Table of Contents
Introduction vii
Defining Numerical Fluency viii
The Challenge: Teaching in Ways We Were Not Taught x
Our Goals for This Book xii
Part 1 Building Understanding of Numerical Fluency 1
Chapter 1 Nine Pivotal Understandings for Numerical Fluency 3
Pivotal Understanding 1: Everything Begins with Counting 4
Pivotal Understanding 2: All Quantities Are Composed of Parts and Wholes 5
Pivotal Understanding 3: Acquiring the Language of Operations Before Learning Facts 8
Pivotal Understanding 4: Properties of Operations 9
Pivotal Understanding 5: Using 5 and 10 11
Pivotal Understanding 6: 9 and 10-1 Are the Same Number 12
Pivotal Understanding 7: Multiplication by 2, 3, 5, and 10 14
Pivotal Understanding 8: Equivalence in Equations and the Meaning of the Equal Sign 16
Pivotal Understanding 9: Place Value Understanding 17
Chapter 2 Six Processes for Developing Numerical Fluency 19
The Six Processes 19
Putting the Six Processes Together 31
Conclusion 33
Chapter 3 Classroom Structures for Developing Numerical Fluency 34
Guiding Principles for Teaching Structures 34
Number Talks 35
Games 37
World Problem Banks 40
Problem-Solving Activities 42
Student-Made Materials 44
Conclusion 46
Part 2 Developing Addition and Subtraction Fluency 47
Chapter 4 It All Begins with Parts and Wholes 49
Why Parts and Wholes Matter 49
Key Ideas and Skills 50
Classroom Activities 53
Chapter 5 Developing Fluency with Addition and Subtraction Facts 67
Key Ideas and Skills 68
Classroom Activities 80
Chapter 6 Developing Fluency Finding Sums and Differences 86
Key Ideas and Skills 87
Classroom Activities 93
Part 3 Developing Multiplication and Division Fluency 101
Chapter 7 Giving Meaning to Multiplication and Division 103
Key Ideas and Skills 104
Classroom Activities 106
Chapter 8 Developing Fluency with Multiplication and Division Facts 113
Key Ideas and Skills 114
Classroom Activities 123
Chapter 9 Developing Fluency Finding Products and Quotients 130
Key Ideas and Skills 130
Classroom Activities 138
Part 4 Strategies for Creating a Schoolwide Culture of Fluency 147
Chapter 10 Activities and Resources for Establishing a Culture of Fluency and Fun 149
Chapter 11 It Takes a School to Develop Numerical Fluency 158
Making Better Use of Meetings 159
Teacher Collaboration 161
Garnering Administrative Support 163
Appendix 165
References 169
