Teaching Arithmetic: Lessons for Introducing Fractions, Grades 4–5


Through hands-on investigations, students learn to name fractional parts of wholes and sets; use standard notation to represent fractional parts; understand equivalence; compare, order, and combine fractions; and make reasonable estimates when solving problems involving fractions.

The Marilyn Burns Fraction Kit, Grades 4–6 is recommended to help implement the lessons in this book.

This book is part of the Teaching Arithmetic, Complete Series.

Marilyn Burns
192 Pages

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Review by Scott Bartley, mathematics abstractor. “Lessons for Introducing Fractions, Grades 4–5” in ENC Focus: A Magazine for Classroom Innovators, 9 (4), 68. Reprinted with permission from Scott Bartley and ENC Focus, © 2002.

This teacher resource, part of the Teaching Arithmetic series, contains lesson plans and vignettes designed to help teachers of grades 4 and 5 help their students obtain a basic understanding of fractions. The Teaching Arithmetic series is designed to teach elementary students mathematical concepts by helping them think critically and apply their understanding of mathematics to solve real-world problems.

Each lesson plan in this book contains a vignette of actual classroom presentation of the lesson and a discussion of the children’s reaction. Besides a description of the lesson activities, the chapters contain information on assessment, teaching styles, and important concepts.

The book relates fractions to parts of a whole and to parts of a group, and reminds students not to forget the whole or group of which the fraction is a part. Students are asked to write about fractions, have organized discussions with a neighbor, and involve their parents. Assessment places equal value on correct answers and the students’ explanation of their reasoning. Included are blackline masters of class worksheets and common questions that teachers might have about a lesson with responses.

In an introductory lesson, fraction kits are made by the students and are used in activities that provide a concrete example of how fractions relate to each other. Students are given five strips of colored paper; they cut four strips into a different number of equal pieces (two, four, eight or sixteen). One strip is left uncut, and students cover this strip with the different fraction pieces to show how two halves make a whole, or three fourths and two eighths make a whole, and so on.

Review by David Chia, Assistant Principal at Weller Road Elementary School in Silver Spring, Maryland. From the February/March 2002 issue of Intersection. Reprinted with permission from Intersection, © 2003, by ExxonMobil Corporation.

If I’m at work for nine hours today and I spend one-third of half of my workday co-teaching with a new teacher, how many minutes did I spend with her? It’s questions like this that sometimes cause students (and teachers) to scream, “I hate fractions!” For students, fractions can be a tough concept and fraction applications are not always easily mastered. For teachers, teaching fractions can be a challenge and sometimes a frustration. In this book, author Marilyn Burns notes “learning about fractions in the upper elementary grades is hard. Really hard. Fractions are hard not only for children to learn but for teachers to teach.” With this in mind, the author sets out on a reflective journey as she teaches fractions to fourth- and fifth-grade students.

There are fifteen lessons organized into individual chapters beginning with introducing fractions, developing a fraction kit, and exploring fractions with various manipulatives. In the middle chapters, lesson topics focus on using one-half (1/2) as a benchmark fraction, comparing fractions, and finding fractional parts. The final chapters conclude with comparing and combining fractions. Each chapter and its lesson is organized with an overview, a materials list, suggested timeline for lessons, teaching directions, teaching notes, a vignette of the lesson with reflective thinking, sample student work, extensions, assessments, and questions and discussions which address issues that other teachers have asked. Several assessments and numerous blackline masters are included along with an index.

While the author recommends beginning with the introductory lessons and then chunking the remaining lessons throughout the course of a year, I don't believe that is always necessary. Each chapter is so well outlined that depending on the outcomes and indicators you are teaching, you could find and use the chapter and its lesson for the area of  “greatest need.” The “greatest need” could be your students’ struggle in attaining a concept or your need as a teacher to expertly deliver a lesson. The most intriguing parts of each chapter are the shared vignette and the question and discussion pages. I find each vignette interesting because it shares a situation I can relate to as a math teacher or it broadens my perspective of how other students learn and how other teachers teach. Additionally, the question and discussion pages allow me to review issues and concerns that other teachers might have when teaching a similar lesson. The quality in reflective thinking about how students learn is certainly one of the highlights of the book.

If you are an upper elementary teacher who would like to broaden your thinking and expertise in teaching fractions, this book will be an added resource to you. If you are a new teacher wondering about how students really learn fractions or asking yourself how you can begin to help your students learn fractions, this is an excellent resource that will guide you in introducing fractions to upper elementary students.

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These lessons provide all students the foundation they need to experience success with fractions.

More or Less Than One-Half
by Marilyn Burns

Nicholas’s Game
by Marilyn Burns

When Is a Fraction Worth One-Half?
by Marilyn Burns

Exploring Halves
by Maryann Wickett

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