Transcription

NEW GENERALMATHEMATICSfor Junior Secondary SchoolsJSS Teacher’s Guide 32013NERDCCurriculumZI Chima, GU Garba, AO Kalejaiye, MF Macrae

Pearson Education LimitedEdinburgh GateHarlowEssex CM20 2JEEnglandand Associated Companies throughout the world Pearson Education Limited 2014 All rights reserved. No part of this publication may be reproduced,stored in a retrieval system or transmitted in any form or by any means,electronic, mechanical, photocopying, recording, or otherwise, withoutthe prior permission of the publishers.First published in 2014ISBN 9781447978343It is illegal to photocopy any page of this book without the writtenpermission of the copyright holder.Cover design by Dion RushovichTypesetting by MartingraphixAcknowledgements:The Publishers would like to thank the following for the use ofcopyrighted images in this publication:Cover photo/artwork from Carol and Mike Werner/ Alamy / AfripicsA09T98Every effort has been made to trace the copyright holders. In the event ofunintentional omissions or errors, any information that would enable thepublisher to make the proper arrangements will be appreciated.

IntroductionThis is the first time in two decades that a teacher’s component has been prepared for theNew General Mathematics series, which previously consisted of the Student’s Book andthe Student’s Practice Book. In this revision, the Student’s Practice Book has been calledthe Workbook. This Teacher’s Guide supports the New General Mathematics for JuniorSecondary Schools 1–3 series as revised to align to the 2013 NERDC curriculum.The Teacher’s Guide contains: information on how to use the course as a whole a suggested scheme of work for the year and a curriculum matching chart additional chapters that were not included in the Student’s Book. You can use these withyour class, as time permits suggested lesson plans of how to break each chapter down into teachable portions, as wellas notes on foundation knowledge required and assessment milestones printable test papers for the chapter revision and term revision tests answers for the puzzle corners, Chapter revision tests, and term revision tests, which weredeliberately excluded from the Student’s Book workbook marking sheets.We hope that you will find this guide a useful resource for you as a teacher. We welcome anycomments or suggestions you may have, and ask you to direct your comments through thepublisher, using our website address www.pearsonnigeria.com.Introductioniii

ContentsIntroduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iiiJSS3 Scheme of Work and Curriculum Matching Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vMethodology and Features of the Student Book, Teacher’s Guide and Workbook . . . . . . . . . . . . . . . . . . . .ixSection 1: Additional material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Preliminary chapter: Review of previous coursework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2Enrichment chapter: ICT and computers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Section 2: Lesson plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20Chapter 1 Binary system: Operations and applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21Chapter 2 Word problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23Chapter 3 Factorisation 1: Common factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25Chapter 4 Geometrical constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27Chapter 5 Area of plane shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29Chapter 6 Formulae: Substitution; change of subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31Chapter 7 Similarity 1: Similar shapes and scale factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33Chapter 8 Trigonometry 1: Tangent of an angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35Chapter 9 Factorisation 2: Quadratic expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37Chapter 10 Equations 1: Equations with fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40Chapter 11 Compound interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42Chapter 12 Similarity 2: Area and volume of similar shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44Chapter 13 Proportion: Direct; inverse; reciprocal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46Chapter 14 Equations 2: Simultaneous linear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48Chapter 15 Trigonometry 2: Sine and cosine of angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50Chapter 16 Everyday statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52Chapter 17 Rational and non-rational numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54Section 3: Revision tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56Chapter revision test sheets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57Chapter revision test answers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87Term revision test sheets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90Term revision test answers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Section 4: Workbook answer sheets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118IndexivContents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

JSS3 Scheme of Work and Curriculum matching chartThe chart on the following pages also appearsin the Students’ Book. It combines a Scheme ofWork for JSS3 with corresponding themes andobjectives that appear in the current NERDC basicmathematics curriculum for Junior Secondaryschools.Scheme of WorkThe Scheme of Work appears in the three left-handcolumns of the chart. The scheme follows thechapter order of New General Mathematics JSSStudent's Book 3 and is based on an average schoolterm of ten effective teaching weeks. For Terms 1and 2, the chapters in the book have been carefullyarranged in a sequence that combines a logicalcoverage of the curriculum topics with a spiralapproach to learning. By spiral approach, we meanthat instead of treating a curriculum theme (suchas algebra) all at once, the chapters return to atheme during Terms 1 and 2, enabling step-by-steplearning so as to develop competence and capacityover time. Term 3 is devoted to whole–courserevision. In this case it is more appropriate to revisethe course theme by theme.Note that the Scheme of Work makes allowancefor end-of-term revision and testing, an importantcomponent of the school year.The chapter order provides a sound and carefullythought-out Scheme of Work. However, otherschemes are perfectly possible. Your school, districtor State may have a preferred approach. We advisethat you follow the official scheme where it exists.Otherwise, simply follow the chapter order of NewGeneral Mathematics JSS Student's Book 3.In Section 1 of this Teacher's Guide there is anenrichment chapter: ICT and computers. Thischapter is only appropriate if students have accessto computers and a relevant spreadsheet program.Refer to this chapter if possible, bearing in mindthat it is not examinable at JSCE level.Curriculum matching chartThe two right-hand columns of the chart showhow, in Terms 1 and 2, the chapters of New GeneralMathematics JSS Student's Book 3 match with theNational Curriculum as published by NERDC in2013. The first column shows the five curriculumthemes and related topics and the page number inthe NERDC curriculum where they may be found.The curriculum themes are: Number and numeration Basic operations Algebraic processes Mensuration and geometry Everyday statisticsThe final column contains related curriculumperformance objectives.Together, these columns show that NewGeneral Mathematics JSS Student's Book 3 fullycovers the NERDC curriculum. However, due tospace restrictions, NERDC references have beenabbreviated. We advise that you refer to the full36-page Mathematics Curriculum document(NERDC, 2013).We wish to draw your attention to theperformance objectives. The objectives state whatstudents should be able to do after they have beentaught a topic. Objectives are spelled out in fullat the beginning of each chapter of New GeneralMathematics and are reflected in the ChapterSummary that appears at the end of the chapter.Each chapter contains an end–of–chapter test tohelp you to measure student attainment of theobjectives.JSS 3 Scheme of Work and Curriculum matching chartv

