RUKUN NEGARA
Bahawasanya Negara Kita Malaysia

mendukung cita-cita hendak:

Mencapai perpaduan yang lebih erat dalam kalangan
seluruh masyarakatnya;

Memelihara satu cara hidup demokrasi;

Mencipta satu masyarakat yang adil di mana kemakmuran negara
akan dapat dinikmati bersama secara adil dan saksama;

Menjamin satu cara yang liberal terhadap
tradisi-tradisi kebudayaannya yang kaya dan pelbagai corak;

Membina satu masyarakat progresif yang akan menggunakan
sains dan teknologi moden.

MAKA KAMI, rakyat Malaysia,
berikrar akan menumpukan

seluruh tenaga dan usaha kami untuk mencapai cita-cita tersebut
berdasarkan prinsip-prinsip yang berikut:

KEPERCAYAAN KEPADA TUHAN
KESETIAAN KEPADA RAJA DAN NEGARA

KELUHURAN PERLEMBAGAAN
KEDAULATAN UNDANG-UNDANG
KESOPANAN DAN KESUSILAAN

(Sumber: Jabatan Penerangan, Kementerian Komunikasi dan Multimedia Malaysia)

RUKUN NEGARA.indd   1 4/10/16   8:55 PG
YEAR   4
MATEMATIKMATHEMATICS

DUAL LANGUAGE PROGRAMME

TEXTBOOK

WRITERS

• CHAN YOOK LEAN

• RAMLAH MAJID

• KHADIJAH NOORDIN

EDITORS

• MARIATI JOSEPHA MUSTAFA

• ASMAHANIM AB RAHMAN

ILLUSTRATOR

• MOHAMAD SHARIF
       MOHD YASIN

TRANSLATOR

• SUGARA ABDUL LATIF
GRAPHIC DESIGNER
• AINI ABD. HAMID

Dewan Bahasa dan Pustaka
Kuala Lumpur

2016
KK 513-221-0102021-49-1248-20101

ISBN 978-983-49-1248-2

First Printing 2016

© Dewan Bahasa dan Pustaka 2016

All Rights Reserved. No parts of this book may
be reproduced or transmitted in any form or by
any means, electronic or mechanical, including
photocopying, recording or any information storage
and retrieval system without permission in writing
from the Director-General, Dewan Bahasa dan
pustaka, P.O. Box 10803, 50926 Kuala Lumpur,
Malaysia. Negotiation is subject to the calculation of
royalty or honorarium.

Publisher:

Dewan Bahasa dan Pustaka,
Jalan Dewan Bahasa,
50460 Kuala Lumpur.
Telephone: 03-2147 9000 (8 hunting lines)
Facsimile: 03- 2147 9643
Website: http://www.dbp.gov.my

Design and Typeset:
Dewan Bahasa dan Pustaka

Text Typeface: Azim
Text Typeface Size: 14/16 points

Printed by:

Ultimate Print Sdn. Bhd.,
Lot 2, Jalan Sepana 153,
Off Persiaran Selangor Seksyen 15,
40200 Shah Alam,
Selangor Darul Ehsan.

The Ministry of Education, Dewan Bahasa dan
Pustaka, and the panel of writers would like to
express their appreciation for the contributions
made by the following parties:

  The Panel of Evaluation,

Textbook Division, Ministry of Education.

	 Officers of the Texbook Division,
 Ministry of Education.

		The Panel of Evaluation,
 Dewan Bahasa dan Putaka.

  SK Kubu, Melaka.

  SK Taman Bukit Maluri, Kepong, Kuala Lumpur.

  All parties involved in the process of publishing of
this book.

ACKNOWLEDGEMENTSSerial No.: 0194
6  MIXED OPERATION      ...............  61
 Addition and subtraction   ............  61
 Multiplication and division   ...........  63
 Solve the problems    .....................  66

7  FRACTIONS    ...............................  69
 Recognise mixed numbers and
          improper fractions     .................  69
  Relationship between improper
          fractions and mixed numbers   ..  73
 Addition of fractions   ....................  77
 Subtraction of fractions   ...............  80
 Addition and subtraction
      of fractions    .............................  83
 Solve the problems    .....................  86

8   DECIMALS   ..................................  89
 Recognise decimals    ................... 89
 Relationship between fractions
          and decimals    .........................  92
 Compare decimals    .....................  94
 Addition of decimals    ..................  96
 Subtraction of decimals   ..............  98
 Multiplication of decimals  ............ 100
 Division of decimals    ................... 102
 Solve the problems    ....................104

9 PERCENTAGE    .............................109
 Relationship between
          percentages and decimals   .... 109

SELF-TEST    .................................. 113

1  NUMBERS UP TO 100 000  .........   1
 Recognise number    ......................    1
 Numbers explore    ........................  4
 Place value and digit value   ........  4
 Partition numbers    ......................  5
 Numbers value   ...........................  7
 Estimate quantity    ....................... 10
 Number patterns   ....................... 12
 Round off numbers   ..................... 14

2  ADDITION   ................................. 17
 Addition     ..................................... 1 7
  Solve the problems    ................... 22
 Unknown in addition   ................. 25

3   SUBTRACTION   .......................... 29
 Subtraction   ................................. 29
 Subtract consecutively  ................ 31
 Solve the problems  ..................... 34
 Unknown in subtraction     ........... 37

4  MULTIPLICATION    ....................41
 Simple multiplication    .................41
 Let’s multiply     .............................44
 Solve the problems    ....................48

5 DIVISION    ................................51
 Simple division    ...........................51
 Let’s divide   ..................................53
 Solve the problems    ....................57

iii

CONTENTSCONTENTS
iv

10 MONEY   ........................................117
 Combination of money     ............ 1 1 7
 Round off values of money   ........ 1 19
 Addition of money     .................... 121
 Subtraction of money    ................1 23
 Addition and subtraction of money ..125
 Multiplication of money    ............. 127
 Division of money    ..................... 129
 Solve the problems    ....................1 31
 Recognise foreign currency   ....... 137
 The value of foreign currency ...... 140
 Payment instruments    ................. 141

11 TIME    ........................................... 145
 Recognise time    .......................... 145
          Day and hour    ........................ 145
          Week and day   ....................... 147
          Year and month    .................... 148
 Addition of time     ......................... 150
 Subtraction of time    .................... 153
 Multiplication of time     ................. 156
 Division of time    .......................... 159
 Solve the problems    ................... 161

12 LENGTH    ......................................165
 Recognise units of length    .......... 165
 Relationship between centimetres and
     millimetres    ............................. 166
 Relationship between kilometres
     and metres    ............................ 167
 Measure length of objects    ......... 168
 Estimate distance    ...................... 169
 Addition of length     ..................... 171
 Subtraction of length    ................. 174
 Multiplication of length   .............. 176
 Division of length    ....................... 178
 Solve the problems    .................... 180

13 MASS    ..................................187
 Addition and subtraction of
     mass   ............................... .187
 Multiplication and division of
     mass     ............................... 190
 Solve the problems   ..............193

14  VOLUME OF LIQUID   ..........197
 Addition and subtraction of
     volume of liquid   ............... 197
 Multiplication and division of
     volume of liquid   ...............200
 Solve the problems    .............203

15  SPACE   ..................................207
 Recognise angles   ................207
      Recognise lines  ....................209
      Parallel lines    ..................209
          Perpendicular lines    .........210
 Perimeter    ............................212
 Area    ...................................214
 Volume      ..............................217

16 COORDINATES    ...................221
 Recognise position    ..............221
 Determine the position   .........226

17  RATE    ...................................229
 Rates    ..................................229

18 DATA HANDLING    ..............235
 Recognise and compare
 information    ........................235
  Pictograph    ....................235
  Bar chart    ........................237
  Pie chart   .........................239

SELF-TEST    .............................243

ANSWERS    ............................249
The publication of the Standard-Based Curriculum for Primary Schools (KSSR) textbooks has moved
forward to Level 2 with the publication of Mathematics Year 4 KSSR Textbook. The writing of Mathematics
Year 4 Textbook pursues the goal of KSSR based on the National Philosophy of Education and the
National Education Policy, and taking into consideration of the 21st century challenge, New Economic
Model (MBE) and the latest learning theories. The Mathematics Year 4 Textbook stresses on the moulding
of a balanced human capital from the aspects of physical, emotion, spiritual, intellect and social.
To ensure that the vision is achieved hence the elements of EMK, namely Creativity and Innovation,
Entrepreneurship and Information Technology and Communication inclusive of the existing elements
are embodied to complete the efforts of strengthening the quality of the future human capital to drive
Malaysia as a developed nation.

The Mathematics Year 4 Textbook consists of 18 topics that are arranged in parallel with the Standard-
Based Curriculum for Primary Schools (KSSR) Year 4 published by the Curriculum Development Division,
Ministry of Education. The content of the textbook delivers the knowledge of concepts and skills that
contains of pupil-centered activity Learning Standards. The content of the book is equipped with formative
and summative exercises to help pupils acquire and reinforce the skills learnt, and helps teachers to
evaluate the level of pupils’ acquisition of a certain topic.

The Mathematics Year 4 Textbook functions as a complete and fun learning source with teacher’s notes
which provide ideas for teachers to plan an effective teaching and learning activites. The suggestions on
surfing suitable websites help pupils to apply the usage of information technology in learning. Teachers
need to encourage pupils to think and answer questions posed by the mascots to acquire the process
of reasoning. The Brain Teaser activities help to develop critical and creative thinking thus enhancing the
Higher Order Thinking Skills (HOTS). In addition, the Mind Stretcher which acts as a summative exercise
matches the School-Based Assesment (SBA), HOTS and TIMSS (Trend in International Mathematics and
Science Study).

The Mathematics Year 4 Textbook is also designed to be a fun learning tool with reinforcement and
enrichment activities incorporated in games and projects. The content of the book also inculcates unity
through national integration which are presented by various race and ethnic characters. The usage of
this Mathematics Year 4 Textbook will be more effective if the functions of characters, mascots and icons
are fully understood.

v

INTRODUCTIONINTRODUCTION
Enrichment activity.

Encourage critical and creative
thinking.

Recreational activity with individual
title incorporating the elements
of fun learning and HOTS.

Formative exercise to evaluate the
acquisition of the new skill learnt.

Summative exercise.

Revision exercises to enhance
pupils’ understanding.

Lists of answers for
Mind Booster and Self-Test.

TOPIC
Topic based on
learning area.

SUBTOPIC
Mathematical skills
to be acquired.

MASCOT
Poses questions that stimulate
pupils’ mind to encourage
reasoning.

CONTENT STANDARD
AND LEARNING STANDARD
As per in Year 4 Mathematics
KSSR document.

INFORMATION
Key information in learning
activities.

Additional activity guidance.

Suggested websites.

10.1 (i)

2 ADDITIONADDITION

vi

FUNCTIONS OF ICONS
IN TEXTBOOK

FUNCTIONS OF ICONS
IN TEXTBOOK

Writers

TEACHER’S
NOTES  ANSWERS ANSWERS

INFORMATION

Say the first two
numbers followed
by the next three
numbers.
1

TEACHER’S
  NOTES

Read and say the numbers on computer display, flash cards and newspaper
      cuttings correctly.
"

1.1 (i)

School1

1

NUMBERS UP TO
100 000
NUMBERS UP TO
100 000

Recognise number

49 562

Ten thousand and
eighty boxes will be
sent to Zone B.

Forty-nine thousand
five hundred and sixty-two

81 104

93 006

64 205

17 017

What is the purchase quantity of Zone C?

Say the numbers written
on this board.

What is the purchase quantity of Zone D and Zone E?

Say the first two
numbers followed
by the next three
numbers.

INFORMATION

Zone A purchased twenty thousand
and four hundred boxes.
2

TEACHER’S
  NOTES

Thirty
 thousa

nd

and
 twenty-
nine

Say and write numbers from various sources including the Internet.

http://www.ixl.com/math/grade-6/place-values-in-whole-numbers

"

1.1 (i)

2

3

4

17 801 Eighty-three thousand
and fifteen. 83 015

Seventeen
thousand eight
hundred and one.

Thirty-nine thousand
   and forty-four

AT A GLANCE

On 15   Oktober 2012

Felix
Baumgartner
from Australia succeeded in breaking the

world record
after the diving from the stratosphere at
the height of

39 044 m
as comparison, the Everest Mountain
is only 8848 metres high while the normal
altitude of the commercial flight is at
11 000 metres.

He also made a record of free

diving
at the lowest level of 29 metres only
from earth, which is from a statue
monument in Brazil in 1999.

th

AT A GLANCE

On 15   Oktober 2012

Felix
Baumgartner
from Australia succeeded in breaking the

world record
after the diving from the stratosphere at
the height of

39 044 m
as comparison, the Everest Mountain
is only 8848 metres high while the normal
altitude of the commercial flight is at
11 000 metres.

He also made a record of free

diving
at the lowest level of 29 metres only
from earth, which is from a statue
monument in Brazil in 1999.

th

Source: Utusan Malaysia. 8th December 2012

Write the number represented
on the spike abacus in words
and numerals.
3

TEACHER’S
  NOTES

Create six 5-digit numbers starting with     . The

two        digits must be next to each other. Say and

write the numbers.

Make a scrapbook of 5-digit numbers from newspaper or magazines.
      Rewrite the numbers in words.
"

1.1 (i)

8 1

0

2
0

5

2  Write the numbers in words and numerals.
   a       b

Forty thousand and
twenty-nine

Which card matches
the number word?

Ten     Thousands  Hundreds   Tens     Ones
thousands

Ten      Thousands  Hundreds   Tens    Ones
thousands

40 20942 009 40 029

Number    Words

69 810

44 007

17 602

Ninety-five thousand and ninety-one

Fifty thousand and thirty-four

8

0

1  Complete the table.
4

TEACHER’S
  NOTES

Use number cards to identify and write the place value and the digit value. "

1.1 (ii)

1

2

Numbers explore

19 365

Nineteen thousand three
hundred and sixty-five

Place value of 9 is
thousands. The digit
value of 9 is 9 000.

