This book places a premium on mathematical thinking. The authors make the compelling case using myriad examples that fluency requires reasoning and relies on conceptual understanding. If you want your students to confidently choose and flexibly use a range of strategies when working with rational numbers and algebraic equations, dig into the treasure trove of engaging activities in this book!

Grace Kelemanik

Sixth grade is a challenging time for fluency development—some students are still working on basic fact fluency, while others are starting to engage in a more sophisticated way of algebraic thinking. This book is an excellent resource for scaffolding middle school students on a personal level wherever they may be on the fluency continuum!

Kiersten Campbell

Figuring Out Fluency is a necessary resource for every middle school mathematics educator seeking to grow their knowledge base, learn effective teaching strategies, and gain access to teaching activities they can immediately implement.

Kristopher J. Childs, Equity, and Social Justice Officer—Open Up Resources

This book is exactly what the mathematics world needs. Even as a veteran teacher, I need to be reminded that students need explicit strategy instruction. Students need to see that there are efficient ways to solve problems and the standard algorithm isn’t always the best. This companion book is overflowing with ideas for the classroom teacher to improve mathematical fluency!

Elizabeth Uden

Despite striving for students to develop fluency with number and operations, inconsistent definitions of what it means to be fluent and a lack of understanding to implement effective fluency-building practices can leave you feeling defeated. Enter the action-oriented Figuring Out Fluency book that clarifies what it means to be fluent with number and operations while providing content specific examples that can be implemented in your classroom to begin seeing the fruit of your professional learning efforts.

Kyle Pearce

This is a book you keep on your teacher-desk! It’s full of classroom activities for your classroom while at the same time, it teaches you how to build your own activities so you can build mathematical fluency for your students.

Jon Orr, Lambton Kent District School Board

This book is like a full-course meal. Each course complements the other, from the amuse-bouche to the main course where each module, from operations of whole numbers to solving systems, leaves the reader satisfied with figuring out fluency. Lastly, as sweet as the dessert, developing fluency puts it all together. This is the most practical math book for secondary instruction of this time.

Valentin Sotomayor, Seminole County Public Schools

When most educators hear “fluency,” they immediately think of elementary school. The authors do a masterful job of pushing us to think of fluency at the middle grades as well and provide concrete examples of what it looks like. The activities are ready to implement immediately to bring to life the key ideas around fluency for rational numbers and algebraic equations.

Kevin J. Dykema

This book is the instruction tool I have been looking for with essential insights to effective mathematical teaching without unnecessary details. Filled with explicit ideas on how to build fluency, the book merges conceptual and procedural learning goals perfectly. A must-have tool for both educators and students looking for a deeper understanding of mathematics.

Kirk Redford

This brilliantly crafted book stresses the importance of teaching mathematical fluency as equipping learners with multiple strategies that are not only efficient and flexible but also lead to accurate solutions and are appropriate for the given situation. The fun and engaging activities, examples, and games all stress that fluency is also a matter of equity and access for all learners.

Kanita K DuCloux, Western Kentucky University

This book is awesome! What stood out to me was the deep understanding I gained about what fluency actually means. Too often the message has been to focus on fluency and accuracy, especially at the middle school level. By providing teachers with tools for building fluency with integers, expressions, and algebra, this book shifts that message to also focus on flexibility and strategy selection.

Lindsey Henderson, Utah State Board of Education

Building fluency certainly does not end in elementary! This book guides teachers seeking to help students make essential connections between first, rational number operations and familiar whole-number strategies, and second, number sense and solving abstract algebraic equations. What a great resource for novice and experienced teachers to explore together!

Tiffany Spralding

Figuring Out Fluency succeeds in delivering a true understanding of mathematical fluency. It encourages a shift from basic memorization of facts to developing and mastering one’s math psyche and revelatory understanding

Steven Geiger, Volusia County Schools

Operations With Rational Numbers and Algebraic Equations is an excellent addition to the Figuring Out Fluency series. This book brings to light how fluency is carried through to the higher grades—a must for math teachers. Bay-Williams and SanGiovanni highlight how fluency beyond whole numbers is possible and should be promoted in all of our students.

Pam Harris, Texas State University

This book paints a vibrant picture of the life fluency can live beyond the confines of basic math facts and memory exercises starting with early grade areas of fluency, through rational reasoning, and stretching far into the heart of algebraic reasoning.

Rachel Bachman, Weber State University

The resource that every middle school educator needs whether you are new or experienced in teaching operations with rational numbers and algebraic equations! The authors walk you through how procedural fluency is achieved by incorporating research-based strategies. There are routines, games, and activities for supporting instruction in the classroom to empower your students as mathematicians!

Micaela Wang

This latest edition to the Figuring Out Fluency series is written specifically to address the needs of middle school learners. Finally, middle school math educators have a playbook of research-aligned strategies to support fluency. The focus on the importance of reasonableness, the three moves to support reasonableness, and 100+ classroom-ready activities are a welcome addition to any classroom!

Latrenda Knighten

A fantastic resource! For years, I have pulled from multiple sources to help teachers develop a comprehensive view of teaching middle grades mathematics. Now it is all in one place! Not only does Figuring Out Fluency elaborate on the trajectory of mathematical content, but it also offers a variety of activities, games, and routines to help students reason, strategize, and develop “real” fluency.

Rodrigo Gutiérrez, University of Arizona CRR Co-Director