Figuring Out Fluency--Ten Foundations for Reasoning Strategies With Whole Numbers

A Classroom Companion
John J. SanGiovanni - Howard Public School System
Jennifer M. Bay-Williams - University of Louisville, KY
Susie Katt - Lincoln Public Schools, Nebraska
Figuring Out Fluency--Ten Foundations for Reasoning Strategies With Whole Numbers
March 2024 | 280 pages | Corwin
Create Flyer

Purchase

eBook
ISBN: 9781071938300
Available from January 0001
Paperback
ISBN: 9781071916957
Available from January 0001

Description

Because fluency practice is not a worksheet.

Fluency in mathematics is more than basic facts or using algorithms. It is not about recall or speed. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is a matter of equity and access for all learners.

The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency. It explained the seven Significant Strategies for fluency and offered a plethora of pragmatic tools for shifting classrooms toward a greater fluency approach. However, in order to become truly adept with these strategies, children must first have certain underlying foundational concepts and skills in place. 

Figuring Out Fluency-Ten Underlying Foundations for Reasoning Strategies with Whole Numbers explores the ideas that are essential to reasoning: Number Relationships; Subitizing and Decomposing; Distance to 10, 100, and 1,000; Counting and Skip-Counting; Properties of Addition and Its Inverse Relationship with Subtraction; Properties of Multiplication and Its Inverse Relationship with Division; Multiplying by 10s and 100s; Multiples and Factors; Doubling and Halving; and Computational Estimation. With this book, elementary teachers can

  • Help children develop these foundational understandings, critical to reasoning and number sense.
  • Leverage over 100 classroom-ready routines, centers, and games to develop these concepts both in first instruction, practice, and intervention.
  • Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation

Develop each and every students’ knowledge and power to become skilled and confident mathematical thinkers and doers.

Contents

Part I: Figuring out Fluency Foundations: Big Ideas

Part I: Figuring out Fluency Foundations: Big Ideas

Part 2: Foundations Modules

Part 2: Foundations Modules

Module 1: Number Relationships: Comparison and Estimation

Module 1: Number Relationships: Comparison and Estimation

Module 2: Subitizing to Decomposing

Module 2: Subitizing to Decomposing

Module 3: Distance to 10, 100, and 1,000

Module 3: Distance to 10, 100, and 1,000

Module 4: Counting and Skip-Counting

Module 4: Counting and Skip-Counting

Module 5: Properties of Addition and Its Inverse Relationship with Subtraction

Module 5: Properties of Addition and Its Inverse Relationship with Subtraction

Module 6: Properties of Multiplication and the Inverse Relationship with Division

Module 6: Properties of Multiplication and the Inverse Relationship with Division

Module 7: Multiplying by 10s and 100s

Module 7: Multiplying by 10s and 100s

Module 8: Multiples and Factors

Module 8: Multiples and Factors

Module 9: Doubling and Halving

Module 9: Doubling and Halving

Module 10: Computational Estimation

Module 10: Computational Estimation

Part 3: Taking Action

Part 3: Taking Action

Appendix A: Activity List

Appendix A: Activity List

References

References

Resources

companion website

Description

Because fluency practice is not a worksheet.

Fluency in mathematics is more than basic facts or using algorithms. It is not about recall or speed. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is a matter of equity and access for all learners.

The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency. It explained the seven Significant Strategies for fluency and offered a plethora of pragmatic tools for shifting classrooms toward a greater fluency approach. However, in order to become truly adept with these strategies, children must first have certain underlying foundational concepts and skills in place. 

Figuring Out Fluency-Ten Underlying Foundations for Reasoning Strategies with Whole Numbers explores the ideas that are essential to reasoning: Number Relationships; Subitizing and Decomposing; Distance to 10, 100, and 1,000; Counting and Skip-Counting; Properties of Addition and Its Inverse Relationship with Subtraction; Properties of Multiplication and Its Inverse Relationship with Division; Multiplying by 10s and 100s; Multiples and Factors; Doubling and Halving; and Computational Estimation. With this book, elementary teachers can

  • Help children develop these foundational understandings, critical to reasoning and number sense.
  • Leverage over 100 classroom-ready routines, centers, and games to develop these concepts both in first instruction, practice, and intervention.
  • Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation

Develop each and every students’ knowledge and power to become skilled and confident mathematical thinkers and doers.