Place value of 1 is ten
thousands. The digit value
of 1 is 10 000.

State the place values and the digit
values of 3, 6 and 5.

Place value and digit value

95 702

Complete the place value and the digit
value of this number.

Every digit in a number has a
place value and digit value.

Digit

Digit

Place value

Place value

Digit value

Digit value

1

9

90 000 700 0

5

thousands

7 0 2

10 000

ten

thousands

thousands hundreds tens ones

9

9 000

3

300

6

60

5

5

The Number 19 365

Ten     Thousands  Hundreds   Tens      Ones
thousands
5

TEACHER’S
  NOTES

40 609 = 4          + 0 thousands + 6 hundreds +
        0         + 9

Discuss the difference between partitioning into place value and digit value.

http://www.ixl.com/math/grade-6/place-values-in-whole-numbers

1.1 (iii)

What is the number for this expanded form?

1

2

Partition numbers

5 ten thousands + 0 thousands + 7 hundreds + 6 tens + 2 ones

50 000 + 700 + 60 + 2

The number is fifty thousand
seven hundred and sixty-two.

Can 40 609 be partitioned into
600  + 40 000 + 9? Explain.

"

Partition 73 519 according to the place value and digit value.

Partition 40 609 into place
value and digit value.

ten thousands thousands hundreds tens ones

7              3            5            1          9

partitioning

partitioning

Place value

Digit value

Place value

Digit value

73 519 = 7 ten thousands + 3 thousands +
               5 hundreds + 1 tens + 9 ones

partitioning

partitioning

73 519 = 70 000 + 3 000 + 500 + 10 + 9

40 609 = 40 000 +           +          +           +

50 762

Partitioning number is to write number
in expanded form according to the place

value or digit value.

INFORMATION

Ten     Thousands  Hundreds  Tens   Ones
thousands
6

TEACHER’S
  NOTES

http://www.bbc.co.uk/bitesize/ks2/maths/number/place_value_headings/play

1.1 (iii)

hundred         ten         thousands  hundreds  tens  ones
 thousands  thousands

10               0              0         0       0

hundred         ten         thousands  hundreds  tens  ones
 thousands  thousands

1                   0               0              0         0       0



1 hundred thousands = 100 000

10 ten thousands
equals 1 hundred
thousands.

Are 17 thousands and 170 hundreds have the same value? Explain.

a    11 261         b    38 617        c    61 582      d    96 453

10 ten thousands  = 100 000

c

7
4
1

0 .

2 3

5 6
8 9

–

x

=

÷

4

3

The buttons   3   and  6   of this calculator is
 not functioning. Show two ways to display the
 number 43 769 using partitioning.

1    Write the place value and digit value of 6 in each number.

2   Complete these.
      a   14 735, the digit in the ten thousands place is           .
      b   37 601, the digit           is in the hundreds place.
      c    5          9          2  , the digit 1 is in the tens place and digit 8 is in the

thousands place. What is the number?

3   Complete these.
      a   800 + 4 000 + 60 000 + 5 =
      b   50 000 + 5 000 + 8 =
      c              = 0 hundreds + 2 ten thousands + 0 ones + 9 thousands + 2 tens
7

TEACHER’S
  NOTES

Compare the value of numbers using the spike abacus or abacus. "

1.1 (iv)

Which bicycle has the highest and the lowest sale?

Bling is the highest in sale.

Aki is the lowest in sale.

1

How about the arrangement of numbers in descending
order? Explain.

The arrangement of the numbers above is in ascending
order. The value of numbers increases from left to right.

Numbers value

Arrange these numbers on the number line.

Sales

12 600 units 11 800 units 12 200 units 13 400 units

ZEES AKI MOMO BLING

11 600 11 800      12 200 12 400 12 600  12 800          13 200   13 400
12 000             13 000

Aki Momo Zees Bling

11 800, 12 200, 12 600, 13 400Ascending order

13 400, 12 600, 12 200, 11 800Descending order
8

TEACHER’S
  NOTES1.1 (iv)

Compare and arrange numbers using flash cards."

2 Arrange these numbers in ascending and descending order.

Step 1     Find the smallest value.

Step 2     Find the largest value.

Look at the digit in the
ten thousands place.
The digit 3 is the
largest. So, 30 469 is
the largest value.

3 078 is the smallest
value because it has
only four digits.

Ascending order

30 469, 26 115,            , Descending order

, 26 105,           ,

26 105 3 07830 469 26 115

ten
thousands

ten
thousands

ten
thousands

thousands

thousands

thousands

hundreds

hundreds

hundreds

tens

tens

tens

ones

ones

ones

2

3

2

6

0

6

3

6

0

6

6

6

1

4

1

0

1

4

1

1

1

0

6

1

7

0

6

1

5

9

5

8

5

9

5

5

5

2

3

2

2

2

The value of digits in the
ten thousands, thousands
and hundreds places are
the same. So, look at the
digits in the tens places.
The value of digit 1 is more
than 0. So, 26 115 is
more than 26 105.

0

1
9

TEACHER’S
  NOTES

9

Materials    Number wheel,       Players    4 pupils

1 Determine each player᾽s turn.

2 Spin the wheel 5 times according to the player᾽s turn.

3 Record the numbers on a piece of paper.

4 All 4 players compare their numbers.

5 Arrange the 4 numbers in ascending order.

6 Repeat steps 2 to 5.

7 Then arrange the numbers in descending order.

1 Say the smallest number.

a   72 210, 82 118, 74 450  b   13 622, 13 066, 13 226

c    28 976, 27 312, 29 115  d   70 629, 76 431, 62 725

2  What is the largest number?

a            b           c

3    Arrange the groups of numbers in:
 a    Ascending order

b    Descending order

Use the numbers created by pupils in Number Tracking activity to reinforce
       the skills of comparing values of numbers.

http://www.ixl.com/math/grade-3/put-numbers-in-order

"

1.1 (iv)

Steps

pen, A4 Paper.

1

2

3
4

56
7

8

9
0

40 049

49 032

40 900

11 642

11 634

11 694

93 820

93 208

91 330

76 732, 71 845, 76 855, 78 237

ii 94 001, 83 109, 42 870, 67 237, 74 324

i

3 065, 28 165, 3 402, 29 892i

14 321, 29 109, 18 001, 27 237, 14 324ii
10

TEACHER’S
  NOTES

Estimate the number of chocolates in jar B.

2    What is the estimated number of beads in jar Q?

The estimated number of beads in jar Q is
                                 between 450 pieces to         pieces.

1.2 (i)

Discuss the importance of estimation in everyday life.

"

A

---------------------

---------------------

---------------------

P Q

150 pieces

400 pieces

A B

B

The chocolates in jar B is less
than 400 pieces.

1

The number of chocolates in jar B is about 200 pieces.

Jar A consists of 400
pieces of chocolates.

Estimate quantity

Almost half of jar B is filled
with chocolates.

The beads in jar Q is
more than 150 pieces.
11

TEACHER’S
  NOTES1.2 (i)

3  Estimate the volume of water in tank Y.

The estimated volume of water in tank Y is about 60 litres.

Complete the reasonable estimates of quantities.

How do you determine the estimated volume
of water in tank Y is reasonable? Discuss.

20 litres  litres

x

Y

Introduce words related to estimation such as more than half, almost full,
more or less, about and approximately.
Carry out simulation for estimation activities.

"

"

The volume of water
in tank Y is more than
the volume of water in
tank X.

a

c d

600 cm
60 mm

150 pieces

b

--------

--------

-------------

60 kg

The number of chocolates in jar B is about 200 pieces.
12

TEACHER’S
  NOTES1.3 (i)

5 600 5 800 6 100 6 500

9 000 8 600 8 4008 800

12 742 12 342 12 142  12 542

16 066 16 266 16 966   16 566

20 153  20 157 20 161  20 165

+ 4 + 4 + 4

17 028  17 032 17 036 17 040

+ 4 + 4 + 4

66 137  66 127 66 117  66 107

– 10 – 10 – 10

11 242  11 232   11 222  11 212

– 10 – 10 – 10

How do Zeti and Johan classify their number sequences?1

Discuss the two number cards that have not been classified in the stimulus picture.
Prepare sets of cards or use number lines with various patterns to carry out number
pattern activities.

"
"

The patterns for these
two sets of number cards
decrease by tens.

In these two sets of
number cards, the
patterns increase by fours.

What about these two sets
of number cards?

Group the number
sequence based
on its pattern.

Number patterns
13

TEACHER’S
  NOTES

Find information about the speciality of Fibonacci sequence by
surfing the related websites.
"

1.3 (ii)

2 What are the following numbers in this number pattern?

a

b

Study this number pattern. What are the 10th and the 15th numbers?

1    Group the number sequence according to the same pattern.
       a           b

2    Complete the number sequence.
 a    300, 600, 900, 1 200,       ,         ,

b    907, 892, 877,        , 847,         ,

3     D o  7 077 and 7 112 belong to the number sequence of
       7 007, 7 017, 7 027, 7 037, 7 047? Show it.

This number pattern is minus 23.

+2 +3

1 1 2 3 5 8 13 21

34

10 201 10 178 10 155

– 23

17 845, 17 835, 17 827, 17 821

11 077, 11 143, 11 209, 11 275

54 306, 54 372, 54 438, 54 504

10 001, 9 991, 9 983, 9 977

26 007, 26 507, 27 507, 28 007

80 000, 79 550, 79 100, 78 650

11 350, 11 850, 12 850, 13 350

15 050, 14 600, 14 150, 13 700

25 003       25 005                         25 012

This is Fibonacci
number sequence.

INFORMATION
14

TEACHER’S
  NOTES

•  Look at the digit to the right of
 ten thousands place.
•  The digit 2 is in Group    .
•  Retain the digit in ten thousands place.
•  Change the digits in ones, tens, hundreds
 and thousands place to 0.

1.4 (i)

1 Round off the quantity of Jumbo detergent bought in January to the
nearest ten.

19 862 rounded off to the nearest ten is 19 860.

2 Round off 32 716 to the nearest ten thousand.

Discuss rounding off numbers done by the workers in stimulus picture.
 Practise rounding off based on the information given.
 Emphasise the importance of rounding off in everyday life.
"
"

"

19 860 19 87019 865

19 862

1 862 is nearer to 1 860.

Round off the quantity of detergent Jumbo bought
in the month of February to the nearest thousand.

Round off numbers

About 19 900
boxes.

• If the digit on the right is in Group    ,
 retain the digit to be rounded.
• If the digit on the right is in Group    ,
 add 1 to the digit to be rounded.
•  Then change all digits on the right
 to 0.

Group            Digit
             0, 1, 2, 3, 4
            5, 6, 7, 8,

What is the quantity
of detergent bought
in January?

3              0           0   0        0

ten
thousands

thousands hundreds tens ones

3 2 7 1 6







INFORMATION

Jimat Supermarket Purchase of Jumbo Detergent
Month

January

February

March

Quantity

19 862

11 257

12 999

32 716 rounded off to the nearest ten thousand is 30 000.
15

TEACHER’S
  NOTES

Drilling exercise to identify numbers that can represent a given number rounded off
to the nearest ten, hundred, thousand and ten thousand.
"

1.4 (i),(ii)

Why the number of citizens in Pokok Sena,
Kedah is not mentioned? Discuss.

40 637

30 000 35 000
40 000

44 999

45 000 50 000

36 192
43 011

38 471
49 506

-------------------------- --
--

--
--

3 Will the number of citizens in all districts be 40 000 people when
rounded off to the nearest ten thousand?

The number of citizens in Tongod, Cameron Highlands, Jeli and Rembau
will be 40 000 people when rounded off to the nearest ten thousand.

The numbers 35 000 to 44 999 become 40 000

when rounded off to the nearest ten thousand.

1  Round off the following numbers to:

2  Give two numbers which become 52 300 when rounded off to the
    nearest hundred.
  3  Which largest number becomes 90 000 when rounded off to the
   nearest ten thousand?

Rembau, Negeri Sembilan: 43 011
Cameron Highlands, Pahang: 38 471
Jeli, Kelantan: 40 637
Pokok Sena, Kedah: 49 506
Tongod, Sabah: 36 192

Source: Malaysia Population
   Census 2010

Number

67 369

10 065

Nearest
ten

Nearest
hundred

Nearest
thousand

Nearest
ten thousand

Let᾽s identify the
district with about
40 000 people.
16

TEACHER’S
  NOTES

40, 1 970, 50 50, 1 970, 60 1 970, 40, 1 960

61 033 58 600 54 600 62 000 67 114          55 321

a b

1    Write the numbers in numerals or words.

a   28 603        b   50 901  c   Forty-seven             d     Eighty thousand
                         thousand and eleven    and twenty-five

2   State the place value and digit value of 5.
     a   75 603        b   54 284  c   12 532                 d   83 158

3   Partition each number according to the place value and digit value.

a   26 317         b   62 839   c   70 116                 d   34 001

4   Compare the numbers. Arrange them in ascending order and
     descending order.

a    34 461         39 562        30 561        34 726        39 894

b    90 425        97 281         89 372        90 753        87 201

5   Write the estimates for the following quantities.

6   Group these numbers according to the patterns.

7   2 000 , 20 , 1 990 , 30 , 1 980 ,           ,           ,
     Which number group completes the number pattern above?

8   Which of these numbers becomes 60 000 when rounded off to the
     nearest ten thousand?

a cb

13 116   13 136  13 156  13 176

125      375     1 125   3 375 64 109  64 129  64 149  64 169

1 041     3 123    9 369   28 107

16

150 books 13 000 mℓ
17

TEACHER’S
NOTES

WELCOME TO

RESERVED FOREST

School

VISIT MALAYSIA YEAR

Relate other daily situations involving addition.
Tell stories about experiences of visiting certain places which can be
related to addition.2.1 (i)

1  What is the total number of
  tourists in June?

5 806 + 21 345 =

5 806 + 21 345 =  27 151

The total number of tourists in June is 27 151.

