About the Book
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 Whole Numbers. 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 multi-digit whole numbers, including worked examples, routines, games, and centers
• Find activities for assessing all components of multiplication and division fluency 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.
Table of Contents:
PART 1: FIGURING OUT FLUENCY: KEY IDEAS
PART 2: STRATEGY MODULES
Module 1 Break Apart to Multiply Strategy
Module 2 Halve and Double Strategy
Module 3 Compensation Strategy
Module 4 Partial Products Strategy
Module 5 Think Multiplication Strategy
Module 6 Partial Quotients Strategy
Module 7 Standard Algorithms for Multiplication and Division
PART 3: PUTTING IT ALL TOGETHER: DEVELOPING FLUENCY
APPENDIX: TABLES OF ACTIVITIES
REFERENCES
About the Author :
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.
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). Rosalba Serrano is an elementary mathematics consultant in New York and is the founder of Zenned Math, where she provides online professional development and coaching for elementary mathematics teachers. Rosalba has used her experience as a classroom teacher and mathematics coach to support teachers in deepening their understanding of mathematics and their use of effective teaching practices.
A frequent speaker at both regional and national conferences, Rosalba is also active in mathematics organizations such as the National Council of Teachers of Mathematics, where she contributes to multiple committees. She has also worked as a professional development facilitator for various mathematics organizations and consults as a math editor for a number of publishing companies.
Review :
"This text provides a clear definition of what fluency really is and provides strategies to deepen students’ number sense and make them fluent mathematicians."
"I wish I’d had this book when I was in the classroom 10 years ago. The authors clearly lay out a pathway to procedural fluency, including intentional activities to understand and practice specific strategies, while also advocating for space for students to make decisions and feel empowered as mathematical thinkers and doers."
"This book is a must-read for teachers wanting to learn more about focused math fluency instruction. The steps are clear and easy to follow. You will have all the steps to help your students become fluent math thinkers."
"Are you ready to help your students connect their Number Talks and number routines to the real world? Figuring Out Fluency will give you the routines, games, protocols, and resources you need to help your students build their fluency in number sense (considering reasonableness, strategy selection, flexibility, and more). Our students deserve the opportunity to build a positive and confident mathematics identity. We can help support them to build this identity by providing them with access to a variety of strategies and the confidence to know when to use them."
"Figuring Out Fluency goes beyond other resources currently on the market. It not only provides a robust collection of strategies and routines for developing fluency but also pays critical attention to the ways teachers can empower each and every student as a mathematical thinker who can make strategic decisions about their computation approaches. If you are looking for instruction and assessment approaches for fluency that move beyond getting the right answer, this is the resource for you."
"As principal of a Title I school and former mathematics specialist, I appreciate this resource for what it is; a true teacher’s companion! The authors provide explicit strategy instruction in whole number multiplication and division to foster flexibility, efficiency, and true fluency in ALL students."
"This is the book classroom teachers have been waiting for! It provides extensive support as students gain confidence with multiplying and dividing whole numbers, and it does so with a deep esteem for educators and learners. The authors, highly respected in the field of mathematics education, provide careful explanations of effective strategies that will help students build their number sense and their computational fluency. There are routines for supporting instruction in the classroom, games and centers for practicing the strategies, and prompts to encourage sense making and extend learning. Kudos to all three authors for writing such an important, no-nonsense book. I cannot wait to share it with my colleagues!"
"For years research has indicated that fluency is much more than speed, yet timed assessments and traditional instruction persist for teachers without a clear vision or tools to change their practices. This series provides teachers with the explicit examples, resources, and activities needed to bring that research to life for their students and will quickly become a well-worn guidebook for every fluency-focused classroom. This is the toolkit teachers have been yearning for in their journey toward fluency with their students."
"Fluency isn’t a dry landscape of disconnected facts—it is a rich soil for developing and connecting diverse perspectives and ideas. This book series equips you with a deep understanding of fluency and a variety of activities to engage students in co-constructing ideas about multiplication and division that will last a lifetime."
"This is the book we (educators) have been waiting for! Figuring Out Fluency – Multiplication and Division With Whole Numbers provides classroom teachers, special ed teachers, and instructional coaches with the support they need to develop true fluency for every child. This book is packed with great activities; quality practice that is not a worksheet; examples, routines, games, and centers; and a companion website with resources ready to use! Any question you may have— about how and when to teach a specific strategy, how to engage your students in meaningful practice, or assessing your students’ fluency—will be answered in this book! Any educator that is serious about understanding how basic fact strategies grow into general reasoning strategies and how to advance their students’ fluency will want this book! True fluency is a way of thinking, rather than a way of doing!"
"Figuring Out Fluency – Multiplication and Division With Whole Numbers is a must-have for all educators who teach multi-digit multiplication and division. With a focus on equity embedded throughout, this practical, ready-to-use resource provides everything needed to teach students to become strategic thinkers while giving all children access to reasoning."
"This book—indeed this series—is a must-read for elementary and middle level teachers, coaches, and administrators. Within this resource you will find a synthesis of important research organized to help readers develop a clear and common understanding of fluency paired with a large collection of teaching activities that provide concrete ways to support students’ fluency development. Figuring Out Fluency provides a much-needed roadmap for teachers looking to increase computational proficiency with multiplication and division."
"The authors John J. SanGiovanni, Jennifer M. Bay-Williams, and Rosalba Serrano shine a bright light on how math fluency is the equity issue in mathematics education. How refreshing to have a book that equips math educators with the research and strategies to make a difference for all students! Let’s implement these strategy modules in this book and help kids figure out fluency once and for all!"
"In Figuring Out Fluency – Multiplication and Division With Whole Numbers, John J. SanGiovanni, Jennifer M. Bay-Williams, and Rosalba Serrano have provided readers with a thorough education that guides them through the entire fluency journey. Grounded in research and packed with illustrative examples, this book is a must-have that delivers practical strategies, tools, resources, and recommendations that will immediately enhance your practice. In a sea of books on fluency, this one stands out. In a word . . . wow!"
"John J. SanGiovanni, Jennifer M. Bay-Williams, and Rosalba Serrano hit the mark with Figuring Out Fluency – Multiplication and Division With Whole
Numbers. The activities are fun and engaging and encourage students to think more flexibly and fluently as they work with multiplication and division strategies. Bravo!"
"The number one topic teachers grapple with every year is fluency. This companion book is an all-encompassing resource that takes the guess work out of multiplication and division fluency instruction and practice! With a focus on reasoning, understanding, and reasonableness, this is a practical, easy-to-follow guide for teachers. The strategy modules contain teaching prompts, routines, games, center activities, and a very critical component missing in most resources—strategy briefs for families."
