Table of Contents

PART 1: FIGURING OUT FLUENCY: KEY IDEAS
PART 2: STRATEGY MODULES
Module 1 Good (and Necessary) Foundations for Reasoning Strategies
Module 2: Break Apart (by Addends) and Partial Products
Module 3: Compensation for Multiplying Fractions and Decimals
Module 4: Break Apart to Multiply (by Factors)
Module 5: Think Multiplication
Module 6: Partial Quotients
Module 7: Algorithms for Fraction Multiplication and Division
Module 8: Algorithms for Decimal Multiplication and Division
PART 3: PUTTING IT ALL TOGETHER: DEVELOPING FLUENCY

About the Author

Jennifer M. Bay-Williams is a professor of mathematics education at the University of Louisville, where she teaches preservice teachers, emerging elementary mathematics specialists, and doctoral students in mathematics education. She has authored over 40 books and 100 journal articles/book chapters, many of which focus on procedural fluency and developing mathematical proficiency. Beyond the Figuring out Fluency series, these include Math Fact Fluency, and Everything you Need for Mathematics Coaching and Elementary: Teaching Developmentally and Middle School Mathematics. Jennifer′s national leadership includes NCTM Board of Directors, the TODOS: Mathematics for All Board of Directors, and as president and secretary of the Association of Mathematics Teacher Educators (AMTE). 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 passionate about growing new mathematics leaders in the district and through McDaniel College. In addition to the 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 Fostering Perseverance. John is a national mathematics curriculum and professional learning consultant who also speaks frequently at national conferences and institutes. He is active in state and national professional organizations, recently serving on the board of directors for the National Council of Teachers of Mathematics (NCTM) and on the board of directors for NCSM.

Sherri Martinie, a Professor of Curriculum and Instruction in the College of Education at Kansas State University, teaches undergraduate and graduate courses in mathematics education. Prior to taking her position at Kansas State, she taught elementary, middle and high school mathematics for a combined 20 years. She is continually seeking innovative ways to support preservice and in-service teachers in the development and refinement of effective mathematics teaching practices.  Jennifer Suh is a mathematics educator at George Mason University, leading efforts to enhance K-8 math instruction through strength-based formative assessments and bridging activities. In partnership with the Virginia Department of Education, her project, Bridging for Math Strength, focuses on using rich mathematics tasks across grade levels, unpacking the learning progression to enhance teaching and learning. Jennifer uses this project for math intervention and multi-tiered instruction, working closely with special education and general education math teachers to meet diverse learners′ needs. She directs the Center for Outreach in Mathematics Professional Learning and Educational Technology (COMPLETE), conducting Lesson Study in schools emphasizing problem-based tasks to promote equitable access to 21st-century skills, including creativity, critical thinking, communication, and collaboration, particularly for diverse student populations.

Reviews

This book places mathematical thinking front and center! The authors make the compelling case using myriad examples that fluency requires reasoning and relies on conceptual understanding. They provide a treasure trove of engaging activities teachers can use to help their students develop fluency with fractions and decimals. If you want your students to confidently choose and flexibly use a range of strategies when working with fractions and decimals, you must read this book!
*Grace Kelemanik*

As a high school mathematics teacher, I listened year after year to students who said they lost their passion for mathematics right around the time they began to learn fractions. Thankfully, Figuring Out Fluency—Multiplication and Division With Fractions and Decimals is a book designed to make fractions more accessible and understood by all students. The book is a must-read for mathematics educators. This book clearly defines fluency and also shares action steps and strategies teachers can employ to help students develop a deeper understanding of, and fluency with, fractions and decimals.
*Mona Toncheff*

This book is such an eye-opener for providing interventions and strategies for students and supporting teachers that I coach. Fluency isn’t about timed tests or ‘drill and kill’ but providing students with rich discourse, games, tasks, routines, and more. I’m so excited to delve into this much-needed resource more.
*Chapel Hill-Carrboro City Schools*

Figuring Out Fluency—Multiplication and Division With Fractions and Decimals is an essential resource for math educators who teach fraction and decimal operations. This companion book connects the strategies introduced in the anchor book to multiplying and dividing with decimals and fractions. The explicit strategy instruction provided in the book allows access for ALL students in a practical, hands-on approach. This is a go-to for all math educators, coaches, specialists, and interventionists!
*Jefferson County Public Schools, Louisville, KY*

A needed addition to mathematics education! This book establishes a broader definition of fluency and emphasizes the importance of helping students develop and use relationships and strategies to solve problems. Bay-Williams, SanGiovanni, Martinie, and Suh outline which major relationships and strategies students need to develop stronger mathematical reasoning!
*Texas State University*

Figuring Out Fluency: Multiplication and Division With Fractions and Decimals is the resource that the educational world has been wishing and waiting for as it works to tackle mathematical concepts that traditionally leave students confused and teachers frustrated. This carefully crafted guide will inspire and support educators in their journey to integrate quality and rigorous fluency practice. It provides a plethora of practical, well-designed activities and games rooted in research that will actively engage students in rich discussion, critical thinking, and the strengthening of their conceptual understanding needed to select appropriate strategies to multiply and divide fractions and decimals accurately and efficiently. As an instructional leader, I view this text as the catalyst for refocusing the goals of math instruction so both teachers and students can confidently engage in practices that build mathematical proficiency.
*Emporia Public Schools*

Figuring Out Fluency—Multiplication and Division With Fractions and Decimals is a must-have for any classroom teacher, mathematics supervisor, or anyone that wants to think about advancing their students’ fluency with fractions and decimals. The ideas in this book are supported through the key ideas of figuring out fluency and the detailed ways of its strategy model of looking at fractions and decimals. The numerous resources that are highlighted in this book support anyone from a new teacher all the way to a 25-year veteran. The ease of use is what will help anyone improve their practice.
*Spencer Jamieson*