

1 Counting & Cardinality and Number & Operations in Base Ten 17

Topics 17

The Big Ideas for Counting & Cardinality and for Number & Operations in Base Ten 18

Open Questions for Prekindergarten-Grade 2 19

Open Questions for Grades 3-5 28

Parallel Tasks for Prekindergarten-Grade 2 36

Parallel Tasks for Grades 3-5 43

Summing Up 48

2 Number & Operations-Fractions 49

Topics 49

The Big Ideas for Number & Operations-Fractions 50

Open Questions for Grades 3-5 51

Parallel Tasks for Grades 3-5 57

Summing Up 64

3 The Number System 65

Topics 65

The Big Ideas for The Number System 65

Open Questions for Grades 6-8 66

Parallel Tasks for Grades 6-8 70

Summing Up 74

4 Ratios & Proportional Relationships 75

Topics 75

The Big Ideas for Ratios & Proportional Relationships 76

Open Questions for Grades 6-8 76

Parallel Tasks for Grades 6-8 84

Summing Up 90

5 Operations & Algebraic Thinking 91

Topics 91

The Big Ideas for Operations & Algebraic Thinking 92

Open Questions for Prekindergarten-Grade 2 93

Open Questions for Grades 3-5 98

Parallel Tasks for Prekindergarten-Grade 2 108

Parallel Tasks for Grades 3-5 111

Summing Up 116

6 Expressions 8r Equations and Functions 117

Topics 117

The Big Ideas for Expressions & Equations and for Functions 118

Open Questions for Grades 6-8 118

Parallel Tasks for Grades 6-8 128

Summing Up 134

7 Financial Literacy 135

Topics 135

The Big Ideas for Financial Literacy 136

Open Questions for Prekindergarten-Grade 2 137

Open Questions for Grades 3-5 139

Open Questions for Grades 6-8 143

Parallel Tasks for Prekindergarten-Grade 2 147

Parallel Tasks for Grades 3-5 149

Parallel Tasks for Grades 6-8 151

Summing Up 156

8 Measurement & Data 157

Topics 157

The Big Ideas for Measurement & Data 158

Open Questions for Prekindergarten-Grade 2 159

Open Questions for Grades 3-5 169

Parallel Tasks for Prekindergarten-Grade 2 181

Parallel Tasks for Grades 3-5 187

Summing Up 196

9 Geometry 197

Topics 197

The Big Ideas for Geometry 198

Open Questions for Prekindergarten-Grade 2 199

Open Questions for Grades 3-5 205

Open Questions for Grades 6-8 211

Parallel Tasks for Prekindergarten-Grade 2 224

Parallel Tasks for Grades 3-5 227

Parallel Tasks for Grades 6-8 231

Summing Up 240

10 Statistics & Probability 241

Topics 241

The Big Ideas for Statistics & Probability 242

Open Questions for Grades 6-8 243

Parallel Tasks for Grades 6-8 252

Summing Up 262

Conclusions 263

The Need for Manageable Strategies 263

Developing Open Questions and Parallel Tasks 264

The Benefits of These Strategies 266

Appendix A Mathematical Practices Addressed in This Resource 267

Appendix B Worksheet for Open Questions and Parallel Tasks 268

Glossary 270

Bibliography 280

Index 283

Index of Subjects and Cited Authors 283

Index of Big Ideas 286

About the Author 290

What People are Saying About This

From the Publisher

“When I read Marian Small’s work, I see the power of math revealed, but I also see her work opening that power to so many students who might never otherwise experience it…I am a disciple of her approach to differentiating math!”
—From the Foreword by Carol Ann Tomlinson, University of Virginia

“Successful instruction causes students to wonder, conjecture, investigate, collaborate, and talk math. Good questioning is central to all the above, and for ‘knowing what students know.’ Small’s book focuses on the big ideas of mathematics, with questions, examples, and parallel tasks that assess student understanding and promote learning. This book is a must-read for every preservice and inservice teacher.”
—Carole Greenes, professor emerita, mathematics education, Arizona State University

“In a classroom full of students, it can be hard to meet the needs of all learners. That is where this book has your back. Marian Small provides meaningful tasks while modeling how simple tweaks and intentional number choice can unlock students’ mathematical potential.”
—Graham Fletcher, math specialist

“Throughout her career, Marian Small has shown that ‘differentiation’ in math class does not mean ‘ability grouping’ or breaking mathematics down into tiny, digestible subskills. Marian’s kind of differentiation means focusing on big ideas, offering students choice, and being curious about students’ thinking. In the 4th edition of this essential book, Marian teaches us powerful questioning techniques with her trademark clarity and provides plenty of specific examples across the content strands and grade bands. We can use these questions with our students immediately and internalize Marian’s teaching strategies through practice. How lucky for us that she has crafted these questions that will encourage student thinking, build our curiosity, and teach us to craft good questions of our own.”
—Tracy Johnston Zager, math coach

“I just finished teaching an elementary math methods course to teacher candidates in a graduate program. I wish I had had Marian Small’s Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom to use with these preservice teachers. Small covers all the key content in the Common Core PreK–8 math curriculum, and she addresses the topic of open questions in a very accessible way. She walks the reader step-by-step through how to teach the big ideas in the CCSS PreK–8 math curriculum using specified open questions. At the same time, she provides a menu of choices so teachers can draw from their own expertise to select the open questions that they see fit. Each chapter explains math content in an easy-to-reference manner. It is like having a reference book and a teaching coach all in one book. This semester, I watched teacher candidates struggle with how to lead a Number Talk, because they were not sure which open questions to ask to facilitate learning. Small’s book provides the guidance that they need. I look forward to using Small’s book the next time I teach Elementary Math Methods to teacher candidates. Inservice teachers will also benefit from the practical ideas about how to promote higher-order math thinking by asking the open questions outlined in Good Questions.”
—Felicia Darling, math instructor at Santa Rosa Junior College

Editorial Reviews

"I recommend this book for pre-kindergarten through eighth grade mathematics teachers wanting to learn classroom differentiation strategies and to those wanting to extend their knowledge of open questions and parallel tasks"

—Mathematics Teaching in Middle School

“A must for any educator who is serious about reaching more students more often and achieving more positive results.”

—Resources for the Mathematics Educator (from previous edition)

From the Publisher