The number of tourists in July is 3 650 more than the previous
month. Calculate the total number of tourists for the two months.

ADDITIONADDITION
2

Addition

ten thousands

2

2

thousands
1

1
5

7

hundreds

3
8

1

ones

5
6

1

tens
1

4
0

5

+

In June, 5 806
local tourists
visited this place.

Foreign tourists
were 21 345.

5

1
6

4

5
0

1

7
5

3

1
8

2

2
+

1 1
18

TEACHER’S
NOTES

Use Diene’s block, place value chart and number cards to carry out addition
activities in pairs or groups.

Use abacus skills and mental calculation from the largest to the smallest value
 (left to right).
 http://interactive.onlinemathlearning.com/chain addition.php?action=generate
 &numDigits=5&numAddends=3&numProblems=8

2  Below are the number of leaflets distributed according to zones.

Calculate the number of all leaflets.

21 407 + 15 854 + 893 =

21 407 + 15 854 + 893 =   38 154

The number of all leaflets is 38 154.

3   Add up 42 313, 905 and 6 450.

42 313 + 905 + 6 450 =

42 3 13        40  000  +  2 000  +           300          +  1 0  +  3

905         900          +    0   +  5

6 450      +                         6 000  +           400          +  50  +  0

40 000   +  8 000  +        1 600        +  60   +   8

40 000   +  8 000  +    1 000 + 600   +  60  +  8  =  49 668

42 313 + 905 + 6 450 =   49 668

The total of  42 313, 905 and 6 450 is 49 668.

2.1 (i)

2   1    1

2 1   4 0 7
    1 5   8 5 4
+    8 9 3

3 8   1 5 4

Partition
numbers
according
to the digit
value and
add up.

Which is faster, 8 + 8 or 2 × 8? Why?

Add the 10 addends and
add the same digits.

Central
Zone

15 854
sheets

North
Zone

21 407
   sheets

East
Zone

893
sheets
19

TEACHER’S
NOTES

1    1  1

4 1   0 4 5
+     3  9 5 5

4 5  0 0 0

1   1

2 4  0  1 1
+          8 9

2 4  1 0 0

Use the 10 addends for suitable numbers to calculate faster.
 Use simpler number analogy to enhance pupils’ understanding.

2.1 (i)

4  Calculate the total number of souvenirs
  sold as shown.

53 139 + 2 481 + 27 641 =

53 139               53 000
                                  2 481         2 000
                          +  27 641           +  28 000

83 000

1 1  1  1

53 139
                          2 481
                    + 27 641

83 261

83 261 is close to 83 000. So, the answer is reasonable.

53 139 + 2 481 + 27 641 =   83 261

The total number of souvenirs sold is 83 261.

5  Add 41 045, 89, 3 955 and 24 011.

41 045 + 89 + 3 955 + 24 011 =

Method 1           Method 2

41 045 + 89 + 3 955 + 24 011 =   69 100

27 641

Then,
add up.

Estimate the answer
by rounding off to the
nearest thousand.

4  1   0 4 5
   2  4  0  1  1
       3  9 5 5
+            8 9

2 0
           1 8 0
           9 0 0
      8   0 0 0
+ 6 0   0 0 0

6 9  1 0 0

2 481

53 139

Does the total of  4 859, 1 273 and 4 902 give a 4-digit answer?
Estimate the answer and explain.

19

Key
chain Magnet

Postcard

4 5  0 0 0
 + 2 4 1 0 0

6 9  1 0 0

Add up the two
subtotals.

1

1
20

TEACHER’S
NOTES

Encourage pupils to surf the Internet to know about the number of tourists visiting
 places of interests in Malaysia.
 Use number cards randomly or magic square to create addition number sentences
 and solve them.

2.1 (i)

6

Calculate the number of tourists in Gunung Kinabalu.

3 500 +             + 8 211 + 20 015 = 38 219

1                         1      1

2 0  0  1  5      3  1    7  2  6
      8  2  1  1          +      6    4  9  3
         +    3  5 0 0

3 1  7 2 6

3 500 +  6 493   + 8 211 + 20 015 = 38 219

The number of tourists in Gunung Kinabalu is 6 493 people.

Use the numbers 4 830 up to 4 836.

Fill in the  so that every row has

the same total.

Number of tourists

3 500

?

8 2 1 1

20 0 1 5

38 219

Interesting places in Sabah

Pulau Sipadan

Gunung Kinabalu

Kolam Air Panas Poring

Pasar Kraf Tangan
    Kota Kinabalu

Jumlah

3  8    2  1  9
21

TEACHER’S
NOTES2.1 (i)

Materials

Cards, pen.

Steps

1 Choose a leader.

2 Leader says the numbers 0 to 9
 randomly 14 times. Numbers can be repeated.

3 Each player writes the numbers in the blank square cards.

The numbers written cannot be erased.

4 Each player adds up their numbers respectively.

5 The largest answer is given 2 marks.

6 Repeat five times the steps 2 to 5.

7 Player with the highest score is the winner.

1 Add.

a    40 217 + 3 521 =

b    34 608 + 735 + 11 329 =

c             = 71 026 + 451 + 16 290 + 9 132

d           + 638 + 2 147 = 41 211

e    6 291 + 24 310 + 8 654 +         = 90 000

2 State the number 1 000 more than 56 821.

3 Find the total of 27 048, 19, 5 084 and 3 617.

4

14 650           P    14 950   15 100     Q              R

Find the total value of P, Q and R based on the number line above.

21

+
22

TEACHER’S
NOTES

Solve problems by drawing diagram or trying a simpler case.
 Use various strategies in calculation.

http://interactive.onlinemathlearning.com/chain addition.php?action=generate&
 numDigits=5&numaddends=3&numProblems=

2.2 (i)

Calculate the total number of tourists from Singapore and China.

1

Source: MASB, Sabah/Immigration Department, Sabah/AirAsia

The table above shows the number of tourists visiting Sabah from 3
  countries. What is the total number of tourists?

Given            The number of tourists from Singapore is 10 127,
                   Japan 8 839 and China  71 152.

Find               The total number of tourists.

Operation    Addition.

Solve        10 127 + 8 839 + 71 152 =

1  1   1 1

7 1  152
                     10 127
                          +    8 839

90 1 18

Check     10 127   10 000
          8 839             9 000
        71 188  71 000
        10 000 + 9 000 + 71 000 = 90 000
        90 118 is close to 90 000.
        The answer is reasonable.

10 127 + 8 839 + 71 152 =   90 118

The total number of tourists is  90 118.

The number of tourists in Sabah (Jan – May 2012)

Countries

Singapore

Japan

China

Number of tourists

10 127

8 839

71 152

Solve the problems

Check the answer
by estimating to the
nearest thousand.

Taman
Bukit

Tawau

Kudat

Tawau

Kota Kinabalu

S  A  B  A  H

Tanjung Aru

Batu Punggul

Gua Gomantong

Gua Madai

Pulau Langkayan

Pulau
    Tiga

Pulau
Layang-Layang

Pulau Sipadan
Pulau Mabul

Taman Laut
Pulau Penyu

Orang Utan
Sepilok

Gunung
Kinabalu
23

TEACHER’S
NOTES

1
    1  0  5 8 5
+ 8 5  5 0

9 6  0 8 5

Use the simplifying method to solve more complex problems.

2.2 (i)

The total number of beads in the yellow and green
containers is calculated this way. Is it correct? Explain.

Container

Total

Number of Beads

10 285

300 more than
blue container

?

29 420

13
                 1    1             8     3  12

1  0   2  8 5          2 9  4 2 0
+ 1  0  5 8 5          – 2 0  8 7 0

2 0  8 7 0         8  5 5 0

Is there a
different way
to check the
answer?

Check

10 385, 10 485, 10 585.

Calculate the number
of beads in the yellow
container first. The
yellow container
contains 10 585 beads.

Gua Madai

Construct a table.

2  The number of beads in three containers is 29 420. The blue
  container contains 10 285 beads. The number of beads in the

yellow container is 300 more than those in the blue container.
   What is the number of beads in the green container?

10 285 + 10 585 +             = 29 420

1    2    1

1  0   2  8 5
     1  0  5 8 5
   +     8  5 5 0

2 9 4 2 0

10 285 + 10 585 +   8 550   = 29 420

The number of beads in the green container is 8 550.
24

TEACHER’S
NOTES

Solve.

1 In conjunction with the “Green Earth” campaign, 17 020 trees are
 planted in Petaling Jaya and 8 960 in Shah Alam.
 What is the total number of trees planted?

2

Calculate the number of cards received by the two post offices.

3        Fruit Juice Sale
           Joha Supermarket    a    Calculate the sale of juice in:
                       i   January     ii   February   iii  March

b    Find the total sale of:
                i   orange juice    ii   apple juice
                in 3 months.

4          The number of visitors to Computer Gadgets Carnival

a    Calculate the number of visitors from the first to the third day.

b    Which two days total up to the same number of visitors as on the
   second day?

5 The total order for the three items below is 80 980 units. Calculate the
order for    Malaysia badges.

Day

Number of visitors

First

25 708

Third

16 420

Second

41 320

Fourth

15 612

Post office

Number of cards

Seri Setia

42 317

Seri Aman

3 682 more than Seri Setia

? 39 480 27 852

2.2 (i)
24

Juice

Orange

Apple

January

10 527

9 368

February

8 745

12 689

March

13 631

7 239

Number of cartons
25

TEACHER’S
NOTES

1

9 add up to a certain number of pages is 20

9 plus how many is 20

9 +         = 20

unknown

2
 The number of cup cakes in the opened
 box is not known.
 The number of cup cakes in the closed
 box is 70 pieces.
 The total number of cup cakes is 150
 pieces.

The quantity of cup cakes that is not
 known is unknown.

Carry out simulation activities to identify the unknowns.

Yesterday, I read 9
pages of this storybook.
Today, I read a certain
number of pages. I
have read 20 pages
altogether.

The certain number
of pages that you
read today is called
unknown.

2.3 (i)
2.4 (i)

Unknown in addition

9 + ✩ = 20

Is the number sentence      + 70 = 150  suitable? Explain.

Can I write this
way?



70 pieces

Unknown means
a quantity that is

not known.

INFORMATION
26

TEACHER’S
NOTES

3 382 boys and girls took part

in the    Malaysia aerobic exercise.

Identify the unknowns and write the number sentences.

a A generous man donated a number of storybooks and 510
magazines to a library. The total number of reading materials
donated is 1 000 books.

b A company printed 30 800 newspapers. 14 530 of them are Bahasa
Malaysia newspapers and the rest are English newspapers.

c 10 000 terrapin eggs are collected. 1 620 eggs are sent to
 Bota Terrapin Breeding Centre and the rest are sent to
 other terrapin breeding centres.

d  The Solar System consists of 8 planets. All the planets have moons
except for 2 planets, namely Mercury and Venus.

e The total number of adult and child spectators who watched a charity
concert was 865.

What are the
unknowns for the
sentence above?
Write the number
sentence.

Create worksheets using math.com.

http://www.mathdrills.com/algebra.shtml2.3 (i)
2.4 (i)

The unknowns are the number
of boys and the number of girls.

B   +   G   =  382
27

TEACHER’S
NOTES

Customise activities according to pupils’ ability such as using a calculator.

Question card

a. 9 435 + 10 712 + 28 516
b. 36 107 + 683 + 7 245
c. 89 + 21 904 + 30 037 + 8 006
d. 24 036 + 7 813 + 694 + 61 048

Materials

Question card, MS Excel software.

Steps

1 Execute MS Excel.

2 Type the number 9 435 in A1 cell, 10 712 in B1 cell, 28 516 in C1 cell.

3 a   Enter the formula in D1.
      Type the formula = A1 + B1 + C1

or

b   Click the menu Sum.

4 Click Enter to get the total.

5 Repeat steps 2 to 4 for other questions.

6 Save the worksheet in Mathematics file.
28

TEACHER’S
NOTES

1 Add.
 a   10 314 + 7 253 =   b   65 127 + 19 095 =

c   27 681 + 2 103 + 936 =  d   40 128 + 76 + 379 + 18 127 =

e   5 342 +         + 28 107 = 90 146

f    50 018 + 9 634 +          + 250 = 70 000

2     Use the same number cards to create the largest
     and the smallest numbers. Find the total.

3    a   Find the total value of the underlined digits.

b   What value must be added to 62 475 to get a total
         value of 84 900?

4

Find the values of P and Q. Then calculate the total of the four numbers.

5 Solve.
 a   Roti Enak Company sold 4 570 kaya buns, 12 914 cheese buns

and 8 695 red bean buns in a month. Calculate the total
     number of buns sold.

b  Below is the number of visitors at an international book fair.

i   Calculate the number of visitors on the first and second days.

ii   How many visitors should be there on the fourth day to reach
       the target of 1 hundred thousand visitors?

6 Identify the unknowns and write the number sentences.
 a   Pak Din sells 40 chocolate ice creams and some durian

ice-creams. The total number of ice creams sold is 260.

b   The total number of chickens and ducks reared by a farmer

is 1 280.

21 060 P Q

62 475

20 960

0 1 6 3 8

28

Day

Number of visitors

First

21 382

Third

27 639

Second

20 407

Fourth
29

TEACHER’S
NOTES

School3

3.1 (i)

Relate various examples of daily situations in business involving subtraction.
 Subtract using coloured chips that represent the values of ten thousands,

thousands, hundreds, tens and ones.

1

a    How many black tablets left?

12 654 – 2 664 =

12 654 – 2 664 =   9 990

The number of black tablets left is 9 990 units.

b    What is the difference between the number of black tablets that is
     left and the number of white tablets?

