DOCUMENT RESUME ED 166 042 SE 026 555 TITLE Mathematics for Georgia Schools,' Volume II: Upper Elementary 'Grades. INSTITUTION Georgia State Dept. of Education, Atlanta. Office of Instructional Services. e, PUB DATE 78 NOTE 183p.; For related document, see .SE 026 554 EDRB, PRICE MF-$0.33 HC-$10.03 Plus Postage., DESCRIPTORS *Curriculm; Elementary Educatia; *Elementary School Mathematics; Geometry; *Instruction; Meadurement; Number Concepts; Probability; Problem Solving; Set Thory; Statistics; *Teaching. Guides ABSTRACT1 ' This guide is organized around six concepts: sets, numbers and numeration; operations, their properties and number theory; relations and functions; geometry; measurement; and probability and statistics. Objectives and sample activities are presented for.each concept. Separate sections deal with the processes of problem solving and computation. A section on updating curriculum includes discussion of continuing program improvement, evaluation of pupil progress, and utilization of media. (MP) ti #######*#####*########.#*###*######*****######*########*##########**#### * Reproductions supplied by EDRS are the best that can be made * * from the original document. * *********************************************************************** U S DEPARTMENT OF HEALTH, EDUCATION & WELFARE IS NATIONAL INSTITUTE OF.. EDUCATION THIS DOCUMENT HA4BEEN REPRO- DuCED EXACTLY AS- RECEIVEDFROM THE PERSON OR ORGANIZATIONORIGIN- ATING IT POINTS OF VIEWOR 01NIONS STATED DO NOT NECESSARILYEpRE SENT OFFICIAL NATIONAL INSTITUTEOF TO THE EDUCATION4 EDUCATION POSITION OR POLICY INFORMATION CEN1IE USERS OF THE ERIC S. mathematicsfor georgias 't I VOLUME II UPPER ELEME Y GR`ADESN O r , , IP ' VC. 1j. O App.- Problem 10 4 Computation Number \ Sentence Charles McDanielState Superintendent of SchoolsGeorgia Department of EducationReprint 1978 47) 4. mathematics forgeois schools VOLUME II UPPER ELEMENTARY GRA ,. i 4i" . 'AA Computation Number Sentence. J Division of Curriculum Development and Pupil Personnel Services Office of Instructional Servic8 Georgia Department of Education Atlanta, Georgia 30334 4.3 ( ti '1 Copyright 1971 State of Georgia Georgia Department of Education Atlanta, Georgia 30334 0 FOREWORD The Georgia'Department of Education is constantly alert to the curricularchanges which seem desirable as a result of studies and experiments in various fields. A committeewas appointed in 1969 to rewrite the mathematics curriculum guides for the elementary schoolsincorporating findings from current curriculum studies in mathematics. This committee was composed of rural and city public schoolteachers and supervisors, college teachers and one out -of -state consultant who is nationally known in mathematics education. Theylooked at the nation's best programs in mathematics education. They considered creativeideas of teaching which fit the age of space but which are as fundameri al as adding two and two. They recognized thatmathematics is an essential part of life itself and is a'dailynecessity for all people. The committee, taking the positionthat mathematics instruction is a process of initiating and nurturing 'understanding,felt that it would be neces- sary to discover techniques for accommodating the differing rates at which children devefop. 6 \N LETTER TO UPPER ELEMENTARY GRADE R$ This guide has hern written to assist you in improving the teaching ofmathematics in the upper elementary grades. The committee andI have worked diligently for sevet5I years preparing this material and trust that theformat is arranged so that it will be useful to you. The guide has keen organized/around six central concepts called strands. Theyare etitled (f) Sets, Numbers and Numera- ,tion. (2) Operations, Their Properties and Number Theory, (3) Relations and Functi. ns,"(4) Geometry, (5)Measurement, (6) Probability and Statistics. These strands include.the major mathematicalconcepts which undergird an updated mathematics program for children. The concepts are threads running through the curriculum andare expanded and enlarged in a spiral approach. , . _ . Fad) strand is introduced in terms of broad performance objectives which the teachercan ake more specific by adapting them to the neecE of particular children: There are one or more activities keyedto each objective. The list of objectives for each strand is placed at the end of the. strand on a fold-out sheet. This allowsthe teacher to view the objectives as he selects activihesto implement specific objectives. These activitiesare not suffici nt to thieve the objectives. They are suggestions of kinds of experiences which will help reach the objectives. The strands on Probability and Statistics and on Relations and Functionsare included particularly because of new ideas in elementary school