DOCUMENT RESUME ED 221 338 SE 035 008, AUTHOR ,LeBlanc, John F.; And Others TITLE Multiplication and Division. Mathematics-Methods 12rogram Unipt. INSTITUTION Indiana ,Univ., Bloomington. Mathematics Education !Development Center. , SPONS AGENCY ,National Science Foundation, Washington, D.C. REPORT NO :ISBN-0-201-14610-x PUB DATE 76 . GRANT. NSF-GY-9293 i 153p.; For related documents, see SE 035 006-018. NOTE . ,. EDRS PRICE 'MF01 Plus Postage. PC Not Available from EDRS. DESCRIPTORS iAlgorithms; College Mathematics; *Division; Elementary Education; *Elementary School Mathematics; 'Elementary School Teachers; Higher Education; 'Instructional1 Materials; Learning Activities; :*Mathematics Instruction; *Multiplication; *Preservice Teacher Education; Problem Solving; :Supplementary Reading Materials; Textbooks; ;Undergraduate Study; Workbooks IDENTIFIERS i*Mathematics Methods Program ABSTRACT This unit is 1 of 12 developed for the university classroom portign_of the Mathematics-Methods Program(MMP), created by the Indiana pniversity Mathematics EducationDevelopment Center (MEDC) as an innovative program for the mathematics training of prospective elenientary school teachers (PSTs). Each unit iswritten in an activity format that involves the PST in doing mathematicswith an eye towardaiplication of that mathematics in the elementary school. This do ument is one of four units that are devoted tothe basic number wo k in the elementary school. In addition to an introduction to the unit, the text has sections on the conceptual development of nultiplication and division, developing thebasic niultiplication and division facts, and computational algorithms for my.tiplication and division. (MP) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** MATHEMATICS EDUCATION DEVELOPMENT CENTER INDIANA UNIVERSITY John F. LeBlanc, Director Donald R. Kerr, Jr., Assistant Director The following is a list of faculty and project associates who have contributed to thedevelopment of the Mathematics-Methods Program. Mathematics Education Mathematics Faculty Faculty George Springer, Frank K. Lester, Jr. Co-principal Investigator Sally H. Thomas Billy E. Rhoades . Paul R. Trafton Maynaml Thompson Ronald C. Welch Project Associates Project AsS'ociates Mathematics Mathematics Education Glenn M. Carver Gertrude R. Croke A. Carroll Delaney Carol A. Dodd-Thornton Alfred L. LaTendresse Nancy C. Rsher Bernice K. O'Brien -Fadia F. Hank Robert F. Olin Kathleen M. Hart Susan M. Sanders Tom S. Hudson Barbara D. Sehr Calvin J. Irons Karen R. Thelen Graham A. Jones Richard D. Troxel 'Charles E. Labb Karen S. Wade Richard A. Lesh Carter S. Warfield Barbara E. Moses Lynnette 0. Womble Geraldine N. Rossi Thomas L. Schroeder Resource Teacher Carol L. Wadsworth Barbara E. Weller Marilyn Hall Jacobson Larry E. Wheeler Continued on inside back cover 3 MULTIPLICATION AND DIVISION JOHN F. LE BLANC Substantial contributors DONALD R. KERR, JR. Calvin J. Irons Graham A. Jones ,v ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo Park, California London Amsterdam Don Mills, Ontario Sydney 1 This book is in the ADDISON-WESLEY SERIES IN MATHEMATICS The preparation of this book was supported by National Science Foundation Grant #GY-9293. However, the opinions, findings, conclusions or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the National Srience Foundation. Except for the rights to material reserved 1., others, the publisher and copyright owner will grant permission without charge for use of this work and related material in the English language after December 31, 1981. For conditions of use and permission to use materials contained herein for foreign publications in other than the English language, apply to either the publisher or the copyright owner. Piiblication pursuant to such permission shall contain the statement: "Some (all) of the materials incorporated in this work were developed with the financial support of the National Science Foundation. Any opinions, findings, conclusions or recommendations expressed herein do not necessarily reflect the views of the National Science Foundation." Reproduced by AddisonrWesley from camera-ready copy supplied by the authors. Copyright ©1976 by Indiana University Foundation. Philippines copyright 1976 by Indiana University Foundation. All rights reserved. No part of thii publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, orotherwise, without the prior written permission of the copyright owner or the publisher. Printed in the United States of America. Published simultaneously in Cdnada. MON 0 201 14610.X ASCDEFGJOK AL 79876 5 , PREFACE The