24 396 – 9 990 =

24 396 – 9 990 =  14 406

The difference between the number of black tablets that is left
       and the number of white tablets is 14 406 units.

Subtraction

SUBTRACTIONSUBTRACTION

1  13   13
    2 4   3 9 6
–     9   9 9 0

1 4   4 0 6

Total: 12 654 units
Sold: 2 664 units

Total: 24 396 units

29

INFOR M AT ION
TECHNOLOGY

CARNIVAL
  2014

ten
thousands

thousands hundreds tens ones

1
0 1

11 15
5 15

2
2
9

6
6
9

5
6
9

4
4
0

–
30

TEACHER’S
NOTES

Materials

MS Word, 4 sets of digit groups.

Steps

1 Create empty boxes using MS Word.

2 Fill in numbers from one digit group
 given in the empty boxes to find the
 largest difference as in the example.

3 Add up all the digits of the answer.

4 Repeat steps 1 to 3 for the other
 digit groups. What do you get?

5 Discuss your findings with friends.

6 Save your findings in Mathematics file.

1 Subtract.

a   72 684 – 1 506 =   b   54 231  –  6 918 =

c   85 734 – 5 744 =   d   90 810 – 10 923 =

2 Solve.

a   Find the difference between  61 245 and 85 609.

b   Reduce 34 567 from 92 154.

c   What must be reduced from 89 462 so that the remainder

becomes 62 000?

3.1 (i)

In pairs carry out Mathematics quiz using MS PowerPoint, to find differences.
  Encourage pupils to create different digit groups to explore the pattern.

7      0      1
 6      2

5      9
0      2      3

1      8      7
6      4

3      6
0      8      3

1 Create empty boxes
using MS Word.

–

7 0  1
 6   2Example:

2
7    6   2   1   0

–   1   0   2   6   7

6   5   9   4   3

3   6 + 5 + 9 + 4 + 3 = 27
31

TEACHER’S
NOTES

1                 Sale of mobile phones at
    Pintar Company

How many mobile phones left?

27 436 – 10 365 – 3 002 =

Method 1
                           3   2  16

1 0   3 6 5          2 7  4 3 6
           +     3  0 0 2               –  1 3  3 6 7

1 3   3 6 7           1 4  0 6 9

Method 2
        3 13
        2 7  4 3 6                       17 071  –   3 002   =
       –  1 0  3 6 5

1 7  0 7  1                         3 000     2

27 436 – 10 365 – 3 002 =  14 069

The mobile phones that are not yet sold is 14 069 units.

3.2 (i)

Encourage pupils to subtract numbers without regrouping before
   subtracting using suitable strategies.

http://interactive.onlinemathlearning.com/subtraction.php?addition=generate&
 numDigits0=1&numDigits1=5&numProblem=

12

27 436

10 365

3 002

Initial amount

January Sale

February Sale

Try to solve. Is the answer
the same?

– 1 0  3 6 5

2 7  4 3 6
–    3  0 0 2

Subtract consecutively

1 7  0 7  1
 –    3  0 0 0

1 4  0 7 1

14 069    14 070     14 071

–1 –1
32

TEACHER’S
NOTES

2  47 504 – 12 996 – 31 500 =

47  504       16 004 – 12 996 =

– 31  500

16  004       16 008 – 13 000 = 3 008

47 054 – 12 996 – 31 500 =   3 008

3   84 125 – 12 950 – 29 760 =

84 125     84 000

12 950      13 000

29 760     30 000

41 415 is close to  41 000.

The answer is reasonable.

84 125 – 12 950 – 29 760 =   41 415

+ 4+ 4

3.2 (i)

Carry out simulation activities involving consecutive subtraction using
 smaller numbers.

Calculate the
actual answer.

8 4  0 0 0      7 1  0 0 0

–   1 3  0 0 0  –  3 0  0 0 0

7 1  0 0 0      4 1  0 0 0

10                                 10

3    0  12                    6    0    11

8 4  1 2 5              7  1   1 7 5

–  1  2  9 5 0           – 2 9  7 6 0

7 1   1  7 5               4 1  4 1 5

Round off the numbers to the
nearest thousand.

Estimate the
answer.
33

TEACHER’S
NOTES

4               – 53 712 – 8 435 = 27 904

1  1                                      1  1        1

2 7  9 0 4          3 6  3 3 9

+    8  4 3 5       + 5 3  7 1 2

3 6  3 3 9          9 0  0 5 1

90 051  – 53 712 – 8 435 = 27 904

1 Subtract.

a   65 437 – 13 025 – 2 302 =      b   94 630 – 46 109 – 9 315 =

c   59 000 – 928 – 8 457 =                   d   86 123 – 609 –          = 2 074

e   72 251 –          – 24 039 = 15 846    f             = 90 010 – 43 617 – 8 255

2
        P         30 600     31 100    Q

Based on the number line, find the value of 80 000 – P – Q.

3 Subtract 52 147 from one hundred thousand, then find the difference

between 37 609 and the answer from the subtraction.

4 What is the difference between the calculation below and
 the actual answer?

82 317 – 4 105 – 290 =

8 2  3 1 7      8 2  2 1 2
             –     4  1 0 5  –         2 9 0

8 2  2 1 2      8 2  0 8 2

3.2 (i)

http://www.adaptedmind.com/v.php?tagld=374

10  –  5  –  3  =  2

10  =  2  +  3  +  5

Can 8 435 be subtracted from 53 712 first,
then added to 27 904? Discuss.
34

TEACHER’S
NOTES

1 A factory produced 13 580 baulu.
 2 250 baulu were donated to old folks
 homes during festive season.
 How many baulu left?

Given           There are 13 580 baulu.
           Donated 2 250 baulu.

Find              Number of baulu left.

Operation    Subtract.

Solve        13 580 – 2 250 =

13 580
                 –   2 250

11 330

Check         Estimate the answer to the nearest hundred.

13 580        13 600

2 250         2 300

13 600 – 2 300 = 11 300

11 330 is close to 11 300.
The answer is reasonable.

13 580 – 2 250 =  11 330

The number of baulu left is 11 330.

3.3 (i)

Solve problems using suitable methods such as simulation activities and diagrams.
 Answer questions on question cards or quiz.

http://www.adaptedmind.com/v.php?tagld=374

Solve the problems

Is there other ways to check the
answer? Explain.

ten
thousands

thousands hundreds tens ones
35

TEACHER’S
NOTES3.3 (i)

Create various questions that can be solved using other methods, such as working
backwards and mantic reasoning.

Why didn’t you choose C?
Explain.

2 The total number of Level 1 and Level 2 participants for Nilam
 Programme is 1 800. The number of Level 1 pupils is 200 less than
 Level 2 pupils. What is the number of Level 1 pupils?
 Which of the following is the correct option of answer?

Option       Level 1      Level 2

A.           1 000            800

B.             800            1 000

C.      900             700

1     The total number of Level 1 and Level 2 pupils must be
         1 800.  Discard C.

2    Find the difference.

Option A: 1 000 – 800 = 200
          Level 1 is 200 pupils more than Level 2.

         Option B: 1 000 – 800 = 200
          Level 1 is 200 pupils less than Level 2.

The number of Level 1 pupils is 800.
                    The correct answer option is B.

I use the trial and
error method.

Gather Informations

Total number of Level 1 and
Level 2 pupils:

1 800

The number of Level 1 pupils:
 200 less than Level 2 pupils

Calculate the number of Level 1
pupils based on the answer options.
36

TEACHER’S
NOTES3.2 (i)

Solve.

a A factory produced 45 190 pieces of compact discs. 32 040 pieces
 have been distributed. Calculate the number of compact discs left.

b The table below shows the number of people in three villages.

i      Calculate the difference between the number of people in
       Desa Setia and Desa Permai.

ii    How many more people are there in Desa Permai compared to
     Desa Murni?

c A publisher has printed 83 460 magazines in April. The
 number of magazines printed in May decreased by 11 235. What is the
 number of magazines printed in May?

d Calculate the number of fishling
 that must be added into the pond so
 that the total becomes 10 thousand.

e

The number of button Q is 7 185 more than button R. The number of
button P is 450 less than button R. Calculate the number of button P.

36

P     Q    R
40 026

1 265 fishlings

Desa Murni

20 920

Desa Setia

50 127

Desa Permai

27 469

Name

Number of
people
37

TEACHER’S
NOTES3.4 (i)

3.5 (i)

Provide more examples of unknowns in subtraction based on everyday life.
  Pupils identify unknowns in given oral statements.

Unknown in subtraction

1

The number sentence is written as

2       A raft of ducks is swimming in a
        bank. 7 of them waddle to the bank.
       10 ducks are still swimming in the

pond.

A raft of ducks is the unknown.

The number sentence is          – 7 = 10

What is the quantity that is not known?

50  –         =  42

Can you substitute         with ?

Please give a few
stamps to your
brother.

Mother, I have
collected 50
stamps of various
countries.

Brother, please take a few
stamps. I still have 42 stamps.

A few stamps. So, the unknown is a
few stamps.
38

TEACHER’S
NOTES

3

♦  –  ✥  =  192

✤  –  192 =  ★

The scale shown below is balance.

Write the number sentence involving unknown for the above diagram.

Identify the unknowns and write the number sentences.

a     There are several eggs in a tray. 4 eggs are broken.
There are 17 good eggs.

b There were 83 storybooks in the reading corner. Most of the
 books have been borrowed. The number of books remains is 12.

c The flood victim relief centres A and B received a number of mineral
water bottles. The difference between the number of mineral water
bottles received is 350.

3.4 (i)
3.5 (i)

Guide pupils to identify unknowns in various everyday situations.
 Demonstrate subtraction of two numbers involving unknowns using flash cards
 or simulation and get pupils to tell stories.

The difference between the number of
evaporated milk cans and condensed
milk cans is 192 cans.

Which number sentence is correct? Discuss.

A B
39

TEACHER’S
NOTES

Materials       Players

White laminated papers,     2 pupils as
marker pens, A4 papers,     players and one
stopwatch and a duster.     as a judge.

Steps

1 Each player takes a piece of white laminated paper.

2 Write a 4-digit or 5-digit number.

3 Turn the paper so that it faces the table.

4 When the judge says start, the players turn
 their paper and find the difference
 between the numbers in 30 seconds.

5 The judge checks the answer.

6 The player who answers correctly in 30 seconds
 gets 5 marks. The player who answers correctly
 in more than 30 seconds gets 2 marks.

7 Repeat steps 2 to 5 for five times.

8 The player with the highest mark is the winner.

Improvise activities according to pupils’ ability.

39
3.1 (i)
40

TEACHER’S
NOTES

40

1 Calculate using standard written method.
 a   10 450 – 320 =       b    90 563 – 23 104 =

c   72 618 – 9 419 =       d   93 100 – 27 631 – 839 =

e   56 207 – 578 – 21 514 =           f            – 12 483 = 48 730

g   15 817 = 46 058 –                   h    30 thousand =         – 9 056

i  85 019 –        – 13 405 = 42 240    j               –          = 11 046

2 a   Subtract 61 378 from 91 010.

b   The difference between two numbers is 62 485. The smaller

number is 27 809. What is the larger number?

3 Solve.
 a    The table below shows the hobby of 20 813 pupils from a few
       schools.

i    Calculate the number of pupils who like to surf the Internet.

ii    Find the difference in number of the two hobbies.

b       The difference between the number
       of beads in containers P and R is
       10 beads more than the number of

beads in container Q. What is the
       number of beads in container Q?

4 Identify unknowns and write the number sentences.
 a 750 story books are donated to children welfare centres. Some

are non-fiction books and 380 are fiction books.

b    Some coconuts are plucked. 13 690 coconuts are distributed to
  sundry shops. The remainder of the coconuts is 5 862.

c 10 000 pieces of fabrics are to be sold in a bazaar. A number of

fabrics were sold in a week and 400 pieces more are not yet sold.

R
12 610

P
10 320

Hobby

Number of pupils

Surfing the Internet Reading books

6 219

Q
41

TEACHER’S
NOTES

Relate the usage of multiplication with examples in daily life.

4.1 (i)

1

What is the number of books supplied?

3 × 2 120 =

2  1 2 0
                                            ×            3

6  3 6  0

3 × 2 120 =   6 360

The number of books supplied is 6 360.

Calculate by adding
repeatedly and in
standard written method.

School

MULTIPLICATIONMULTIPLICATION

Simple multiplication

4

0 2 120 4 240 6 360

+ 2 120           + 2 120          + 2 120

We will supply books to 3 shops.
Each shop will receive 2 120 books.

What is the number of books sent to 9 bookshops?

Ma
ju book shop
42

TEACHER’S
NOTES

2 485 = 2 000 + 400 + 80 + 5

14 000 + 2 800 + 560 + 35 = 17 395

Drill pupils to multiply a number by 10, 100 and 1 000 using mental calculation.
 Encourage pupils to multiply using the multiplication tables.

http://fivejs.com/math-strategies-multiplication-division-video-tutorial/
4.1 (i),
(iii), (iv)

Calculate by
partitioning.

2  A supermarket placed an order of 2 485 sets
  of stationaries every month. Calculate the order
  of stationaries for 7 months.

7 x 2 485 =

Method 1         Method 2

3     5  3

2   4 8 5
         ×                7

1 7   3 9 5

7 x 2 485 =    17 395

The order of stationaries for 7 months is 17 395 sets.

3  2 139 × 10 =   4 156 × 100 =

2   1 3 9     156 × 1 hundred = 156 hundreds
  ×              1 0                     = 15 600

2 1   3 9 0

2 139 × 10 =   21 390   156 × 100 =   15 600

5  84 × 1 000 =

8 4
  ×     1  0 0 0

8 4  0 0 0

84 × 1 000 =   84 000

2 000

14 000

400

2 800

80

560

5

35

×

7

84 × 10 =

84 ×    = 8 400

× 1 000 = 84 000

Complete and talk about the
multiplication pattern of these numbers.
43

TEACHER’S
NOTES

10

43

5   0  9  4
×                   0

2  7   2  8  0

7 000

35 000

300 60

300

×

5 72 000

100

320

5

40

×

8

Fill in the blanks.

