## Features and Benefits

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
• 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

Appendix

References