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

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

March 2024 | 280 pages | Corwin

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.

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

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
Ocala, FL

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
Williamsville, NY

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
Baton Rouge, LA

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
Newington, CT

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
Columbus, NE

The ten foundations for reasoning strategies shared in this book are practical and designed for immediate classroom application. They encompass methods to teach, practice, and assess fluency, which foster a supportive learning environment that cultivates a positive math identity among students.

Janel Marr
Windward District
Kaneohe, HI

This book provides teachers with an understanding of how to support and solidify foundational skills for students. It gives teachers a toolkit of assessments, games, and centers that are easily accessible and effortless to implement. It also challenges the traditional classroom, pushing the teacher to become more of the facilitator while encouraging an equitable education for all students.

Marissa Giangrosso
Blue Springs, MO

I own every book in the Figuring Out Fluency series, and this is the missing piece. This book examines the why and how number sense works in building procedural fluency with tools both for student practice and assessment of understanding. The structures and strategies are explained in a way that new and veteran teachers can implement in the classroom.

Christina Worley
St Lucie Public Schools
Port Saint Lucie, FL

John J. SanGiovanni

John J. SanGiovanni is a mathematics coordinator in Howard County, Maryland. There, he leads mathematics curriculum development, digital learning, assessment, and professional development. John is an adjunct professor and coordinator of the Elementary Mathematics Instructional Leadership graduate program at McDaniel College. In addition to this Figuring Out Fluency series, some of his many Corwin books include Daily Routines to Jump-Start Problem Solving, Grades K-8, Answers to Your Biggest Questions about Teaching Elementary Math, the Daily Routines to Jump-Start Math series, and Productive Math Struggle: A 6-Point Action Plan for... More About Author

Jennifer M. Bay-Williams

Susan K. Katt

Susie Katt is the K-2 Mathematics Coordinator in Lincoln, Nebraska, where she leads professional learning, assessment, and math curriculum development. She is an author of Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance and Answers to Your Biggest Questions About Teaching Elementary Math. She is also a national math curriculum consultant. Susie speaks at state, regional, and national conferences. She served the National Council of Teachers of Mathematics (NCTM) as the chair of the editorial panel for the journal Teaching Children Mathematics, as department editor for Mathematics Teacher: Learning and Teaching PK... More About Author

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ISBN: 9781071916957