1 Multiply.

a       4 123             b       6 012             c       6 576             d       8 025
            ×        2                  ×         5                  ×         7                  ×         9

e   3 × 4 822 =                 f   4 × 9 051 =                  g   6 × 9 730 =

h   7 × 5 463 =                 i   8 × 7 006 =                  j   9 × 8 142 =

2 Calculate mentally.

a   5 318 × 10 =        b   981 × 100 =       c   69 × 1 000 =

d   4 326 ×      = 43 260   e   570 ×      = 57 000    f         × 100 = 99 000

3 Fill in the blanks.

a           9  6 0 1                    b           8  2 6 0                    c          9  7 3 0
      ×                3                        ×                6                       ×                7

0 8  0 0 3                             4 0  5 0 0                            3 3  8 0 7

4 Multiply.

a   5 × 7 362 =       b   8 ×          = 73 160
44

TEACHER’S
NOTES

Drill pupils to reinforce the multiplication concept using Diene's block or
square grid.

1

What is the total number of books received by 34 pupils?

34 × 12 =

Multiply the ones digit         Multiply the tens digit      Add up the products

3 4        3 4               3 4

×  1 2          ×     1 2                                    ×     1 2

6 8   34 × 2       6 8                                   1  6 8
                       +  3 4 0   34 × 10                    +  3 4 0

4 0 8

34 × 12 =  408

The total number of books received is 408.

2  67 × 23 =

Multiply the ones digit    Multiply the tens digit Add up the products

2           2                                                                 2

6 7        6 7                 6 7

×     2 3                ×         2 3              ×         2 3

2 0 1   67 × 3        2 0 1                      2 0 1
             +  1 3  4 0    67 × 20       +  1  3 4 0

1  5 4 1

67 × 23 =  1 541

4.1 (ii)

Let's multiply

1 1

Congratulations to 34 pupils who
will receive a present of 12 books
each in this Nilam Award.
45

TEACHER’S
NOTES

3  182 × 45 =

Method 1      Method 2

182 = 100 + 80 + 2

4 500 + 3 600 + 90 = 8 190

182 × 45 =   8 190

4  603 × 52 =

603     600

52     50

600
                                               ×         50
                                          30 000

31 356 is close to 30 000. The answer is reasonable.

603 × 52 =   31 356

5  548 × 73 =

548 × 73 =  40 004

Carry out quiz activity or mental calculation.

http://www.superteacherworksheets.com4.1
(ii), (iv)

5 4 8 ×

7

3
4

0

8

2

6

4
21 1

13 1522
5

5

0     0     4

1

603
×      52

1 206    603 × 2

+  30 150    603 × 50

31 356      Actual
                      answer

Round off 603 and
52 to the nearest
ten to estimate the
answer.

Next, solve
using standard
written method.

100
4 000

500
4 500

80
3 200

400
3 600

2
80
 10
90

×
40
5

1 8 2
×         4 5
      1 0         2 ×   5
   4 0 0       80 ×   5
        5 0 0      100 ×   5
   8 0         2 × 40
    3  2 0 0       80 × 40
+  4  0 0 0     100 × 40

8  1 9 0
46

TEACHER’S
NOTES

6  852 × 99 =

852 × 99 =  84 348

7             × 80 = 58 160
                                                                                727
                                 8 ) 5 8 16
                    –  5 6
                2 1

–  1 6
                  56
              –  56
                         0

727   × 80 = 58 160

1 Complete the calculations.
 a           2 1       b               5 2 4      c            3 7 8
      x      4 6             ×            5 5            ×         2 6

1  2                    2     2 0               6 8
   +                +     6  2 0              +     5
     6                 2 8     2 0                      8

2 Multiply.
 a    41 ×  14 =       b    36 × 25 =       c    52 × 37 =
 d    487 × 62 =                 e    913 × 99 =        f            × 70 = 98 490

3 Calculate.
 a   The product of 95 and 46.    b   5 hundreds multiply by 18.
 c    Multiply 34 tens by 9 tens.        d   288 hundreds is      multiply 10 tens.

4.1
(ii), (iv)

http:www/.superteacherworksheets.com

11  9
           4    12 10 10

8 5  2 0 0
–         8 5 2

8 4  3 4 8

Relate multiplication to division.

7  ×  8  =  56

7  =  56  ÷  8

852 × 99 = 852 × 100 – 852
                = 85 200 – 852

852 × 100 = 85 200
852 × 1     = 852

× 80 = 58 160
  = 58 160 ÷ 80

58 160
80

99 is 100
minus 1.
47

TEACHER’S
NOTES

Do exercises or times table quiz to reinforce multiplication skill.

4.1
(i), (ii)

Materials A set of number  (0 – 9), A4 paper, empty box and calculator
   for each group.

Players     5 pupils in a group.

Steps

1 Put 1 set of number card in the empty box.

2 A member of the group takes 4 number cards from the box.
 Example:

3 Arrange the number cards for multiplication of 2 by 2-digit number.

4 Create as many multiplication number sentences as possible.
 Record on an A4 paper and solve it.
 Example: 26 × 70 =      , 60 × 27 =      , 70 × 62 =      , 67 × 20 =

5 Discuss the outcomes with members of the group.

6 Check the answers using a calculator.

7 Repeat steps 2 to 6 by taking 5 number cards to create multiplication
of 3-digit number by 2-digit number.

8 Collect outcomes and keep them in Mathematics file.

Complete the cross number puzzle.

2 6 70

aj h

c g

b

f

d

k

e

i

l

Across

a.  58 × 66 =

b.  232 × 15 =

c.  111 × 64 =

d.  50 × 1 000 =

e.        × 100 = 43 300

f.   275 ×      = 27 500

Down

g.  1 360 × 9 =

h.  466 × 2 =

i.    72 ×       = 72 000

j.           × 20 = 13 460

k.        × 42 = 42 000

l.    7 ×       = 59 150
48

TEACHER’S
NOTES4.2 (i)

Solve problems using various strategies such as repeated addition.
 Encourage pupils to create number sentences orally based on problems
 posed on story cards.

http://www.youtube.com/watch?v=jwMmCYRNpTs.com

Solve the problems

1    4

8  2 8 0
×               6

4 9  6 8 0

6 × 8 293 =   49 680

The total number of eggs ordered is  49 680.

1  Every month a grocery orders the same number of eggs, which is
  8 280 from a dairy farm. What is the total number of eggs ordered
  in 6 months?

Given            The number of eggs ordered every month: 8 280

Find             Total number of eggs ordered in 6 months

Operation     Multiplication

Solve         6  ×  8 280 =

Check

8  2 8 0
              +      8  2 8 0
       1 6   5 6 0
           +     8  2 8 0
      2 4  8 4 0
           +    8  2 8 0
      3 3  1 2 0
           +     8  2 8 0
      4 1  4 0 0
           +     8  2 8 0

4 9  6 8 0

8 280 8 280 8 280 8 280 8 280 8 280

Check your answer by
adding repeatedly.

What is the number of eggs ordered in a year?
How do you do a speedy calculation?
49

TEACHER’S
NOTES

http://www.youtube.com/watch?v=jwMmCYRNpTs

2  A factory produces 950 pairs of shoes
  every day. What is the number of shoes
  produced in 30 days?

Information:
  950 pairs of shoes produced every day.
  Find the number of shoes produced in 30 days.

950 × 30 =     Check

950 × 30 =   28 500

The total number of shoes produced in 30 days
          is 28 500 pairs.

Solve.

a 42 groups took part in “Seni Tari” competition. Each group has 35
dancers. What is the total number of dancers taking part in the
competition?

b When a bear hibernates in cold season, its heartbeat
 reduces to 8 heartbeats per minute. What is the total
 number of its heartbeat in 1 440 minutes?

c A furniture factory gets an order of 114 chairs for a company.
 28 companies place the same number of order. What is the total

number of chairs ordered?

4.2 (i)
49

9 5 0 ×

3

0

5

0

0

0

2

0

0

0

1

0
7

0
2

8
5     0     0

Source: Mark Carwardine.
                Animal Records.
                Page 35, 2008

9 500
      9 500
+    9 500

28 500

12
50

TEACHER’S
NOTES

1 Multiply.

a        6 021               b      8 433               c       76               d       892
     ×        4                    ×        6                    ×  45                    ×    73

2 Calculate.
 a   3 × 2 121 =                   b   5 × 6 018 =               c   8 × 7 109 =
 d   42 × 33 =                     e   82 × 60 =                  f   664 × 94 =
 g   174 × 100 =                  h   78 × 1 000 =             i   53 ×       = 53 000
  j          × 1 000 = 92 000    k    4 ×         = 8 812          l            × 30 = 8 940

3 Find the product of the underlined digits on the cards below.

4 In the calculation on the right, the
 answer 4 344 is incorrect. Correct
 the mistake in the calculation.

5 Solve.
 a   A factory produces 200 reams of paper daily. Calculate the total

reams of paper produced in 15 days.

b   The Heathrow Airport, London receives 7 926
    passengers every hour. Find the total number of
   passengers in 5 hours.

c   625 schools were involved in the National Education Carnival.
   Each school sent 40 pupils to the carnival. What is the total
            number of pupils sent?

d   A supermarket places an order of 1 000 boxes of cereal biscuits.
            The total number of cereal biscuits ordered is 20 000 boxes.

Calculate the number of supermarkets that places the same order.
   Banyakkan latihan yang merangkumi pelbagai bentuk soalan untuk mengukuhkan

kefahaman murid.
2.3 (i)
2.4 (i)

5 4 3
×         6 2
    1  0 8 6
+  3  2 8 8

4  3 4 4

50

3 1944 756

Source: Airport Council International
51

TEACHER’S
NOTES5.1 (i)

Emphasise the steps of division in detail.

http://fivejs.com/math-strategies-multiplication-division-video-tutorial

School5

1

DIVISIONDIVISION

Simple division

How many bags are distributed to each school bookshop?

   39 630 ÷ 3 =

1 3 2 1 0
        3 ) 3 9  6 3 0
                           –  3
                               0 9
                     –     9
                         0  6
                              –      6
                              0 3
                          –      3
                       0 0
                             –     0
                           0

39 630 ÷ 3 =  13 210

The number of souvenir bags distributed to each school
  bookshop is 13 210.

Our company has printed 39 630
souvenir bags like this. Please
distribute the bags equally to 3
school bookshops.

Division Guide

1.  Divide ten thousands digit

2.  Divide thousands digit

3.  Divide hundreds digit

4.  Divide tens digit

5.  Divide ones digit

INFORMATION
52

TEACHER’S
NOTES

Revise division basic facts using flash cards and objects. Guide pupils to identify
the pattern of 1-digit tables.

5.1 (i)

2  50 475 ÷ 6 =           3 78 600 ÷ 100 =

8  4 1 2       Method 1
 6 ) 5 0  4 7 5
       –  4 8      78 600 ÷ 100 = 78600 = 786
               2  4                                  100
           –  2  4
                   0 7     Method 2
               –      6
                      1 5     78 6 0 0 . ÷ 1 0 0 = 786
                  –  1 2
                          3       Remainder
        78 600 ÷ 100 =   786
 50 475 ÷ 6 =   8 412 remainder 3

4  93 021 ÷ 1 000 =

9 3
  1 000 ) 9 3 0 2 1
           – 9 0 0 0
        3 0 2 1
     – 3 0 0 0
     2 1

93 021 ÷ 1 000 = 93 remainder 21  93 012  ÷ 1 000 = 93 remainder 21

1 Divide.

a   2 ) 8 246          b   5 ) 50 735          c   7 ) 68 901          d   9 ) 15 782

e   37 465 ÷ 4 =            f         ÷ 1 000 = 91        g    87 006 ÷ 8 =

2 Calculate mentally.

a   54 210 ÷ 10 =             b   73 200 ÷ 100 =           c   5 6013 ÷ 1 000 =

d  76 700 ÷      = 767  e          ÷ 100 = 543   f          ÷ 1 000 = 91 remainder 5

Remainder must
be less than the
divisor.

Check      The inverse of division
         is multiplication.

93 021 ÷ 1 000 = 93 remainder 21

Multiply:       Add remainder:

9 3         9 3  0 0 0
×     1  0 0 0     +            2 1

9 3  0 0 0         9 3  0 2 1
53

TEACHER’S
NOTES

Farmors Association

5.1 (i)

1

16 baskets

752 ÷ 16 =

4 7
              16 ) 7 5 2
                       –  6 4
                       1 1 2
                          –  1 1 2

0

752 ÷ 16 =  47

2  6 950 ÷ 30 =

Method 1          Method 2

2 3 1            200   +     30   +      1
 30 )  6  9 5 0           30 ) 6 000   +   900   +   50
     –  6  0               –  6 000   –   900   –   30
          9 5                   0          0        20 remainder
      –  9 0
             5 0
                  –  3 0
              2 0

6 950 ÷ 30 =  231 remainder 20

Guide pupils to build times tables. In the 16 times table example, retain the ones
digit in the 6 times table and add the tens digit in the 1 and 6 times tables.

http://fivejs.com/math-strategies-multiplication-division-video-tutorial

752 durians
are packed
equally.

200 + 30 + 1 = 231

Build the 16
times table
based on 1 and
6 times tables.

Let's divide

Partition 6 950 to
6 000 + 900 + 50.
Then, divide one
by one.

6
06

12
   1 8

24
30
36
42
48
54

16
   1 6

32
48
64
80
96

1 1 2
128
144

1
1
2
3
4
5
6
7
8
9
54

TEACHER’S
NOTES5.1 (i)

3  Encik Wahab distributed 34 800 quail eggs equally to
  25 customers. Each customer receives             quail eggs.

34 800 ÷ 25 =

6   9 6 0
          5 ) 3 4  8 0 0
            –  3 0
                          4  8
                  –  4  5
               3 0
                          –  3 0
                     0 0
                     –    0
                   0

34 800 ÷ 25 =  1 392

Each customer receives  1 392 quail eggs.

