GRADE 9 Topic MATHEMATICS

Topic

DEPARTMENT OF EDUCATION

GRADE 9

Topic

MATHEMATICS

UNIT 2

PATTERNS AND CHANGE

Published by:

FLEXIBLE OPEN AND DISTANCE EDUCATION

PRIVATE MAIL BAG, P.O. WAIGANI, NCD FOR DEPARTMENT OF EDUCATION PAPUA NEW GUINEA

2013

GR 9 MATHEMATICS U2

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TITLE PAGE

GRADE 9

MATHEMATICS

UNIT 2

TOPIC 1: DIRECTED NUMBERS TOPIC 2: INDICES TOPIC 3: ALGEBRAIC EXPRESSIONS TOPIC 4: EQUATIONS

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ACNOWLEDGEMENT

Acknowledgements

We acknowledge the contribution of all Secondary and Upper Primary teachers who in one way or another helped to develop this Course.

Special thanks are given to the staff of the Mathematics Department- FODE who played active role in coordinating writing workshops, outsourcing of lesson writing and editing processes involving selected teachers in Central and NCD.

We also acknowledge the professional guidance and services provided throughout the processes of writing by the members of:

Mathematics Department- CDAD Mathematics Subject Review Committee-FODE Academic Advisory Committee-FODE . This book was developed with the invaluable support and co-funding of the GOPNG and World Bank.

MR. DEMAS TONGOGO Principal-FODE

. Flexible Open and Distance Education Papua New Guinea

Published in 2016

@ Copyright 2016, Department of Education Papua New Guinea

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 any other form of reproduction by any process is allowed without the prior permission of the publisher.

ISBN: 978- 9980- 87- 729-1

National Library Services of Papua New Guinea

Written by: Mrs. Estrella V. Tuguinay

Compiled and finalised by: Mrs. Luzviminda B. Fernandez SCO -Mathematics Department-FODE

Printed by the Flexible, Open and Distance Education

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CONTENTS

CONTENTS

Contents................................................................................................... Secretary's Message................................................................................... Unit Introduction......................................................................................... Study Guide.............................................................................................. TOPIC 1: DIRECTED NUMBERS.............................................................

Lesson 1: Directed Numbers in Practical Situations............................... Lesson 2: Adding Directed Numbers.................................................. Lesson 3: Subtracting Directed Numbers............................................ Lesson 4: Multiplying Directed Numbers............................................. Lesson 5: Dividing Directed Numbers................................................ Lesson 6: Solving Mixed Problems....................................................

Summary........................................................................ Answers to Practice Exercises 1-6....................................... TOPIC 2: INDICES................................................................................. Lesson 7: Squares and Square Roots................................................ Lesson 8: Multiplication Laws of Indices............................................. Lesson 9: Division Laws of Indices.................................................... Lesson 10: Zero and Negative Indices................................................. Lesson 11: Scientific Notation............................................................ Lesson 12: Combined Index Operations............................................... Summary....................................................................... Answers to Practice Exercises 1-6....................................... TOPIC 3: ALGEBRAIC EXPRESSIONS..................................................... Lesson 13: Number Patterns............................................................. Lesson 14: Algebraic Expressions...................................................... Lesson 15: Simplifying Algebraic Expressions....................................... Lesson 16: Evaluating Algebraic Expressions....................................... Lesson 17: Factorization.................................................................. Summary....................................................................... Answers to Practice Exercises 1-6....................................... TOPIC 4: EQUATIONS........................................................................... Lesson 18: Simple Equations............................................................ Lesson 19: Solving Equations Involving Grouping Symbols...................... Lesson 20: Solving Equations Involving Unknowns on Both Sides............. Lesson 21: Equations Involving Fractions............................................ Lesson 22: Changing Subjects of Simple Equations............................... Lesson 23: Transposing Formulae...................................................... Lesson 24: Solving Word Problems.................................................... Summary........................................................................ Answers to Practice Exercises 1-6.......................................

REFERENCES.........................................................................................

Page 3 4 5 6 7 9 15 20 24 27 30 34 35 39 41 46 51 55 59 66 70 71 73 75 82 88 94 99

105 106 109 111 119 124 130 136 140 145 154 155 159

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SECRETARY'S MESSAGE

MESSAGE

Achieving a better future by individuals students, their families, communities or the nation as a whole, depends on the curriculum and the way it is delivered.

This course is part and parcel of the new reformed curriculum ? the Outcome Base Education (OBE). Its learning outcomes are student centred and written in terms that allow them to be demonstrated, assessed and measured.

It maintains the rationale, goals, aims and principles of the National OBE Curriculum and identifies the knowledge, skills, attitudes and values that students should achieve.