Mathematics-Methods Program (MMP) has been developed by the Indiana University Mathematics Education DevelopMent Center (MEDC) during the years 1971-75. The development of the MMP was funded by the UPSTEP program of the National.Science Foundation, with thegoal of producing an innovative program for the mathematics training of prospective elementary school teachers (PSTs). The primary features of the MMP are: It combines the mathematics training and the methods training of PSTs. It promotes a hands-on, laboratory approach to teaching in which PSTs learn mathematics and methods.by doing rather than bylis- tening, taking notes or memorizing. It involves the PST in using techniques and materials that are appropriate for use with children. It focuses on the real-world mathematical concerns of children and the real-world mathematical and pedagogicalconcerns-of PSTs. The MMP, as developed at the MEDC, involves a university class- room component and a related publicgchool teaching component. The university classroom component combines the mathematics content courses and methods courses normally taken by PSTs,while the public school teaching component provides the PST with a chance to gain ex- perience with children and insight intoAheir mathematical thinking. A model has been developed for the implementationof the public school teach4ng component of the MMP. Materials" have been developed for the university classroom portion of theMMP. These include 12 instructional units with the following titles: Numeration Addition and Subtraction Multiplication and Division Rational Numbers with Integers and Reals Awareness Geometry Transformational Geometry Analysis of Shapes Measu'rement Number Theory Probabirity and Statistics Graphs: the Picturing of information Experiences in Problem Solving These units are written in an activity formatthat-involves the PST in doing mathematics with an eye towarktheapplication of that math- ematics in the elementary school. The units are almost entirely in- dependent of one another, and any selection of them can bedone, in any order. It is worth noting that the first four units listed per- tain to the basic number work in the elementaryschool; the second four to the geometry of the elementary school; andthe final four to ma(hematical topics for the elementary teacher. For purposes of formative evaluationand dissemination, the MMP has been field-tested at over 40 colleges anduniversities. The field implementation formats have varied widely. They include the following: Ueb in mathematics department as the mathematics content pro- gram, or as a portion of that program; Use in the education sdool as the methods program, or as apor- tion of that program, Combined mathematics content and methods programtaught in vi either the mathematics department, or theeducation school, or jointly; Any of the above, with or without the public schoolteaching ex- perience. Common to most of the field implementations was asmall-group format for,..the univeysity classroom experienceand an emphasis on the use of concrete materials. The various centers that have implemented all or part of the MMP have made a numberoT suggestions for change, many of which are reflected in thefinal form of the program. It is fair to say that there has been a general feelingof satisfaction with, and enthusiasm -or, MMP from those who have beeninvolved in field-testing. A list of the field-test centers of the MMP is asfollowS: ALVIN JUNIOR COLLEGE GRAMBLING STATE UNIVERSITY Grambling, Louisiana Alvin, Texas . BLUE MOUNTAIN COMMUNITY COLLEGE ILLINOIS STATE UNIVERSITY Yendleton, Oregon Normal, Illinois BOISE STATE UPIVER'SITY INDIANA STATE UNIVERSITY ° Boise, Idaho EVANSVILLE BRIDGEWATER COLLEGE INDIANA STATE UNIVERSITY Bridgewater, Virginia Terre Haute, Indiana CALIFORNIA STATE UNIVERSITY, INDIANA UNIVERSITY CHICO Bloomington, Indiana CALIFORNIA STATE UNIVERSITY, INDIANA UNIVERSITY NORTHWEST NORTHRIDGE Gary, Indiana CLARKE COLLEGE MACALESTER COLLEGE Dubuque,_ Iowa St. Paul, Minnesota UNIVERSITY OF COLORADO UNIVERSITY OF MAINE AT FARMINGTON Boulder, Colorado UNIVERSITY OF MAINE AT PORTLAND- UNIVERSITY OF COLORADO AT GORHAM DENVER THE UNIVERSITY OF MANITOBA CONCORDIA TEACHERS COLLEGE Winnipeg, Manitoba, CANADA River Forest, Illinois MICHIGAN STATE UNIVERSITY SHELBY STATE COMMUNITY COLLEGE East Lansing, Michigan Memphis, Tennessee UNIVERSITY OF NORTHERN IOWA UNIVERSITY OF SOUTHERN MISSISSIPPI Cedar. Frs, Iowa Hattiesburg, Mississippi NORTHEr MICHIGAN UNIVERSITY SYRACUSE UNIVERSITY Marque te, Michigan Syracuse, New York NORTHWEST MISSOURI STATE TEXAS SOUTHERN UNIVERSITY UNIVERSITY