Math Matters: Understanding the Math You Teach Grades K-8, 2nd Edition PDF
Preview Math Matters: Understanding the Math You Teach Grades K-8, 2nd Edition
UNDERSTANDING T H EM A T H Y(U) TEAHC SUZANNHE.C HAPIN ARTJ ()HNS(|N chapin130008_fm.qxd 2/8/06 1:48 PM Page i Math Matters Understanding the Math You Teach Grades K–8 Second Edition chapin130008_fm.qxd 2/8/06 1:48 PM Page ii chapin130008_fm.qxd 2/8/06 1:48 PM Page iii Math Matters Understanding the Math You Teach Grades K–8 Second Edition SUZANNE H. CHAPIN ART JOHNSON MATH SOLUTIONS PUBLICATIONS Sausalito, CA Math Solutions Publications A division of Marilyn Burns Education Associates 150 Gate 5 Road, Suite 101 Sausalito, CA 94965 www.mathsolutions.com Copyright © 2006 by Math Solutions Publications All rights reserved. No part of this book may be reproduced in any form or by any means, without written permission from the publisher, except for the inclusion of brief quotations in a review. Library of Congress Cataloging-in-Publication Data Chapin, Suzanne H. Math matters : understanding the math you teach, grades K–8 / Suzanne H. Chapin, Art Johnson.—2nd ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-941355-71-1 (alk. paper) ISBN-10: 0-941355-71-3 (alk. paper) 1. Mathematics—Study and teaching (Elementary) I. Johnson, Art. II. Title. QA135.6.C473 2006 372.7—dc22 2006001876 Editor: Toby Gordon Production: Melissa L. Inglis Cover design: Isaac Tobin Interior design: Angela Foote Book Design Composition: Interactive Composition Corporation Printed in the United States of America on acid-free paper 10 09 08 07 ML 2 3 4 5 chapin130008_fm.qxd 2/8/06 1:48 PM Page v To our daughters Catherine Ann Chapin Elizabeth Jane Chapin Candace Raven Johnson Alexa Brit Johnson who with smiles on their faces shared their understanding of mathematics with us. Thank you. We learned so very much! For my uncle Nicholas Sideris. His integrity and enthusiasm for life have always inspired me. —AJ chapin130008_fm.qxd 2/8/06 1:48 PM Page vi A Message from Marilyn Burns We at Math Solutions Professional Development believe that teaching math well calls for increasing our understanding of the math we teach, seeking deeper insights into how children learn mathematics, and refining our lessons to best promote students’ learning. Math Solutions Publications shares classroom-tested lessons and teaching expertise from our faculty of Math Solutions Inservice instructors as well as from other respected math educators. Our publications are part of the nationwide effort we’ve made since 1984 that now includes • more than five hundred face-to-face inservice programs each year for teachers and administrators in districts across the country; • annually publishing professional development books, now totaling more than fifty titles and spanning the teaching of all math topics in kindergarten through grade 8; • four series of videotapes for teachers, plus a videotape for parents, that show math lessons taught in actual classrooms; • on-site visits to schools to help refine teaching strategies and assess student learning; and • free online support, including grade-level lessons, book reviews, inservice information, and district feedback, all in our quarterly Math Solutions Online Newsletter. For information about all of the products and services we have available, please visit our website at www.mathsolutions.com. You can also contact us to discuss math professional development needs by calling (800) 868-9092 or by sending an email to [email protected]. We’re always eager for your feedback and interested in learning aboutyourparticularneeds.Welookforwardtohearingfromyou. Math Solutions ® PUBLICATIONS chapin130008_fm.qxd 2/8/06 1:48 PM Page viii chapin130008_fm.qxd 2/8/06 1:48 PM Page ix Contents Preface to the Second Edition xv Chapter One: Number Sense 1 1. Classifying Numbers 1 Exploring Irrational Numbers 6 Even and Odd Numbers, Part 1 10 Even and Odd Numbers, Part 2 11 Rectangular Dimensions and Factors 12 Perfect Numbers 14 2. Understanding Numbers 15 Exploring Part-Whole Relationships 18 Exploring Combinations 18 Prime Factors 21 The Number Line 24 3. Our Place Value Numeration System 25 Analyzing a Different Numeration System 26 Place Values Less Than One 29 Teaching Number Sense 29 Questions for Discussion 30 Chapter Two: Computation 31 1. Mathematical Properties 31 How Does Order Affect Differences? 33 How Does Order Affect Quotients? 35 How Do Grouping and Order Affect Answers? 39 2. Basic Facts 42 3. Algorithms 43 Analyzing Students’ Thinking, Addition 45 Analyzing Students’ Thinking, Subtraction 46 Analyzing Students’ Thinking, Multiplication 49 Analyzing Students’ Thinking, Division 51 Teaching Computation 53 Questions for Discussion 54 ix
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