4  79 871 ÷ 79 =

1       Add up the
                                                                          1  0       quotients
                                                                  1  0 0 0

79 )  7 9  8 7 1
                                                                    –  7 9  0 0 0
                                                                               8 7 1
                                                                            –  7 9 0
                                                                                8 1
                                                                     –   7 9
                                                                            2  remainder

1 000 + 10 + 1 = 1 011

1011 remainder 2 is close to1 000. The answer is reasonable.

79 871 ÷ 79 =  1 011 remainder 2

Discuss various division strategies based on pupils’ skills and understanding.

Estimate the answer.

1  3 9 2
5 ) 6  9 6 0
 –  5
     1  9
 –  1  5
         4 6
      –  4 5
            1 0
        –  1 0
               0

5
25
          5

25 = 5 × 5

79 871      80 000
       79       80

1    0 0 0

80 000  =  1 000
    80
        1
55

TEACHER’S
NOTES

55

Latih murid menggunakan jadual sifir untuk membahagi.

5  24 360 ÷ 12 =

2   0 3 0

24 360  =  2 030
      12
          1

24 360 ÷ 12 =  2 030

6              ÷ 52 = 431

÷ 52 = 431

= 431 × 52

22 412   ÷ 52 = 431

In this number sentence, the numbers in
     are the same. What is the number?

Divide.

a    15 ) 2 670           b    20 ) 7 160        c    42 ) 90 807        d    80 ) 39 682

e    8 436 ÷ 12 =                f    26 514 ÷ 17 =              g    53 788 ÷ 29 =

h    72 009 ÷ 36 =              i    81 048 ÷ 49 =              j     96 324 ÷ 64 =

1

4 3 1
×              5 2
  1    1

8 6 2
+  2 1   5 5 0

2 2   4 1 2

6 400 ÷         =

Where is the mistake?
Discuss.

45 155 ÷ 11 =

The inverse of division
is multiplication.

4   11  5

45 155  =  415
     11
        1

1

55

TEACHER’S
NOTES5 .1 (i)

Guide pupils to use the times tables to divide.
56

TEACHER’S
NOTES

Encourage pupils to explore the website www.education.com/worksheets to try out
the games.

Answer the questions and use the alphabetical codes to solve the puzzle.

is the insect that flies the fastest in the world,
which is up to 97 kilometres per hour.

Source: Fastest Insect World Record. mostextreme.org/fastest-insect.php

25 ) 8 100

64 ) 73 923

37 ) 6 921

73 ) 84 972

90 ) 93 060

46 ) 39 974

97 ) 56 653

55 ) 36 905

82 ) 59 794

r

187 remainder
 2

g

671

k

155

l

1 034

d

324

y

584 remainder
5

a

869

n

1 164

f

729  remainder
16

o

1 155
remainder 3

5 .1 (i)
57

TEACHER’S
NOTES

Discuss other methods such as the standard written method and number patterns
to solve problems.

5.2 (i)

1   The floors of a 6-storey building need 48 000 tiles. How many
 tiles are needed for each similar floor?

Given    48 000 tiles for 6 storey building.

Find     Total number of tiles for each floor.

Operation       Division

Solve         48 000 ÷ 6 =

Check     8 000 × 6 = 48 000

48 000 ÷ 6 =   8 000

8 000 tiles are needed for each similar floor.

Solve the problems

48 000

?1st  Floor

2nd Floor

3rd  Floor

4th  Floor

5th  Floor

6th  Floor

8    0 0 0

48 000  =  8 000
     6
        1
58

TEACHER’S
NOTES

Encourage pupils to estimate before calculating the actual answers.
 Use other method to calculate answers such as the standard written method.

5.2 (i)

2  26 907 soya drink bottles are packed in
  several boxes. Each box can be filled with
  24 bottles. Calculate the remainder of the
  soya drink bottles. How many boxes
  are needed?

2 6   9 0 7
                    –  2 4   0 0 0    24   ×  1 000
                            2   9 0 7
                    –     2   4 0 0    24   ×  100
                                5 0 7
                    –          2 4 0    24   ×  10
                       2 6 7
                    –      2 4 0    24   ×  10
                          2 7
                    –        2 4    24   ×  1

remainder 3               1 121

The remainder of the soya drink bottles is 3.
The number of boxes needed is  1 122.

Solve.

a The picture shows a necklace that has 34 beads.
 How many necklaces can be made from 45 730 beads?

b A salesman of a handicraft shop keeps 100 key chains in a
 container. He has 77 809 key chains. Calculate the number of
 containers needed.

c A factory distributed 26 380 caps equally to 52 departments in
conjunction with National Youth Day. What is the number of caps
received by each department? How many remainders?

Why is the number of
boxes needed 1 122?

Total number of soya drink: 26 907 bottles
1 box: 24 bottles
Remainder of soya drink bottles: ?
Number of boxes needed: ?

26 907 ÷ 24 =

24
bottles

26 907 ÷ 24 =   1 121 remainder 3
59

TEACHER’S
NOTES

Prepare enough question sets for a few groups of players.

5.2 (i)

Materials    4 sets of round number cards 0 to 5 of various colours,
      sticky tape, pencils, paper and a few sets of questions.

Players    3 pupils in 1 group (an initiator, a thinker, a checker), a
      reader and a judge.

Steps

1 Arrange the round number cards and place them on the floor.

2 4 initiators from the 4 groups stand at the 0 round number cards
according to the group colours.

3 A reader reads the first question, the thinker of each group do the
calculation and whisper the answer to his initiator.

4 The initiator uses his hands and legs to touch the remainder. The
checker ensures that the answer is correct.

5 The reader continues to read the second question and so on.

6 The group is out if the answer is wrong or if the initiator fails to
 touch the remainder.

59

Stand at 0 round number card Move to touch the remainder

Find the remainder of the quotient.
a.  4 345 ÷ 10 =   434 remainder ?
b.  15 052 ÷ 25 =   602 remainder ?
c.   70 004 ÷ 1 000 =   70 remainder ?
d.  40 013 ÷ 5 =   8 002 remainder ?
e.   72 033 ÷ 8 =  9 004 remainder?
60

TEACHER’S
NOTES

Gunakan blok Diene’s, carta nilai tempat dan kad nombor untuk menjalankan aktiviti
menambah secara berpasangan.

Banyakkan aktiviti yang melibatkan pengiraan secara mental.

http://www.primaryworksheets.co.uk/addws/add54.html

5.2 (i)

1 Complete the following.

a   9 700 ÷ 100 =   b   41 003 ÷ 1 000 =

c             ÷ 1 000 = 93  d   82 506 ÷          = 825 remainder 6

2 Solve.

a   6 ) 24 690     b   9 ) 50 652         c   27 ) 63 669         d   42 ) 36 625

e   8 560 ÷ 20 =            f   67 604 ÷ 38  =         g   84 840 ÷ 60 =

h   94 567 ÷ 11 =            i   36 801 ÷ 100 =         j    90 000 ÷ 1 000 =

3 Complete the table below.

4 Solve.

a    A chef made 8 100 pieces of pineapple tarts in a week.
     What is the number of pineapple tarts made each day if
    the chef takes a day off on Monday?

b    A flower wholesaler sells 12 375 stalks of flowers
     to 75 florists. What is the number of flowers for
     each florist?

c
What is the number of boxes needed to

pack 56 790 packets of biscuits?

d    15 680 participants from 64 teams attended the Labour Day
 parade at Stadium Hang Tuah. What is the number of participants
 in each team if the number is the same?

60

Number

23 385

72 050

Divisor

24

64

Quotient

50

1 270

100 Packets
61

TEACHER’S
NOTES

Guide pupils to master the process involving addition and subtraction based on
 real objects or simulation.
 Carry out role-play to reinforce pupils᾽ understanding.6.1 (i)

1

What is the number of passengers remaining in the bus after the
 second bus stop?

12 + 9 – 6 =

1        1  11

1 2      2  1
             +    9         –    6

2 1      1 5

12 + 9 – 6 =   15

The number of passengers that are still in the bus after the second
 bus stop is 15.

Solve the first
operation, then the
second operation.

School

MIXED OPERATIONMIXED OPERATION

Addition and subtraction

6

Calculate 9 – 6 first. Then, add the answer
to 12. Is the answer the same? Why?

Bus stop 1 Bus stop 2
62

TEACHER’S
NOTES

Use number cards to create mixed operation number sentences.

http://www.funbrain.com/cgi-bin/alg.cgi?A1=s&A2=1

2  9 472 – 295 + 68 =

16
           3  6  12              1  1

9   4 7 2      9   1 7 7
         –      2 9 5         +          6 8

9   1 7 7      9   2 4 5

9 472 – 295 + 68 =   9 245

3  74 204 + 12 798 –             = 83 901

1      1   1                                   6    10

7 4   2 0 4                  8 7   0 0 2
            +  1 2   7 9 8           –  8 3   9 0 1

8 7   0 0 2                   3   1 0 1

74 204 + 12 798 –   3 101   = 83 901

Create number sentences from the cards to
                give the largest and the smallest values.

1 Calculate.

a   708 + 5 360 – 24 =               b   374 + 21 213 – 8 635 =

c   8 765 + 10 642 – 6 826 =     d   40 452 – 11 023 + 32 005 =

e   10 718 + 29 372 –        = 9 390     f          – 17 624 + 6 378 = 81 237

2 15 000 –          + 5 000 =

6.1 (i)

62 394 48 726

50 272 – + =

10 000

6 000

4 000

Add 9 472 and 68. Subtract 295
from the total. Is the answer the
same? Explain.

In the number sentence above,
represents the same number. Which of the
number cards on the left is the value of          ?

7  +   1  –       =  8
        8  –      =  8
   8  –   8  =  0
63

TEACHER’S
NOTES

Guide pupils to understand the process involving multiplication and division
 based on stimulus.
 Drill and practise using number of small values.

1

How many chocolate biscuits must be packed in each jar
as shown in the picture above?

4 × 18 ÷ 3 =

Method 1            Method 2
            3

1 8
             ×    4

7 2

4 × 18 ÷ 3 =   24

24 chocolate biscuits must be packed in each jar.

2  Divide 2 200 by 100 and multiply the quotient by 6.

2 200 ÷ 100 × 6 =

2 200 = 22
                          100

2 200 ÷ 100 × 6 =   132

6.2 (i)

2 4
3 ) 7 2
  – 6
     1 2
  – 1 2
        0

6

4  ×  18   =   4  ×  18
     3                  3
         1

=   4  ×  6
        1

=   24

Multiplication and division

1
      22
×      6

132

All these chocolate biscuits need to
be packed equally in the 3 jars.
64

TEACHER’S
NOTES

Drill and practise to complete number sentences.
 Guide pupils to build multiplication times tables.

2  54 756 ÷ 18 × 11 =
                                      3  0 4 2
                18 ) 5 4  7 5 6
                    –  5 4
                                           0  7
                                  –      0
                                         7 5
                          –  7 2
                        3 6
                    –  3 6
                           0

54 756 ÷ 18 × 11 =   33 462

3  2 550 × 4 ÷           = 1 020

2    2

2  5 5 0         10 200 ÷          = 1 020
      ×               4         10 200 = 1 020 ×  10

1 0  2 0 0

2 550 × 4 ÷   10   = 1 020

1 Calculate.

a    14 × 750 ÷ 12 =             b    18 × 1 010 ÷ 10 =

c    2 048 ÷ 8 × 3 =        d    26 232 ÷ 6 × 10 =

e    1 526 ÷ 14 × 11 =         f     100 × 480 ÷ 16 =

2 Complete the following.

a    7 × 5 000 ÷         = 3 500             b    4 030 ÷ 10 ×          = 8 060

c             × 3 000 ÷ 60 = 1 000          d           ÷ 10 × 80 = 80 000

3 Multiply 62 by 1 004. Then, divide the product by 8. What is the answer?

6.2 (i)

3  0 4 2
×            1 1

3  0 4 2
+  3 0  4 2 0

3 3  4 6 2

8

08

16

24

32

40

18

18

36

54

72

90

1

1

2

3

4

5

Build the 18
times table.
Add the tens
digits and retain
the ones.

1 000  ÷        =  100
          1 000  =  100  ×
                     =  100  ×  10

Relate division to
multiplication.
65

TEACHER’S
NOTES

http://www.funbrain.com/cgi-bin/alg.cgi?A1=s&A2=1

6.1 (i)

Materials 2 laminated number sentence cards, answer cards,
   whiteboard pens, duster and calculator.

Players In pairs (Player A and Player B)

Steps

1 Player A chooses one number sentence card and one answer card.

2 Player B completes the number sentence card based on the answer

card chosen by Player A.

3 Check the answer by using a calculator.

4 The player who completes the number sentence correctly will get 10
marks.

5 Swap turns between both players. Repeat steps 1 to 4.

6 The player who scores more marks is the winner.

Calculate the answer. Complete the alphabets that match the answer.

This bird is a species of a sea bird that can fly with the speed of 81
kilometres per hour. It is among the endangered species of birds in the world.

B    36 × 12 ÷ 6 =    S    16 × 2 ÷ 4 =

R    21 007 – 12 007 + 1 000 =  L     68 + 72 – 11 =

O   8 000 ÷ 20 × 3 =    T    12 × 300 ÷ 10 =

A    3 072 + 1 682 – 754 =

10 5030 7020 6040 80 90

1 740  +   15   –  1 725  =   30

+         –             =            –         +             =

4 000 129 72 4 000 360 10 000 1 200 8 8
66

TEACHER’S
NOTES

1  In conjunction with Environmental Day,
  35 750 red hibiscus and 27 428 white
  hibiscus are planted around Kuala Lumpur.
  31 480 hibiscus have been planted on the
  first day and the remainders on the second
  day. What is the number of hibiscus that
  are planted on the second day?

