Teaching Arithmetic: Lessons for Multiplying and Dividing Fractions, Grades 5–6
Through the lessons in this book, students build conceptual understanding of multiplying and dividing fractions as they develop proficiency. And teachers report that—for the first time—students really understand the underlying rationale for how we multiply and divide fractions and mixed numbers.
This book is part of the Teaching Arithmetic, Complete Series.
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Introducing Multiplication of Fractions
Review by Brian Swan, a fifth-grade teacher at Beach Elementary School in Portland, Oregon. From the Summer 2004 issue of Intersection, a newsletter of the ExxonMobil Corporation and the National Council of Teachers of Mathematics (NCTM). Reprinted with permission from Intersection, © 2004, by ExxonMobil Corporation.
I generally consider myself a fairly competent math teacher, but teaching the multiplication and division of fractions has always been a bit frustrating to me. In school, I learned the algorithm of multiplying across numerators and denominators for multiplication and cross-multiplying for division. I knew how that worked, but the why has always been a little more difficult to explain.
Thankfully, Marilyn Burns has come to the rescue of math teachers who may be uncomfortable teaching the old algorithms and leaving it at that. Her new book, Lessons for Multiplying and Dividing Fractions, Grades 5–6 , part of the Teaching Arithmetic series published by Math Solutions Publications, is a step-by-step guide for teaching real understanding in multiplying and dividing fractions.
The book has twelve lessons, six each for multiplication and division. For those who feel a bit daunted by the teaching of fractions, the lessons in Multiplying and Dividing Fractions are completely scripted. Lessons not only contain directions for the teacher, but also possible student responses. Each lesson builds on the previous lessons.
What I especially like about this book is that rather than having teachers be the sole source of learning, Burns builds on concepts the students already know about multiplication and addition. I teach a fifth grade class and use Investigations in Number, Data, and Space for math. Burns’ book is an excellent fit. Both the multiplication and division sections start with a lesson utilizing basic statements about each. I was also pleased to see the array model used to show the multiplication of fractions; I had never really considered it as a viable method, and since my students were well acquainted with arrays, it made complete sense to them. By the time we got to the fourth multiplication lesson, my students were saying things like, “We already know how to do this,” and “This is easy.” Even more amazing was that by the end of the second division lesson, every student in my class was able to comfortably solve division problems involving fractions.
Multiplying and Dividing Fractions also contains assessment tasks and blackline masters. There are nine assessments, and while each is valuable, you may not need to use all nine. Very little is needed in the way of manipulatives, though in Lesson 11, Burns suggests using the fraction kit pieces in the accompanying Fraction Kit Guide. Each lesson takes 45 minutes to an hour. With twelve lessons and a few assessments, you could easily fit these activities into whatever program you are using.
My students came away with an excellent understanding of how to multiply and divide fractions, and it made sense to them. They now have a firmer grip on what fractions represent and how they relate to each other and other numbers. Marilyn Burns has again published an effective book for math teachers. I highly recommend it to anyone teaching math in fifth or sixth grade.
Review by Susan Eith, from Glen Landing Middle School in Blackwood, New Jersey. From the February 2005 issue of Mathematics Teaching in Middle School, a publication of the National Council of Teachers of Mathematics (NCTM). Reprinted with permission from NCTM, © 2005.
Intended for teachers of grades 5–6, this book contains six chapters of exercises and lessons devoted to multiplication and division of fractions. Assessment activities and blackline masters are also included. Marilyn Burns presents carefully planned lessons that allow students to develop understanding and to further their reasoning of fraction concepts instead of relying on a rote execution of algorithms. Many of the lessons can be used with junior high school students if a solid foundation has not already been established for these concepts.
Each chapter is structured like a conversation with the author, giving explanations and background to aid the teacher in a successful lesson. Visuals and examples of student work are included. The lessons are well designed. In addition, the materials, objectives, teacher directions, teaching notes, specific discussion questions and sample responses, and a transcript of an actual lesson are clearly identified. Although the book contains quality material, it is not a “grab and go” type of lesson. Teachers should be prepared to read the entire chapter and thoroughly prepare to achieve maximum effectiveness when implementing the lesson in the classroom.
For those teachers interested in developing a solid foundation and understanding of concepts for their students, this book is a good choice. Since it is also one in a series by Marilyn Burns, teachers and students can become familiar with the style she uses and branch into other topics.
Review by Margaret A. Godfrey, a K–12 supervisor at Hunter College in New York, New York. From Teaching Children Mathematics (April 2005), page 447. Reproduced with permission from Mathematics Teaching in the Middle School, © 2005 by the National Council of Teachers of Mathematics. All rights reserved.
Offering many specific lessons and techniques for teaching division, the author of this book uses her extensive experience in working with children to select specific lessons and dialogue when presenting concepts and practical problems.
The volume sets forth a structure to help teachers plan and teach lessons in division. This is accomplished through step-by-step directions, specification of material, teaching notes, and extended lesson dialogue, followed by questions and thoughtful answers from the author.
This book is valuable to fourth- and fifth-grade teachers because division is a continuing source of difficulty for students. It presents ideas that can strengthen any elementary or middle school teacher’s repertoire of techniques for teaching division.
Table of Contents
In this book, Marilyn Burns tackles the topic of how to teach students to multiply and divide fractions—and understand what they are doing.