NEW GENERAL MATHEMATICS - Pearson

NEW GENERAL MATHEMATICS

for Junior Secondary Schools

JSS Teacher's Guide 3

2013

C

NERDC

urriculum

ZI Chima, GU Garba, AO Kalejaiye, MF Macrae

Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and 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, without the prior permission of the publishers.

First published in 2014

ISBN 9781447978343

It is illegal to photocopy any page of this book without the written permission of the copyright holder.

Cover design by Dion Rushovich Typesetting by Martingraphix

Acknowledgements: The Publishers would like to thank the following for the use of copyrighted images in this publication: Cover photo/artwork from Carol and Mike Werner/ Alamy / Afripics A09T98

Every effort has been made to trace the copyright holders. In the event of unintentional omissions or errors, any information that would enable the publisher to make the proper arrangements will be appreciated.

Introduction

This is the first time in two decades that a teacher's component has been prepared for the New General Mathematics series, which previously consisted of the Student's Book and the Student's Practice Book. In this revision, the Student's Practice Book has been called the Workbook. This Teacher's Guide supports the New General Mathematics for Junior Secondary 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 with

your class, as time permits ? suggested lesson plans of how to break each chapter down into teachable portions, as well

as 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 were

deliberately 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 any comments or suggestions you may have, and ask you to direct your comments through the publisher, using our website address .

Introduction iii

Contents

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii JSS3 Scheme of Work and Curriculum Matching Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Methodology and Features of the Student Book, Teacher's Guide and Workbook . . . . . . . . . . . . . . . . . . . . ix Section 1: Additional material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

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

iv Contents

JSS3 Scheme of Work and Curriculum matching chart

The chart on the following pages also appears in the Students' Book. It combines a Scheme of Work for JSS3 with corresponding themes and objectives that appear in the current NERDC basic mathematics curriculum for Junior Secondary schools.

Scheme of Work

The Scheme of Work appears in the three left-hand columns of the chart. The scheme follows the chapter order of New General Mathematics JSS Student's Book 3 and is based on an average school term of ten effective teaching weeks. For Terms 1 and 2, the chapters in the book have been carefully arranged in a sequence that combines a logical coverage of the curriculum topics with a spiral approach to learning. By spiral approach, we mean that instead of treating a curriculum theme (such as algebra) all at once, the chapters return to a theme during Terms 1 and 2, enabling step-by-step learning so as to develop competence and capacity over time. Term 3 is devoted to whole?course revision. In this case it is more appropriate to revise the course theme by theme.

Note that the Scheme of Work makes allowance for end-of-term revision and testing, an important component of the school year.

The chapter order provides a sound and carefully thought-out Scheme of Work. However, other schemes are perfectly possible. Your school, district or State may have a preferred approach. We advise that you follow the official scheme where it exists. Otherwise, simply follow the chapter order of New General Mathematics JSS Student's Book 3.

In Section 1 of this Teacher's Guide there is an enrichment chapter: ICT and computers. This chapter is only appropriate if students have access to computers and a relevant spreadsheet program. Refer to this chapter if possible, bearing in mind that it is not examinable at JSCE level.

Curriculum matching chart

The two right-hand columns of the chart show how, in Terms 1 and 2, the chapters of New General Mathematics JSS Student's Book 3 match with the National Curriculum as published by NERDC in 2013. The first column shows the five curriculum themes and related topics and the page number in the NERDC curriculum where they may be found. The curriculum themes are: ? Number and numeration ? Basic operations ? Algebraic processes ? Mensuration and geometry ? Everyday statistics

The final column contains related curriculum performance objectives.

Together, these columns show that New General Mathematics JSS Student's Book 3 fully covers the NERDC curriculum. However, due to space restrictions, NERDC references have been abbreviated. We advise that you refer to the full 36-page Mathematics Curriculum document (NERDC, 2013).

We wish to draw your attention to the performance objectives. The objectives state what students should be able to do after they have been taught a topic. Objectives are spelled out in full at the beginning of each chapter of New General Mathematics and are reflected in the Chapter Summary that appears at the end of the chapter. Each chapter contains an end?of?chapter test to help you to measure student attainment of the objectives.

JSS 3 Scheme of Work and Curriculum matching chart v

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