This is a provision of Flexible, Open and Distance Education as an alternative pathway of formal education.

The Course promotes Papua New Guinea values and beliefs which are found in our constitution, Government policies and reports. It is developed in line with the National Education Plan (2005 ? 2014) and addresses an increase in the number of school leavers which has been coupled with a limited access to secondary and higher educational institutions.

Flexible, Open and Distance Education is guided by the Department of Education's Mission which is fivefold;

to facilitate and promote integral development of every individual to develop and encourage an education system which satisfies the

requirements of Papua New Guinea and its people to establish, preserve, and improve standards of education throughout Papua

New Guinea to make the benefits of such education available as widely as possible to all of

the people to make education accessible to the physically, mentally and socially

handicapped as well as to those who are educationally disadvantaged

The College is enhanced to provide alternative and comparable path ways for students and adults to complete their education, through one system, many path ways and same learning outcomes.

It is our vision that Papua New Guineans harness all appropriate and affordable technologies to pursue this program.

I commend all those teachers, curriculum writers and instructional designers, who have contributed so much in developing this course.

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UNIT 2: PATTERNS OF CHANGE

UNIT INTRODUCTION

Dear Student

This is the second unit of the Grade 9 Mathematics Course. This unit is based on the NDOE Lower Secondary Syllabus and Curriculum Framework for Grade 9.

This Unit consists of four topics:

Topic 1: Topic 2: Topic 3: Topic 4:

Directed Numbers Indices Algebraic Expressions Equations

In Topic 1-Directed Numbers- You will revise directed numbers, then present directed numbers on number lines and relate them to real life situations. You will also learn to perform addition, subtraction, multiplication and division of directed numbers on practical problems in real life situations

In Topic 2- Indices- You will revise squares and square roots and learn to use the table of squares and square roots to find the squares and square root of a given number. You will also learn the different Laws of indices and solve problems involving Scientific notation.

In Topic 3- Algebraic Expressions- You will learn about number patterns. You will also learn translate words, phrases and sentences in to algebraic expressions, then simplify, evaluate and factorize algebraic expressions.

In Topic 4- Equations- You will define simple equations and identify the properties and the steps in solving simple equations. You will also learn to solve equations involving grouping symbols, fractions and unknown on both sides as well as changing the subject and transposition of formulae. Then, solve word problems using equations.

You will find that each lesson has reading material to study, worked examples and a practice exercise. The answers to the practice exercises are given at the end of each topic.

All the lessons are written in simple language with comic characters to guide you. The practice exercises are graded to help you learn the process of working out problems.

We hope you enjoy learning this unit.

Mathematics Department FODE

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STUDY GUIDE

STUDY GUIDE

Follow the steps given below as you work through the Unit.

Step 1: Step 2: Step 3:

Step 4: Step 5:

Start with TOPIC 1 Lesson 1 and work through it.

When you complete Lesson 1, do Practice Exercise 1.

After you have completed Practice Exercise 1, check your work. The answers are given at the end of TOPIC 1.

Then, revise Lesson 1 and correct your mistakes, if any.

When you have completed all these steps, tick the check-box for the Lesson, on the Contents Page (page 3) like this:

Lesson 1: Directed numbers in Practical Situations

Then go on to the next Lesson. Repeat the process until you complete all of the lessons in Topic 1.

As you complete each lesson, tick the check-box for that lesson, on the Content Page 3, like this .This helps you to check on your progress.

Step 6:

Revise the Topic using Topic 1 Summary, then, do Topic test 1 in Assignment 2.

Then go on to the next Topic. Repeat the same process until you complete all of the four Topics in Unit 2.

Assignment: (Four Topics and a Unit Test) When you have revised each Topic using the Topic Summary, do the Topic Test in your Assignment. The Unit book tells you when to do each Topic Test.

When you have completed the four Sub-strand Tests, revise well and do the Strand test. The Assignment tells you when to do the Strand Test.

The Topic Tests and the Unit test in the Assignment will be marked by your Distance Teacher. The marks you score in each Assignment will count towards your final mark. If you score less than 50%, you will repeat that Assignment.

Remember, if you score less than 50% in three Assignments, you will not be allowed to continue. So, work carefully and make sure that you pass all of the Assignments.

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TOPIC 1 TITLE

TOPIC 1

DIRECTED NUMBERS

Lesson 1:

Lesson 2: Lesson 3: Lesson 4: Lesson 5: Lesson 6:

Directed Numbers in Practical Situations Adding Directed Numbers Subtracting Directed Numbers Multiplying Directed Numbers Dividing Directed Numbers Solving Mixed Problems

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