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Developing Numerical Fluency

Making Numbers, Facts, and Computation Meaningful

By Patsy Kanter, Steven Leinwand, Education Consultant, Washington, DC

Numerical fluency is about understanding, not memorization.

In Developing Numerical Fluency, Patsy Kanter and Steven Leinwand take a fresh look at a commonly-asked question: “How do I teach number facts so my students know them fluently?” They apply their decades of experience teaching mathematics to rethinking effective fluency instruction.

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ISBN 978-0-325-09312-3 / 0-325-09312-1 / SKU E09312
2018 / 184pp / Paperback
Grade Level: Kindergarten-5th

Topic: Math

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Full Description

"This is a must-read book for any teachers of math."

—Jo Boaler, Professor of Mathematics Education at Stanford University and author of Mathematical Mindsets

Numerical fluency is about understanding

Numerical fluency is about understanding, not memorization. It comes over time as students engage in active thinking and doing, not endless worksheets and timed tests.

Classroom instruction and materials, however, often don’t feel aligned with these realities.

Classroom-tested ideas you can use right away

Each chapter introduces ideas, techniques, and strategies that contribute to meaningful fluency for all students. You’ll find:

pivotal understandings that illuminate what contributes to real numerical fluency
six instructional processes that support lasting fluency development
classroom structures and activities for building fluency in addition, subtraction, multiplication, and division
suggestions for creating a school-wide culture of numerical fluency.

Patsy and Steve remind us that, “Students do not develop numerical fluency by memorizing and regurgitating rules.” But many of us learned mathematics in exactly this way, making shifting our instruction challenging. Developing Numerical Fluency provides just the right support, offering big ideas for rethinking instruction paired with classroom-tested activities you can use right away.

Additional Resource Information

(click any section below to continue reading)

Podcast

Introduction

Defining Numerical Fluency
The Challenge: Teaching in Ways We Were Not Taught
Our Goals for This Book

PART ONE: Building Understanding of Numerical Fluency

Chapter 1: Nine Pivotal Understandings for Numerical Fluency

Pivotal Understanding 1: Everything Begins with Counting
Pivotal Understanding 2: All Quantities are Composed of Parts and Wholes
Pivotal Understanding 3: Acquiring the Language of Operations Before Learning Facts
Pivotal Understanding 4: Properties of Operations
Pivotal Understanding 5: Using 5 and 10
Pivotal Understanding 6: 9 and 10-1 are the Same Number
Pivotal Understanding 7: Multiplication by 2, 3, 5, and 10
Pivotal Understanding 8: Equivalence in Equations are the Meaning of the Equal Sign
Pivotal Understanding 9: Place Value Understanding

Chapter 2: Six Processes for Developing Numerical Fluency

The Six Processes
Putting the Six Processes Together
Conclusion

Chapter 3: Classroom Structures for Developing Numerical Fluency

Guiding Principles for Teaching Structures
Number Talks
Games
Word Problem Banks
Problem-Solving Activities
Student-Made Materials
Conclusion

PART TWO: Developing Addition and Subtraction Fluency

Chapter 4: It All Begins with Parts and Wholes

Why Parts and Wholes Matter
Key Ideas and Skills
Classroom Activities

Chapter 5: Developing Fluency with Addition and Subtraction Facts

Key Ideas and Skills
Classroom Activities

Chapter 6: Developing Fluency Finding Sums and Differences

Key Ideas and Skills
Classroom Activities

PART THREE: Developing Multiplication and Division Fluency

Chapter 7: Giving Meaning to Multiplication and Division

Key Ideas and Skills
Classroom Activities

Chapter 8: Developing Fluency with Multiplication and Division Facts

Key Ideas and Skills
Classroom Activities

Chapter 9: Developing Fluency Finding Products and Quotients

Key Ideas and Skills
Classroom Activities

PART FOUR: Strategies for Creating a Schoolwide Culture of Fluency

Chapter 10: Activities and Resources for Establishing a Culture of Fluency and Fun

Chapter 11: It Takes a School to Develop Numerical Fluency

Making Better Use of Meetings
Teacher Collaboration
Garnering Administrative Support

Appendix

References

Samples

Companion Resources

Reviews

"This is a must-read book for any teachers of math. Patsy and Steve take us on a journey of all that needs to change in the development of numerical fluency and give critical advice along the way."

—Jo Boaler, Professor of Mathematics Education at Stanford University, co-founder of youcubed.org, and author of Mathematical Mindsets