Scheme of Work: JSS3, Term 1NGMWorksheetChapter titleTERM 1Ch nonoCurriculum matchingNERDC JSS3Themes and TopicsWeek 1 Pre 1Review ofpreviouscourseworkContent summary relating toNERDC performanceobjectives for JSS1 and JSS2Week 2 Ch 1Binary system: 1OperationsandapplicationsNumber and numerationBasic operationsAlgebraic processesMensuration and geometryEveryday statisticsNumber & Numeration, p. 28Sub-theme: Whole numbersTopic 1: Whole numbersWeek 3 Ch 2Wordproblems2Week 4 Ch 3Factorisation1: Commonfactors3Week 5 Ch 4Construction4Week 6 Ch 5Area of planeshapes5Week 7 Ch 6Formulae:Substitution,change ofsubjectSimilarity 1:Place shapes,scale factor67Mensuration & Geometry,p. 33Sub-theme: ShapesTopic 1: Similar shapesTrigonometry1:Tangent of anangle8Mensuration & Geometry,p. 33Sub-theme: ShapesTopic 2: TrigonometryIdentify similar plane figures(triangles, rectangles, squares)in the environmentEnlarge a shape by a givenscale factorDetermine the tangent of anacute angleApply the tangent ratio tofinding distances, lengths andanglesWeek 8 Ch 7Week 9 Ch 8Week Revision Exercises andTests, Ch 1 - 810End of Term 1viJSS 3 Scheme of Work and Curriculum matching chartNERDC JSS3Performance ObjectivesRecall and use binary numberoperationsConvert binary numbers toother bases and vice versaSolve QR problems on binarysystemsBasic Operations, p. 30Topics 1 – 4 Operations with Add, subtract, multiplynumbers in base twobase two numeralsNumber & Numeration, p. 28 Translate word problems intoSub-theme: Whole numbers numerical expressionsTopic 1: Whole numbersFactorise simple algebraicAlgebraic Processes, p. 31expressionsSub-theme: AlgebraicSolve word problemsoperationsinvolving factorisationTopic 1: FactorisationRevise line and angleMensuration & Geometry,bisectionp. 35Construct angles of 90 , 45 ,Sub-theme: Shapes60 , 30 Copy a given angleTopic 5: ConstructionConstruct simple shapesFind the area of triangles,Mensuration & Geometry,parallelograms, trapeziums,p. 34circles, sectorsSub-theme: ShapesTopic 5: Area of plane figures Solve word and QR problemson area (in the home, theenvironment and in relationto land measure)Algebraic ProcessesSubstitute values in a formulaChange the subject of aformulaUse revision exercises and tests to consolidate Term 1 content

Scheme of Work: JSS3, Term 2NGMWorksheetChapter titleTERM 2Ch nonoCh 9Factorisation 2: 9QuadraticexpressionsCh 10Equations 1:Equationswith fractions10Week 3Ch 11Compoundinterest11Week 4Ch 12Similarity 2:Area andvolume ofsimilar shapes12Week 5Ch 1313Proportion:Direct, inverse,reciprocalWeek 6Ch 14Equations 2:SimultaneouslinearequationsWeek 7Ch 15Trigonometry 2: 15Sine andcosine ofanglesWeek 8Ch 16EverydaystatisticsWeek 1Week 21416Curriculum matchingNERDC JSS3Themes and TopicsNERDC JSS3Performance ObjectivesFactorise quadraticexpressionsSolve word problemsinvolving factorisationSolve simple equationsinvolving fractionsSolve word problems leadingto equations involvingfractionsSolve compound interestproblemsApply the use of compoundinterest in daily life activitiesCalculate lengths, areas andMensuration & Geometry,volumes of similar shapesp. 33Use scale factor (k, k2, k3) inSub-theme: Shapesrelation to areas and volumesTopic 1: Similar shapesof similar shapesNumber & Numeration, p. 29 Solve problems involvingSub-theme: Whole numbers direct and inverse proportionApply direct and inverseTopic 1: Whole numbersproportions to practicalproblemsCompile tables of valuesAlgebraic Processes, p. 32Solve simultaneous linearSub-theme: Algebraicequations graphicallyoperationsTopic 3: Simultaneous linear Solve simultaneous equationsusing elimination andequationssubstitution methodsApply methods of solvingsimultaneous equations toreal life activitiesIdentify and determine theMensuration & Geometry,sine and cosine of acutep. 33anglesSub-theme: ShapesApply the sine, cosine andTopic 2: Trigonometrytangent ratios to findingdistances, l