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Figuring Out Fluency – Operations With Rational Numbers and Algebraic Equations
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Figuring Out Fluency – Operations With Rational Numbers and Algebraic Equations
A Classroom Companion



August 2022 | 232 pages | Corwin

“This book is awesome! What stood out to me was the deep understanding I was able to have about what fluency actually means. Too often the message has been 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
Secondary Mathematics Specialist, Utah State Board of Education 
Salt Lake City, UT

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—Operations With Rational Numbers and Algebraic Equations. With this book, teachers can

  • Dive deeper into the Significant Strategies for fluency explained in the anchor book as they apply to rational number operations
  • Explore how these strategies can be applied for proportional reasoning, solving equations for unknowns, and solving systems of linear equations
  • Access over 100 classroom-ready activities, including worked examples, routines, and games.
  • Find activities to explicitly teach students how to use and choose strategies to operate on rational numbers and solve algebraic equations
  • 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.


 
Part 1: Figuring Out Fluency: Key Ideas
 
Part 2: Strategy Modules
 
Module 1: reasoning Strategies for Addition
 
Module 2: Reasoning Strategies for Subtraction
 
Module 3: Reasoning Strategies for Multiplication
 
Module 4: Reasoning Strategies for Division
 
Module 5: Reasoning Strategies for Ratios and Proportions
 
Module 6: Strategies for Solving Equations for an Unknown
 
Module 7: Strategies for Solving Systems of Linear Equations
 
Part 3: Putting it All Together: Developing Fluency

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
Salt Lake City, UT

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
Sanford, FL

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
Palm Coast, FL

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
San Marcos, TX

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
Ulysses, PA

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
Louisville, KY

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
Baton Rouge, LA

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
Tucson, AZ
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ISBN: 9781071825181
$29.95

For large school/district orders, volume discounts, availability and shipping times contact customer service at 800-233-9936
or order@corwin.com.

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