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Figuring Out Fluency - Multiplication and Division With Fractions and Decimals

Figuring Out Fluency - Multiplication and Division With Fractions and Decimals
A Classroom Companion

March 2022 | 224 pages | Corwin

Because fluency practice is not a worksheet.

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also 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, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. Now, teachers have the chance to apply that inspiration through explicit instruction and practice every day with the classroom companion Figuring Out Fluency: Multiplication and Division with Fractions and Decimals. With this book, teachers can:

  • Dive deeper into the Significant Strategies for fluency explained in the anchor book
  • Learn how these strategies grow from and relate to the basic fact strategies children learn 
  • Access over 100 strategy-aligned and classroom-ready activities for fluency instruction and practice in multiplying and dividing fractions and decimals, including worked examples, routines, games, and centers
  • Find activities for assessing all components of multiplication and division fluency for fractions and decimals, plus support for engaging families 
  • Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation.

Give each and every student the knowledge and power to become skilled and confident mathematical thinkers and doers.

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

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
Co-Founder, Fostering Math Practices

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
President, National Council of Supervisors of Mathematics (2019–2021), Preservice Teacher Supervisor, University of Arizona, Author and Educational Consultant, Former District Mathematics Content Specialist and High School, Mathematics Teacher

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.

Tomika R. Altman
Math/Science Specialist, Seawell Elementary School
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!

Nichole DeMotte
K–5 Mathematics Coach, Atkinson Academy
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!

Pam Harris
Owner of Math is Figureoutable
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.

Allyson Lyman
Elementary Principal
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
Past President, Virginia Council of Mathematics Supervision, Mathematics Specialist, Virginia Council of Teachers of Mathematics, Mathematics Educational Specialist, Fairfax County Public Schools

Jennifer M. Bay-Williams

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

Sherri L. Martinie

Jennifer Suh

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ISBN: 9781071825921