COURSEBOOK 2nd Edition 6A · Ldg` ^cV^gh 1@9 L G< & DeZc eVX`Zi d[ XdadjgZY XVcY^Zh# =dl bVcn [ZgZci d[ XdadjgZY XVcY^Zh VgZ i]ZgZ4 =dl bVcn d[ ZVX] VgZ i]ZgZ4 ':ciZg ^c hegZVYh]ZZi#:mVbeaZ/;

Charlotte Collars • Koay Phong Lee • Lee Ngan Hoe • Ong Bee Leng • Tan Cheow Seng (Cert. Ed.) (Ph.D.) (Ph.D.) (B.Sc., Dip. Ed.) (Cert. Ed.)

COURSEBOOK 2nd Edition6A

•APPROVE

DBY

MINISTRY OF EDUCATION

•

for use from 2009–2

017

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creo

Chapter OpenersEncourages active pupil participation in learning.

Friends of Shaping MathsThe themes in the coursebook revolve around Aini, Bala, Caili and David. The characters help to stimulate pupils’ interest and heighten their involvement in the learning process.

PREFACEShaping Maths is an instructional package written according to the latest Primary Mathematics Syllabus provided by the Ministry of Education, Singapore. The package is designed to meet the learning needs of pupils from Primary 1 to 6. For Primary 6, the package consists of two coursebooks, four activity books and a teacher’s resource pack.

Approach

The Primary 6 (2nd Edition) package is designed to provide continuity in the way pupils experience Mathematics through the lower primary packages. Wherever possible, familiar everyday situations are used to introduce new topics so that pupils will be able to relate the application of new concepts learnt with their daily lives. Through its concrete-pictorial-abstract approach in implementing the spiral curriculum, this package seeks to promote pupil engagement and enhance the learning process.

Continuing research in education has resulted in the introduction of new features in the second edition. Through these features, educators are further equipped with various strategies in addressing teaching and pupils’ learning needs. These features also include more open-ended questions so as to encourage exploration and in-depth thinking among pupils. Thus, mathematically inquisitive learners are born!

Features

Recall Activity Marker Emphasises the importance of establishing connections in learning mathematics. The marker directs pupils to a diagnostic exercise, Recall, in the activity book.

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My NotesHelps pupils to consolidate and recall their learning and commit to memory some key ideas.

Review Helps pupils to consolidate their learning.

Question Classifi cation – pre-requisite skills

– reinforcement of current concepts

– higher-order thinking skills

Helps teachers to spend their time more effectively by using the appropriate questions to get pupils to master the necessary skills.

Use of Calculator Inculcates the appropriate use of calculators without compromising basic computational skills through:• introducing pupils to and providing guidance

on the use of calculators,• encouraging pupils to exercise judgement

where the use of calculators is optional, thus appreciating the power of mental computation versus calculator-based computation,

• exposing pupils to investigations involving tedious computation, so that they can appreciate the calculator as a learning tool.

SummaryA one-page summary helps pupils to consolidate their learning for each semester. It also serves as a quick revision guide for pupils, especially when preparing for semestral assessments.

Fun With Maths Engages pupils in interactive mathematical activities that encourage exploration, discovery and active thinking.

π

ππ

π

π

π

π

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1 Algebra 2 • Algebraic Expressions 3 • Simplifi cation and Evaluation 8 • Solving Word Problems 11

2 Fractions 16 • Dividing a Whole Number by a Proper Fraction 18 • Dividing a Proper Fraction by a Proper Fraction 20 • Solving Word Problems 23

Review A 28

3 Percentage 30 • Finding the Whole when a Percentage is Known 32 • Change in Percentage 36 • Solving Word Problems 40 Useful Reminders 50

Revision A 52

CONTENTS

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4 Ratio 60 • Ratio and Fraction 61 • Equivalent Fractions and Ratios 66 • Changing Ratios 76

Review B 86

5 Speed 92 • Speed and Average Speed 93 • Solving Word Problems 97

6 Solid Figures 104 • Drawings of Solid Figures 105 • Nets 108

Review C 116

Revision B 121

Summary 130

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Algebra1

AB 6A Part 1, Recall 1

Algebra! What is it?

It is a branch of Mathematics that uses letters or symbols to represent numbers.

This is a picture of Muhammad ibn Musa al-Khwarizmi. He was a mathematician who lived long ago. The word ‘algebra’ came from the word ‘al-jabr’ in his work on Mathematics.

2

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Algebraic Expressions

Aini’s mother is 23 years older than Aini.

Complete the table.

When Aini is years old, her mother is years old.

We can use a letter to represent the unknown number.When Aini is x years old, her mother is (x + 23) or (23 + x) years old.(x + 23) and (23 + x) are algebraic expressions in terms of x.

Aini is 12 years old. Her mother is 35 years old.

When Aini was 7 years old, her mother was 30 years old.

When Aini was 1 year old, her mother was 24 years old.

Aini’s age Her mother’s age

12 35

7 30

1 24

3


1

When David gets $8, his brother gets $6.

a) When David gets $10, his brother gets $ .

b) When David gets $y, his brother gets $ .

2

There are 16 pieces of chocolate in a box.

a) There are pieces of chocolate in 3 boxes.

b) There are pieces of chocolate in 8 boxes.

c) There are pieces of chocolate in p boxes.

3 Use this machine to fi nd the missing numbers in the table.

What will you get when you put y in the machine?

DavidDavid’s brother

Our father gives us pocket money weekly.

I get $2 less than David.

We write 16 × p as 16p. 16p is an algebraic expression in terms of p.

÷ 5

5In

Out1

We write x ÷ 5as

x5

or 15

× x.

In Out

5 1

10 2

15

x

4


4 The table below shows how toothpicks are used to make fi gures of houses.

a) Count the number of toothpicks used to make the fi gures of houses.

Number of toothpicks = 1 + 4 × number of houses

b) How many toothpicks do you need to make 10 houses? c) How many toothpicks do you need to make n houses?

5 Find the missing numbers or expressions.

Caili is 12 years old.

a) i) 2 years ago, she was years old. y years ago, she was years old.

ii) In 4 years’ time, she will be years old. In y years’ time, she will be years old.

b) Mary is n times as old as Caili.

i) Express Mary’s age in terms of Caili’s age.

ii) How old was Mary 5 years ago?

AB 6A Part 1, Activity 1.1

Figure Number of houses Number of toothpicks

1 5 = 1 + 4

2 9 = 1 + 8

3 13 = 1 + 12

4 17 = 1 + 16

5


Documents

COURSEBOOK 2nd Edition 6A · Ldg` ^cV^gh 1@9 L G< & DeZc eVX`Zi d[ XdadjgZY XVcY^Zh# =dl bVcn [ZgZci d[ XdadjgZY XVcY^Zh VgZ i]ZgZ4 =dl bVcn d[ ZVX] VgZ i]ZgZ4 ':ciZg ^c hegZVYh]ZZi#:mVbeaZ/;