Given  35 750 red hibiscus.
    27 428 white hibiscus.
    31 480 hibiscus planted on the first day.

Find  The number of hibiscus planted on the second day.

Operation Add, then subtract.

Solve           35 750 + 27 428 – 31 480 =

10
                         1   1        2     0 17

3 5   7 5 0           6 3    1 7 8
                        +  2 7   4 2 8       –  3 1    4 8 0

6 3   1 7 8           3 1   6 9 8

12
                             1      1       5  2      11

Check      3 1   6 9 8           6 3   1 7 8
                       +  3 1   4 8 0       –  2 7   4 2 8

6 3   1 7 8           3 5   7 5 0

35 750 + 27 428 – 31 480 =   31 698

The number of hibiscus planted on the second day is  31 698.

Guide pupils to identify the key information and build number sentences based on
the problems given.

6.3 (i)

Solve the problems
67

TEACHER’S
NOTES

Guide pupils to identify the key information based on the problems given.
 Drill on creating number sentences based on the problems given.

2    During Malaysian Food Festival, 80 containers of
  satay were prepared. Each container contained
  250 sticks of satay. The satay were grilled equally
  by 5 workers. What was the number of satay grilled
  by each worker?

Solve          80 × 250 ÷ 5 =

4    0   0  0

2 0  0 0 0  =  4  0 0 0
                                       5
            1

2 5 0
  Check             8 0 ) 2 0  0 0 0
            –  1  6  0
                           4  0 0
                        –   4  0 0
                  0 0
                       –     0
               80 × 250 ÷ 5 =  4 000                        0

The number of satay grilled by each worker was 4 000.

Solve.

a There are 20 736 books in a library. In early February, 9 788 books
 are borrowed, and 5 714 books are returned. How many books left?

b A total of 18 300 tickets to the Military Tattoo show are divided equally
to 25 schools. Calculate the number of tickets received

by 11 schools.

c 26 trays filled with 24 bean buns are distributed
 equally to 12 kindergartens. What is the number
 of bean buns received by each kindergarten?

6.3 (ii)

4

2 5 0
×            8 0

2 0  0 0 0

4  0 0 0
×               5

2 0  0 0 0

24
bean buns

MALAYSIAN FOOD FESTIVAL

MALAYSIAN FOOD FESTIVAL
68

TEACHER’S
NOTES

1 Calculate.

a   197 + 2 386 – 5 =                          b   10 012 – 4 609 + 3 815 =

c   71 892 + 18 543 – 6 799 =      d   98 250 – 62 054 + 25 898 =

e   6 × 5 265 ÷ 9 =         f    18 832 ÷ 22 × 5 =

g   14 × 3 806 ÷ 28 =       h    26 780 ÷ 10 × 34 =

2 Complete the following.

a   712 + 430 –        = 1 000      b   1 245 –        + 312 = 749

c   64 ÷ 8 ×       = 56       d   70 × 2 ÷       = 14

3 Calculate.

a   The product of 7 087 and 3 divided by 19.

b   Amrin adds 7 050 to 38 250.  The total is the reduced to 45 000.
   What is the answer?

c   Subtract 43 000 from a number. Then, add the answer
   to 8 300 to get 50 400. What is the number?

4 Solve.

a   Berjaya Company buys 1 125 boxes of 2B pencils. Each box
    contains 24 pencils. The pencils are repacked with 5 pencils

each. What is the number of packets made?

b   A bus travelled a distance of 9 632 km for 2 weeks from town
   X to town Y. The distance travelled was the same for each day.

Calculate the distance travelled by the bus in 8 days.

c   105 people board the commuter train from KL Sentral to Pelabuhan
    Klang. When it arrives at Subang Jaya Station, 37 people get down

and 28 board the train. Calculate the number of passengers in
   the train after passing Subang Jaya Station.

d   There are 11 920 grade A chicken eggs and 10 750 grade B eggs.
            The grade C chicken eggs are 12 300 less than the total of grade A

and grade B eggs. What is the number of grade C chicken eggs?

Banyakkan latihan yang merangkumi pelbagai bentuk soalan
 untuk mengukuhkan kefahaman murid.

2.3 (i)
2.4 (i)68
69

TEACHER’S
NOTES7.1 (i)

a, b

School7

1

What is the fraction of the kuih bakar ?

1 cake       1  cake                1                       1
                             2                      2

There is 1 1  kuih bakar.
                  2
  1 1  is read as
    2

one, one over two.

Carry out the activity of writing improper fractions and mixed numbers.

Recognise mixed numbers and improper fractions

69

Pizza

Kuih bakarCheese Cake

Banana Cake

Give other examples
of mixed numbers.

There are 1 kuih bakar and     cut cake.

Mixed numbers is written as 1 1
                                                   2

Whole number     Proper fraction

1 1
   2

Mixed number
shows the value
of more than 1.

FRACTIONSFRACTIONS

INFORMATION

1
2
70

TEACHER’S
NOTES7.1 (i)

a, b

9
4

2   What is the fraction for the cheese cake?

1 cake       1 cake             1  cake
                4

1                       1                       1
         4

4          +          4          +          1      =     9
       4                      4                     4             4

Guide pupils to master the concept of improper fractions by simulation activities
and diagrams.

1
4

1
4  1

4 1
4

1
4

1
4  1

4 1
4

1
4

9        numerator
4       denominator

The numerator is
larger than the
denominator.

Give other examples of improper fractions.

One whole cake is cut

into 4 equal parts.

9  parts of a cake is     .

Nine over four is an
improper fraction.

Improper fraction is a
fraction which numerator
is equal or larger than its
denominator.

INFORMATION

9
4
71

TEACHER’S
NOTES

1
2

1
2

1
2

1
2

1

3  Mixed number and improper fraction.

a

1 1           3
                      2           2

b

2 3           13
                      5            5

Mixed number                  Improper fraction

4  What fractions are represented by A, B and C?

Guide pupils to shade improper fractions and mixed numbers on diagrams.
 Build a fraction board.

http://www.edhelper.com/math/fractionstg513.htm
7.1 (i)
a, b

5
4

7
4

8
4

0

A B

1
4

1
4

2
4

2
4

3
4

4
4

6
4

3
4

1 2C

Improper fractionsProper fractions

Is 1
 7

a mixed number?
       5
Discuss.
72

TEACHER’S
NOTES

Place the improper fractions and mixed numbers at the correct
 places on the number line.

1 List out five mixed numbers and five improper fractions.

2 Write the mixed numbers and improper fractions of the shaded parts.

a      b

3 Redraw the diagrams and colour the fractions given.

a     12     b    1 1
      7                                                     4

c    1 2     d    2 4
               3                                                      5

Use paper folding technique and matching cards to recognise, say and write
improper fractions and mixed numbers.

http://www.edhelper.com/math/fractions_tg516.htm
7.1 (i)
a, b

1 2

7
4

11
8

19
8

17
8

13
8

1 7
  8

1 1
  8

1 1
  2

2 1
   2

2 1
   4

1 1
  4
73

TEACHER’S
NOTES

Carry out paper folding activities to help pupils convert improper fractions to
mixed numbers.

7.2 (i)

1  Convert 2 1  to improper fraction.
          2
    2 1  =
                2

1           +           1           +           1           =           2 1
                                                                2                           2

2           +          2          +           1           =           5
         2                       2                       2      2

2 1  =    5
       2        2

2  Convert  7 to mixed number.
       3
    7  =
             3

7  =    2 1
    3           3

1
3

2
3

0 1 21 1
  3

1 2
  3

22
  3

2 1
  3

1
3

2
3

3
3

4
3

5
3

6
3

7
3

8
3

Relationship between improper fractions and mixed
numbers

mixed
number

improper
fraction
74

TEACHER’S
NOTES

Talk about the
mistake made.

3  Convert  9  to mixed number.
        5

9   =
             5

9   =   1 4
    5           5

4  Convert  20  to mixed number.
         6
    20  =
     6

3 2   =   3 2  ÷  2
              6          6  ÷  2
                =   3 1
              3

20  =    3 1
              6            3

5  Convert  2 1  as improper fraction.
           4
       2 1   =
             4
       2 1   =   1   +   1   +   1
          4                            4
               =   4   +   4   +   1
           4        4        4
               =   9
           4
        2 1   =     9
                                                         4           4

Explain to pupils how to use division to convert improper fraction to mixed number.

7.2 (i)

3
6 ) 20
 –  1 8

2

1
5  )  9
   –  5

4

is written as 1 4
               5

16    =
 3

5
 3 ) 16
  –  15
         1

16    =    3 1
 3             5

Use division

operation.  9
is

5
9 divided by 5.
75

TEACHER’S
NOTES

Remind pupils to multiply the numerator and denominator by the same value to get
equivalent fractions.

7.2 (i)

6  Convert  3 1  to improper fraction.
          10

3 1   =
             10

3 1    =  3   +   1
                      10                 10

=   30   +   1
                         10       10

=   31
                       10

3 1    =      31
                      10         10

7  Convert  4 2
to improper fraction.

7

4 2        =
     7

4   2    =    4    ×    7    +    2
               7                        7

=   28   +   2
               7

=   30
                   7

4 2      =     30
                                7             7

0 1 2 3 4

3 1
  10

30
 10

40
1 0

20
1 0

10
1 0

• Multiply 4 by 7.
• Add 2 to the product of
   4 and 7.
• Maintain the denominator 7.
76

TEACHER’S
NOTES7.2 (i)

Materials   MS Word.

Steps

1 Execute MS Word application.

2 Click Insert and Shapes.

3 Choose a shape from Basic Shapes.

4 Copy and paste a few of the shapes.

5 Arrange a few shapes that are the same to form various patterns.

6 Shade a few parts.

7 Write the improper fractions and mixed numbers for the shaded parts
of the diagrams.

1 Convert the following improper fractions to mixed numbers.

a     4          b     10          c     19     d     22         e     30
      3         4                     5     7        8

2 Convert the mixed numbers to improper fractions.

a     5 1  =            b     9 5  =            c     1 1  =            d     2 3  =
        4                6                          9                         10

3 A pizza has 8 parts. How many parts are there in

1 5  pizzas?
   8

12  =  1 5
 7          7

11  =  1 3
 8         8

12  =  2 2
 5           5

76
77

TEACHER’S
NOTES

1    1   +  2  =
   4        4

1   +   2   =       3
    4         4       4

2  What is the total of  3   +   2 ?
                          7         7

3   +   2   =
                         7        7

3   +   2   =      5
                7         7        7

3    1   +   1   =
     2         4

1   +    1   =   3
    2         4        4

1   +   1   =       3
    2        4             4

Use paper strips or objects to reinforce pupils’ understanding.

7.3 (i) a

Addition of fractions

1
4

1
4

1
4

1
4

1
4

1
41

2

0
1
7

2
7

3
7

4
7

5
7

6
7

7
7

8
7

2
7

For fractions with the same
denominators:
(a) Maintain the denominator.
(b) Add or subtract the
 numerators only.
(c) Simplify the answer.

INFORMATION
78

TEACHER’S
NOTES

4       1    +   5   =
     2        7

1    +   5   =   1   ×   7   +   5   ×   2
    2   7         2   ×   7        7   ×   2

=   7   +   10
                                  14         14

=   17
                14

=  1 3
                                    14

1   +   5   =   1  3
    2        7           14

5    4   +   2   +   1   =
    9        9         9

4   +   2   +   1   =   4   +   2   +   1
    9        9         9                  9

=    7
        9

4   +   2   +   1   =      7
    9        9         9      9

6    1   +   3   +   1   =
    4        8         4

2   +   3   +    2  =     7
    8        8         8        8

1   +   3   +   1   =      7
    4        8         4            8

Explain to pupils how to find the Least Common Multiple (LCM) for fractions with
different denominators.

7.3 (i)
a, b

Make the denominators the same.

1
4

1
4

1
4

1
4

1
8

1
8

1
8

1
8

1
8

1
8

1
8

1
8

Multiples of 2, 7
2   2   4   6   8   10   12   14
7   7   14

Find the common denominator
for 7 and 2.

Is this correct?
 1  +  1  =  1

.
3      5      8
Discuss.
79

TEACHER’S
NOTES

7    1   +   2    +   7   =
    2        5        10
     1   +   2   +   7   =   1  ×  5   +   2  ×  2   +   7
      2        5        10        2  ×  5        5  ×  2        10
           =   5   +   4   +   7
                                   10       10       10
            =  16
                                   10

Solve.

a    1   +   1   =    b 2   +   4   =
   3        3               7         7

c    1   +   2   +   1   =   d  1    +   3   +   3   =
   5        5         5             4         4        4

e   2   +   5   =     f  1   +    7   =
   3       6     2        9

g   7   +    1   +   3   =   h 2   +   5   +   2   =
   8        2        8     3        6        3

Study the questions before solving them. Solve fractions with the same
 denominators first.

10
10

Multiples of 2, 5, 10
2
2
4
6
8
10

5
5
10

79

Materials    A4 paper, ruler, pencil, colour pencil, fraction cards  1 + 3
                   8    8
Steps

1 Fold paper into 8 equal parts.

2 Draw lines along the folded parts.

3 Colour 1 part blue and 3 parts red.

4 Calculate the total of the coloured parts.

5 Repeat steps 1 to 4 for other fractions.

1   +   2   +    7   =     1 3
2        5        10            5

16  ÷  2   =   8
10  ÷  2        5
               =  1 3
              5

7.3 (i)
a, b
80

TEACHER’S
NOTES

Carry out simulation of subtracting fractions using fraction strips to reinforce
pupils’ understanding.

7.4 (i)
a

1

How many parts of the cake left?

