Teaching Arithmetic: Lessons for Extending Fractions, Grade 5
While the book builds on Teaching Arithmetic: Lessons for Introducing Fractions, Grades 4–5, it remains accessible and appropriate for all students who have had beginning experiences naming, comparing, and ordering fractions.
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 (NCTM). All rights reserved.
This book expands the topics of comparing fractions in which denominators are not multiples of one another, combining fractions, using fractions in new situations, and strategies for addition and subtraction of fractions. The book also discusses the ways in which children think about fractions and gives student samples of exemplary and fragile understandings.
This text is especially useful for teachers because it fully models the lessons and fully presents levels of student understanding. It is also useful for staff training and in-service courses.
The book explains how to deal with many fraction concepts and explores the thinking of students in a comprehensive way. Some curriculum mandates may limit the amount of time that teachers can spend on these topics, but teachers can select chapters or games for use that most closely fit a student’s needs.
Teachers who pursue this book will find many wonderful ideas and lessons that they can use to teach fraction concepts.
Review by Angiline Powell, an Assistant Professor of Mathematics Education at the University of Memphis, Memphis, Tennessee. Reproduced with permission from Intersection, © Spring 2005, by ExxonMobil Corporation.
Lessons for Extending Fractions by Marilyn Burns is a resource book to extend upper elementary students’ understanding of comparing, ordering, adding and subtracting fractions. As with most of the books in this series, this one also includes explicit teacher directions for introducing the lessons as well as practical classroom assessments. The primary strength of Lessons for Extending Fractions is its detailed and thorough investigation into students' thinking and processing of fractions.
The explicit teacher directions include the following: how to introduce the lesson; what questions to ask (“How might you divide each of these brownies in half?”); suggestions to extend student thinking (“Think of ways that don't use one straight cut . . .”); directions to differentiate instruction; as well as what to do the next day. The book includes process standards for learning mathematics-problem solving, reasoning and proof, communication, connections and representations and professional standards for teaching mathematics (NCTM 2002). These professional standards include building on previous knowledge; having a warm, nurturing classroom environment; encouraging discourse between the teacher and students and among students. The book even suggests when it is appropriate to interrupt student discourse to facilitate learning.
Another strength is the book’s conversations that provide remarkable insights into students’ thinking and levels of understanding fractional numbers. The author proposed this question to a fifth grade class, “Is 101/201 = 11/21?” Burns relates that students’ methods for figuring out the answer were as diverse as the students. One student stated that she thought the fractions were both the same, “just cross out the zeroes.” Another more advanced student thought this was not right. "You just can't do that . . . make tens out of hundreds.” A gifted mathematics student said, “They can’t be the same, because you can’t divide the numerator and the denominator by the same number. I know . . . one hundred one is prime.”
This detailed discourse and the explicit directions are attractive features of this book. These features might serve two different audiences-mathematics specialists and novice teachers. I cannot recommend this book for novice teachers or self-contained classroom teachers. Successful use of this book would require significant amounts of time. New teachers and/or self-contained teachers with five to six daily preparations in different subjects would probably not have time to master the many ideas without extended study. Therefore, I recommend Lessons for Extending Fractions only for experienced mathematics specialists or teachers with time to really develop an understanding of the book.
Table of Contents
Lessons in this book help students strengthen their foundation of fraction knowledge and focus on adding and subtracting fractions.