mathematics. It is hoped that teachers will accept tilt challenge ofnew topics, different approaches and experimental .activities as a means of extending the spiral Darning of mathematics for all pupils accordingto their potential. There are separate sections in the guide which deal speci icallv withprocesses. Problem solving is considered a part of all mathematics and therefore is emphasized in a cross- strand approach. Computation, also., 4 is viewed by the committee as permeating all strands, and the related section is intended to give detitiled development for 'especially difficult procedures. Problem solving is thinking through, and computakion is the Manipulation of various symbOls andterms used to express these. thoughts. Other sections are included to facilitate use of the guide by the teacher. Whilenot prescriptive, the content and methods identified throughout the guide are of increasing importance ina contemporary mathematics program. The section on media lists instructional aids, and the-use of aids i4fuggestecl in the activities of each strand.The correct use of the materials will help in the achievement of the objectives. Teachers should realize the importance ofteaching children correct vocabulary and correct use of symbols. A glossary for the teacher is included to provide definitions which can be simplifiedinto children's language. Words often used iri daily communication, particularlysome geometric terms, have a different meaning when considered mathematically'. Symbols are to be understoodas ain ans of stating problems and recording results after meaningful experiences with physical models of mathematical princips. The teacher, guided tily the Objectives in each strand, should endeavorto determine those topicsand activities most appro- priate for realizing the objectives for the particular children being taught and should correlatethese ideas with those-in texts and other available materials. After a strand has been presented, the teacher should evaluatein terms of the objectives using instruments const'ruc'ted for this purpose. Sample instrumentsare included in the Evaluating Pupil Prooillks section. In the bibliography are suggested materials designed to help implement achievement of theobjectives. Early selection and purchase of materials for the library, a grade level or an individual class will insureaccess to:hooks when needed. Inservice programs for those who need help with he new ideas will result ina 'more competent faculty as well as increased knowledge on the part of the children. Assistance in improving local Programsmay he found in the section Continuing Program Improvement. adys M. Thomason, Coordinator Mathematics Education Georgia Department of Education v TABLE OF CONTENTS FOREWORD LETTER TO UPPER ELEMENT/ 4N- GRADE TEACHERS POINT OF VIEW ,f ix CONCEPTS ACCORDING TO STRANDS / , at, Sets, Numbers and Numeration ti Operations, Their Properties and Number Theory 31 Relations aild Functions 61 Geometry or , 82 Measurement 104 Probability and Statistics III ; ,. a PROCESSES FOR SPECIAL CONSIDERATION .:, 125 V Problein §olving 12 -- Difficulties in Computation . J. 131 UPDATING CURRICULUM 145 Continuing Program Improvement .1 146 Evaluation Pupil Progress , 148 Utilization of Media c 152 o GL SSARY FOR TEACHERS 161 A ) 41, -POINT OF VIE . i C.-- Curriculum plinning is .a continuous process of updating content, improving methods, analyzing objectives,measuring learning and appraising attitudes. The guide, Mathematics for Georgia Schools, istohelp, local curric cotnntitteesand teachers of mathematics to identify the content,procedures and materials which.will strengthen and'en ch themathematics " educational program for thtelementary school children of Georgia, and to measure the effectiveness of theprogram. In the guide objectives are stated in behavioral terms. Local culiculum.cornmitteesmayfind it helpful to state more silecific objectives. The activities support the theory that learning r(experieneing. The objectives and activities are organized intosix strands written for primary grades d upper grades. The ordering of the strands in the ider does not imply the ordering of presentationof subject matter; that is, one strand 'need not ,be completed (or eyen begun) before proceeding to another. The volume of material on,differewtopics does not imply that is more important than the other. Topics especially difficult to present and thosenot generally covered in currentlyavailable extbooks are developed inmore detail. Individualteacherswill need to make appropriate choices according to the needs of their pupils. / pi One strand which has emphasis. is Relations and Functions, since most of 'mathemati6s involves relatiOnsbetween numbers and/or geometric figures.Since relations nd functions