Learning to Think Mathematically About Multiplication

Learning to Think Mathematically About Multiplication

A Resource for Teachers, A Tool for Young Children

Jeffrey Frykholm, Ph.D.

Learning to Think Mathematically About Multiplication A Resource for Teachers, A Tool for Young Children by Jeffrey Frykholm, Ph.D.

Published by The Math Learning Center ? 2018 The Math Learning Center. All rights reserved. The Math Learning Center, PO Box 12929, Salem, Oregon 97309. Tel 1 (800) 575-8130

Originally published in 2013 by Cloudbreak Publishing, Inc., Boulder, Colorado (ISBN 978-0-692-27478-1) Revised 2018 by The Math Learning Center.

The Math Learning Center grants permission to reproduce and share print copies or electronic copies of the materials in this publication for educational purposes. For usage questions, please contact The Math Learning Center.

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The Math Learning Center is a nonprofit organization serving the education community. Our mission is to inspire and enable individuals to discover and develop their mathematical confidence and ability. We offer innovative and standards-based professional development, curriculum, materials, and resources to support learning and teaching.

ISBN: 978-1-60262-564-8

Learning to Think Mathematically About Multiplication

A Resource for Teachers, A Tool for Young Children

Authored by Jeffrey Frykholm, Ph.D.

This book is designed to help students develop a rich understanding of multiplication and division through a variety of problem contexts, models, and methods that elicit multiplicative thinking. Elementary level math textbooks have historically presented only one construct for multiplication: repeated addition. In truth, daily life presents us with various contexts that are multiplicative in nature that do not present themselves as repeated addition. This book engages those different contexts and suggests appropriate strategies and models, such as the area model and the ratio table, that resonate with children's intuitions as they engage multiplication concepts. These models are offered as alternative strategies to the traditional multi-digit multiplication algorithm. While it is efficient, is not inherently intuitive to young learners. Students equipped with a wealth of multiplication and division strategies can call up those that best suit the problem contexts they may be facing. The book also explores the times table, useful both for strengthening students' recall of important mathematical facts and helping them see the number patterns that become helpful in solving more complex problems. Emphasis is not on memorizing procedures inherent in various computational algorithms but on developing students' understanding about mathematical models and recognizing when they fit the problem at hand.

About the Author

Learning to Think Mathematically about Multiplication

Dr. Jeffrey Frykholm has had a long career in mathematics education as a teacher in the public

school context, as well as a professor of mathematics education at three universities across the

United States. Dr. Frykholm has spent

of his career teaching young children,

working with beginning teachers in preservice teacher preparation courses, providing

professional development support for practicing teachers, and working to improve mathematics

education policy and practices across the globe (in the U.S., Africa, South America, Central

America, and the Caribbean).

Dr. Frykholm has authored over 30 articles in various math and science education journals for

both practicing teachers, and educational researchers. He has been a part of research teams that

have won in excess of six million dollars in grant funding to support research in mathematics

education. He also has extensive experience in curriculum development, serving on the NCTM

Navigations series writing team, and having authored two highly regarded curriculum programs:

An integrated math and science, K-4 program entitled Earth Systems Connections (funded by

NASA in 2005), and an innovative middle grades program entitled, Inside Math (Cambium

Learning, 2009). This book,

is part of his

series of textbooks for teachers. Other books in this series

include:

Dr. Frykholm was a recipient of the highly prestigious National Academy of Education Spencer Foundation Fellowship, as well as a Fulbright Fellowship in Santiago, Chile to teach and research in mathematics education.

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Learning to Think Mathematically about Multiplication

Table of Contents

LEARNING TO THINK MATHEMATICALLY: AN INTRODUCTION

4

The Learning to Think Mathematically Series

4

How to Use this Book

4

Book Chapters and Content

5

CHAPTER 1: THE NATURE OF MULTIPICATION AND DIVISION

7

Activity Sheet 1

10

Activity Sheet 2

12

CHAPTER 2: THE TIMES TABLE AND BASIC FACTS

13

Activity Sheet 3

15

Activity Sheet 4

18

Activity Sheet 5

19

Table for Activity Sheet 5

20

CHAPTER 3: THE AREA MODEL OF MULTIPLICATION

26

Activity Sheet 6

30

Activity Sheet 7

33

CHAPTER 4: THE RATIO TABLE AS A MODEL FOR MULTIPLICATION 38

Activity Sheet 8

44

Activity Sheet 9

45

CHAPTER : THE TRADITIONAL MULTIPLICATION METHOD

0

Activity Sheet 1

3

APPENDIX A: THE TIMES TABLE

5

3

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