Contents

Part I: Figuring out Fluency Foundations: Big Ideas

Part I: Figuring out Fluency Foundations: Big Ideas

Part 2: Foundations Modules

Part 2: Foundations Modules

Module 1: Number Relationships: Comparison and Estimation

Module 1: Number Relationships: Comparison and Estimation

Module 2: Subitizing to Decomposing

Module 2: Subitizing to Decomposing

Module 3: Distance to 10, 100, and 1,000

Module 3: Distance to 10, 100, and 1,000

Module 4: Counting and Skip-Counting

Module 4: Counting and Skip-Counting

Module 5: Properties of Addition and Its Inverse Relationship with Subtraction

Module 5: Properties of Addition and Its Inverse Relationship with Subtraction

Module 6: Properties of Multiplication and the Inverse Relationship with Division

Module 6: Properties of Multiplication and the Inverse Relationship with Division

Module 7: Multiplying by 10s and 100s

Module 7: Multiplying by 10s and 100s

Module 8: Multiples and Factors

Module 8: Multiples and Factors

Module 9: Doubling and Halving

Module 9: Doubling and Halving

Module 10: Computational Estimation

Module 10: Computational Estimation

Part 3: Taking Action

Part 3: Taking Action

Appendix A: Activity List

Appendix A: Activity List

References

References

Resources

companion website

SAGE Publishing Logo

Figuring Out Fluency--Ten Foundations for Reasoning Strategies With Whole Numbers

A Classroom Companion


March 2024 | 280 pages | Corwin

Format Published Date ISBN Price
Paperback 01/02/2026 9781071916957 $43.95
Lifetime 01/02/2026 9781071938300 $40.00

Because fluency practice is not a worksheet.

Fluency in mathematics is more than basic facts or using algorithms. It is not about recall or speed. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is a matter of equity and access for all learners.

The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency. It explained the seven Significant Strategies for fluency and offered a plethora of pragmatic tools for shifting classrooms toward a greater fluency approach. However, in order to become truly adept with these strategies, children must first have certain underlying foundational concepts and skills in place. 

Figuring Out Fluency-Ten Underlying Foundations for Reasoning Strategies with Whole Numbers explores the ideas that are essential to reasoning: Number Relationships; Subitizing and Decomposing; Distance to 10, 100, and 1,000; Counting and Skip-Counting; Properties of Addition and Its Inverse Relationship with Subtraction; Properties of Multiplication and Its Inverse Relationship with Division; Multiplying by 10s and 100s; Multiples and Factors; Doubling and Halving; and Computational Estimation. With this book, elementary teachers can

  • Help children develop these foundational understandings, critical to reasoning and number sense.
  • Leverage over 100 classroom-ready routines, centers, and games to develop these concepts both in first instruction, practice, and intervention.
  • Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation

Develop each and every students’ knowledge and power to become skilled and confident mathematical thinkers and doers.


Table Of Contents:

  • Part I: Figuring out Fluency Foundations: Big Ideas
  • Part 2: Foundations Modules
  • Module 1: Number Relationships: Comparison and Estimation
  • Module 2: Subitizing to Decomposing
  • Module 3: Distance to 10, 100, and 1,000
  • Module 4: Counting and Skip-Counting
  • Module 5: Properties of Addition and Its Inverse Relationship with Subtraction
  • Module 6: Properties of Multiplication and the Inverse Relationship with Division
  • Module 7: Multiplying by 10s and 100s
  • Module 8: Multiples and Factors
  • Module 9: Doubling and Halving
  • Module 10: Computational Estimation
  • Part 3: Taking Action
  • Appendix A: Activity List
  • References

Recent Product Reviews:

This most recent addition to the Figuring Out Fluency series is outstanding! It provides guidance and support for building foundational fluency skills and practical ways to implement meaningful assessment and joyful practice. This book could shift mindsets about what it truly means to be fluent in math.
Deborah Peart, My Mathematical Mind
SanGiovanni, Bay-Williams, and Katt have done it—the ultimate fluency resource! The focus is on helping students through their struggles using the lens of the foundational knowledge and skills needed for computational fluency. This is a perfect blend of lesson seeds, routines, games, and centers that provide first instruction or intervention for every student. This book, coupled with self-reflection, humility, and productive struggle, provides a rock-solid foundation so all students can weather any storm!
Ron Perry, Heim Elementary, Williamsville Central School District
Figuring Out Fluency—Ten Foundations for Reasoning Strategies With Whole Numbers is a game changer! In this companion to the Figuring Out Fluency series, the authors provide teachers with hands-on, engaging resources to support teaching and learning of foundational fluency concepts. This resource uses games, routines, and centers to help focus on reasoning about fluency concepts!
Latrenda Knighten, East Baton Rouge Parish School System
Undoubtedly the most impactful book in the series, Figuring Out Fluency—Ten Foundations for Reasoning Strategies With Whole Numbers is a must-have for every elementary teacher. It explains not only the foundational skills and concepts needed for fluency but also the how and why they are necessary for strategic thinking. The look-fors and practical, easy-to-implement ideas for instruction and practice will help students build their mathematical identities and grow as mathematical thinkers.
Brenda Dzwil & Holley Duffy, Newington Public Schools
Get ready for a comprehensive yet accessible read for teachers to lay the roadmap for equipping students with indispensable foundational skills for learning fluency strategies. The authors outline ten foundations and supplement them with descriptions, examples, and teacher-friendly language to implement in the classroom tomorrow. The variety of included activities will create a book filled with dog-eared pages that teachers will reach for regularly.
Marci Ostmeyer, Educational Service Unit 7

Recommendations