Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, Grades 3–5, Second Edition


AAP Pre K–12 Learning 2016 Revere Awards Winner

The focus of Beyond Pizzas & Pies, Second Edition, is on foundational understandings. The authors help teachers and students understand fractions as numbers, including the use of equivalency and thinking about benchmark numbers, so that when students start to compute with fractions (see the companion volume, Beyond Invert & Multiply), they have a solid foundation. You’ll find:

Classroom Scenarios that address common challenges students (and teachers!) encounter as they acquire an understanding of fractions;

What’s the Math? sections intended to clarify the mathematics;

What’s the Research? insights that show why “that’s the way we’ve always done things” might not be the most successful approach;

Classroom Activities with friendly, step-by-step instructions and video clips demonstrating how to teach the concepts;

Reproducibles that are also available in a downloadable, printable format;

Study Questions at the end of each chapter that encourage readers to set concrete goals for implementing what they’ve read; and

Connections to the Common Core for those states implementing the Common Core State Standards for Mathematics.

 (The resource features 30 video clips filmed in actual classrooms. Clips range from 1 minute to 6 minutes in length with a total viewing time of approximately 70 minutes.)

Discussion questions for viewing each video clip

icon pdf How Beyond Pizzas & Pies and Beyond Invert & Multiply work together

Julie McNamara and Meghan M. Shaughnessy
Foreword by Francis (Skip) Fennell
192 Pages

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Author Bio

Julie McNamara is an Assistant Professor of Mathematics Education at California State University, East Bay in Hayward, California. She has also served as Mathematics Specialist with TeachingWorks at the University of Michigan. Julie spent two years supporting elementary and middle school teachers as a fulltime designer and provider of mathematics professional development for Math Solutions, and continues to consult for Math Solutions part-time. She has also taught mathematics methods in the elementary credential programs at the University of California, Berkeley and at Saint Mary’s College in Moraga, California. She is a former classroom teacher in the San Francisco Bay Area. Her experience in the classroom led her to pursue graduate studies in the Development in Mathematics and Science program at the University of California, Berkeley, and to earn her master’s degree and Ph.D. in mathematics education. Her research focuses on the teaching and learning of mathematics concepts that are foundational but considered "hard to teach and hard to learn."

Julie is co-author of Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, 2010, as well as Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fractions Sense, Second Edition, 2015. In addition, Julie has written a follow up fraction book, Beyond Invert & Multiply: Making Sense of Fraction Computation, Grades 3-6, 2015, all published by Math Solutions.

Meghan M. Shaughnessy is a postdoctoral research fellow at the School of Education at the University of Michigan. Her research focuses on the teaching and learning of elementary mathematics. She designs and studies innovative professional development materials for practicing teachers and teaches mathematics methods courses for preservice elementary teachers. Meghan received a Ph.D. in mathematics education from the University of California, Berkeley.

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