5   –   1   =
     6        6

5   –   1   =   4
     6        6        6

5   –   1   =      2
     6        6           3

2  What is the difference between  4 and  2 ?
                                     5          5

4   –   2   =
     5         5

4   –   2   =      2
     5        5           5

3     6   –   1   –    2   =
     7        7        7

6   –   1   –    2   =      3
     7        7        7           7

2
7

0
1
7

1
7

2
7

3
7

5
7

6
7

1
4
7

2
5

4
5

Subtraction of fractions

4   ÷   2   =   2
6   ÷   2        3
81

TEACHER’S
NOTES

Use the Least Common Multiple (LCM) to get the common denominator.

7.4 (i)
b

4  Subtract   1             7 .
                   4            8

7   –   1   =
         8        4

7   –   1   =   7   –   1  ×  2
         8       4      8      4  ×  2

=   7   –   2   =   5
                   8        8         8

7   –   1   =     5
                8        4            8

5        5   –    1    –    1    =
           6        3         6

5   –    1    –    1   =   5   –   2   –   1
        6        3         6        6        6        6

=   5   –   2   –    1
                  6

=    2   ÷   2   =   1
                 6   ÷   2         3

5   –   1   –    1   =      1
           6        3         6            3

6           1   –   1   –    1   =
        2        10        5

1   –   1   –    1   =   1  ×  5   –   1   –    1  ×  2
        2        10        5        2  ×  5         10        5  ×   2

=   5   –   1    –   2
               10       10        10

=   2   ÷   2   =   1
               10  ÷   2         5

1   –    1   –    1   =       1
        2        10       5             5

10 is in the
2, 5 and 10

times tables.

Multiples of 2, 5, 10

2     2 , 4 , 6 , 8 , 10

5     5 , 10

10    10

from
82

TEACHER’S
NOTES

7  7   –   1   –   1   =
     9        2        6

7   –   1   –   1   =   7   ×   2   –   1   ×   9   –   1   ×   3
  9         2        6        9   ×   2        2   ×   9        6   ×   3

=  14   –   9   –   3
             18       18       18

=  14   –   9   –   3
                                  18

=   2
            18

7   –   1   –   1   =      1
                 9        2        6           9

Subtract. Give answer in fraction of the simplest form.

a    3   –   1   =    b 5   –   4   =
    5        5               7         7

c    8   –   5   –   1   =   d 7   –   3    –   1    =
    9         9         9             10       10        10

e    3   –   1   =      f 5   –   1   =
    4        2                                 9        5

g    6   –   2   =    h 5   –   1   –   1   =
    7        3              6        2        6

i    9   –    2   –   1   =     j 2   –   2  –  1   =
     10       5       5    3        9       9

k    4   –   1   –   3   =     l  7   –   1   –   1   =
    5        4       10         8        4        2

http://www.edhelper.com/math/fractionsft213.htm

7.4 (i) b

Make sure the
answer is given in
the simplest form.

9
9
18

Multiples of 2, 6, 9
2
2
4
6
8
10
12
14
16
18

6
6
12
18

2   ÷    2   =   1
18   ÷   2        9
83

TEACHER’S
NOTES

Carry out simulations using real objects or materials.

7.5 (i)
(a)(b)

1       2   +   3   –   1   =
        5        5         5

2   +   3   –   1   =      4
        5         5         5           5

2       7   –   3   +   1   =
       8        8         4

7   –   3   +   1   =   7   –   3   +   1   ×   2
       8        8          4        8        8        4   ×   2

=   7   –   3   +   2
                                        8

=   6
                8

7   –   3   +   1    =      3
       8          8        4            4

Addition and subtraction of fractions

6  –  2  +  4  =  6  –  2  +  4
7      7       7              7
     =  6  –  6
                    7
   =  0
        7

What is the mistake in
the above calculation?

6   ÷   2    =   3
8   ÷   2  4
84

TEACHER’S
NOTES

3        2   +   7   –    1   =
        5       10        2

2   +   7   –    1    =   2   ×   2   +   7   –    1   ×   5
       5       10        2         5   ×   2        10        2   ×   5

=   4   +   7   –   5
                         10       10       10

=   6   ÷    2   =   3
                10  ÷   2        5

2   +   7   –   1   =      3
        5        10       2           5

4       5   –   2   +   3   =
       6        3        4

5   –   2   +   3   =   5   ×   2   –   2   ×   4   +   3   ×   3
       6        3        4         6  ×   2        3   ×   4         4   ×   3

=  10   –   8   +   9
          12       12        12

=  10   –   8   +   9
                     12

=  11
                            12

5   –   2   +   3   =     1 1
       6        3        4           12

Guide pupils to understand the concept of addition and subtraction using
simulations and diagrams.

http://www.education.com/activity/fractions/
7.5 (i)

b

6
6
12

Multiples of 3, 4, 6
3
3
6
9
12

4
4
8
12

0 1
10

2
10

3
10

4
10

5
10

6
10

7
10

8
10

9
10

10
10

11
10

5
10

7
10
7.5 (i)
a, b

Materials    Thinker board card Players       4 pupils in a
      and stationaries.            group.

Steps

1 Each group completes
 the think board card
 based on the topic
 given by the teacher.

2 Demonstrate your work
 in front of the class. Teacher
  acts as a fasilitator.

3 Display your work in the
 Mathematics corner.

1 Solve.

a     5   +   2   –   3   =  b     5   –   1   +   3   =
         7         7        7          6         6         6

c    4   –     1   +   2   =  d     2   +   4   –   3   =
        9          9        3          5         5        4

e     2   +    1   –   7   =   f      9   –   2   +   3   =
         5        3        10          10       5         4

2

1  ℓ
2

7  ℓ
8

85

BA

Think Board Card

Topic:
Add

Fraction

Number
sentence

1  +  1  =  1 1
        2         2

Concrete material/object

Diagram

1   +
1

2

1
1

2

Story
Ali has an apple.

His brother has
1

an apple.
                                    2

Altogether there are 1
1
  apples.

2

1

1

2

2

1

1

Pour the water from container A into

container B. Pour out       of water

from container B. Calculate the

volume of water left in container B.

3
4
ℓ
86

TEACHER’S
NOTES

Get pupils to use picture cards to create stories involving addition and
subtraction of fractions.

7.6 (i)

1  Miss Kim bought   4  kg of tiger prawns and   7  kg of white prawns
                        5                                        10
  at the market. What is the total mass of prawns bought by Miss Kim?

Given          Tiger prawns  4   kg.
             5
        White prawns  7  kg.
              10
  Find         Total mass of prawns.

Operation     Addition

Solve         4   +   7   =
           5         10

4   +   7   =   8   +   7
                    5         10        10        10
                                     =   8   +   7
                                     10
                                     =  15
                                10

Check       1 1   –   7   =   3   –   7
             2       10        2        10
                           =   3   ×   5   –   7
                       2   ×   5       10
                 =   15  –   7
                  10
                 =   8
                       10

4   +  7   =    1 1    kg
            5       10   2

The total mass of prawns bought by Miss Kim is 1 1 kg.
                                                      2

Solve the problems

7
10

7
10

8
10

4
 5

8   ÷   2   =   4
10   ÷   2        5

4
kg

5
 7

kg
10

=   3
      2
         =   1 1
                 2

15  ÷   2
10  ÷   2

What is the
difference in mass
of the two types
of prawns?
87

TEACHER’S
NOTES

2   Jasmin takes  5  hour to finish Mathematics exercise
     6
   and  1  hour for Science exercise. Jasmin helps her mother
         2
   in the kitchen for  3  hour. Calculate the difference between
                     4
         the time she finishes her exercises and helps her mother.

5   +   1   –   3   =            hour
   6         2        4
   5   +   1   –   3   =   5   ×   2   +   1   ×   6   –   3   ×   3
   6         2        4         6   ×   2        2   ×   6        4   ×   3
       =   10   +   6   –    9
             12
                =   7
           12
   5   +   1   –   3   =        7    hour
   6        2        4          12

The difference is   7   hour.
                                  12

Solve.

1  1  m and  7  m ribbons are used to tie
       2              10 two boxes. What is the:

a   total length of ribbons used?
 b   difference between the length of ribbons used?

2 The diagram shows the distance from
 Zaidi’s house to the library. Calculate the
 difference between the distance of route A and route B.

Encourage pupils to use various problem solving strategies such as working
backwards and making models or tables.

7.6 (i)

5  hour
6

1  hour
2

3  hour
4

Zaidi’s
house

Library

1 km
4

1 m
2

7 m
10

1 km
5

3 km
5

A B

Finishes exercises

Mathematics: 5  hour
                           6
    Science: 1  hour
                  2

Helps mother

3  hour
       4

Difference in time
88

TEACHER’S
NOTES

88

1 Fill in the blanks with improper fractions and mixed numbers.

2 Write the improper fractions and mixed numbers for the diagrams
 below.
 a       b

3 Find the value of Q.

4 Calculate.
 a    1  +  1  =                   b     1  +  2  =                   c     1  +  3   +  1  =
    3      3                             5      3                              2       4      6
 d    5  –  1  =                   e    3  –  1  =                   f    9  –  1  –  1  =
       7      7                             8      4                             10     5     2
 g    8  +  7  –  2  =          h    5  –  1  +  1  =            i      1  +  5  –  2  =
     9      9      9                    6        2      3                      4       8      3

5
Based on the diagrams, calculate the fraction

of the shaded parts.

6 a    Asmah uses  3 kg of sugar to make biscuits and
        8
       1  kg of sugar to make cakes. Calculate the total mass of sugar used.
    2

b    Rahmat bought  3  kg of red chillies,  1  kg of green chillies and 4 kg
                                  10                             4                                         5
       of lettuce to garnish his cuisine. What is the difference in mass

between the chillies and the lettuce?

0 321

1
2

1
2

3
2

7
2

5
2

0

1

4
5

1
 1

2
3
10

Q
89

TEACHER’S
NOTES

1.25 metres.

cm
130
129
128
127
126

Tell stories to pupils based on pictures and activities about decimals. For example,
long jump scores and mass of objects or volumes of liquid.

8.1 (i) 95

School

DECIMALSDECIMALS

Recognise decimals

8

1
Thirty-eight point five
degrees Celcius.

89

S P O R T

R E C R E A T I O N

Countries

China

Australia

Malaysia

Score

422.30

366.50

359.20

Source:
http://www.london
2012.com/diving/
event/women-10m/
index.html.

Her score is three
hundred and fifty-nine
point two zero.

Wow! Malaysia
won the third
place! Pandelela
won bronze
medal.
90

TEACHER’S
NOTES8.1

(i),(ii)

Carry out activity in pairs to guess decimal numbers written in numerals in the air
or on pupils’ backs.

http://www.onlinemathlearning.com/word-decimals.html

2

3

This is the smallest fish in the world.
                      Its length is 7.900 millimetres.

Seven point nine                        Seven point nine
                           hundred                                            zero zero

Form a decimal number with
           three decimal places.

Write decimal in
words.

90

Paedocypris Progenetica

Sourcer: http://www.nhm.ac.uk/about-us/

news/2006/jan/news_7501.html

Zero point one
four three

0.14 0.15

1 0.005

One point zero zero five

Three decimal places

Decimal point

1 •  0 0 5

Who wrote correctly?
Discuss.

0.143

• 0 093

Three decimal places is three digits
after the decimal point.

INFORMATION
91

TEACHER’S
NOTES

ones

0

8

tenths

0

hundredths

1

4

thousandths

5

Number

0.317

9.408

Words

six point two
five

8.1
(i), (ii)

Form letters or patterns using square papers. Write the decimal values of the
shaded and unshaded squares in numerals and in words.

9791

•

•

•

•

Materials        Players

Graph paper, scissors, glue,    5 pupils in a group.
A4 coloured paper, pen.

Steps

1 Cut out 1 000 squares from a graph paper. Colour the graph paper
 to form a pattern.

2 Paste the graph paper onto an A4 coloured paper.

3 Write the coloured parts in decimal.

4 Cross-check each members’ work in the group.

5 Keep in Mathematics file or display your work in the Mathematics corner.

1 State the coloured parts in decimal.
 a        b                c

2 Write in words.
 a    0.7                       b    1.43                 c    8.011                   d    64.78
 e    90.054                 f     52.6                 g    371.08               h    109.125

3 Complete the table.
92

TEACHER’S
NOTES

1    There are 1 000 tiles arranged on the wall. 27 of them are
   red. Convert    27  to decimal.
     1 000

27    =
    1 000          27 out of 1 000 parts

is

27 out of 1 000 parts
            is    0 . 0 2 7

27    =  0.027
                      1 000

2
Convert 2

9
to decimal.

1 000

2

9     =
        1 000

2

9      =

2 +    9

1 000             1 000

= 2 + 0.009

= 2.009

2

9    =   2.009
         1 000

Relate decimals to fractions using MS PowerPoint.
 Explain in detail about the movement of the decimal point when changing fractions to

decimals.

http://www.onlinemathlearning.com/word-decimals.html

27
1 000

ones

2

tenths

0

hundredths

0

thousandths

9•

8.2 (i)

Use place
value chart.

3 zeroes

3 decimal
places

9
1 000

1  =  1 000
        1 000

1  =  1 000
        1 000

2

9
       =

2 009

1 000     1 000

=  2.009

92

Relationship between fractions and decimals

0 . 0 2 7
1  0 0 0 ) 2 7 . 0 0 0
      –         0
      2 7   0 0
      – 2 0   0 0
          7   0 0 0
      –  7   0 0 0
            0

27    =  27 ÷ 1 000
1 000
93

TEACHER’S
NOTES

3  Convert 1.076 to fraction of thousandths.

1.076 =

1.076 =

1 + 0.076

= 1 +
    76

1 000

= 1
   76

1 000

1.076 = 1 +  0  +   7   +     6
                                10     100     1 000
                                = 1 +    70    +     6
                                1 000      1 000
                                = 1    76
                                     1 000

1.076 =  1   76
                    1 000

1 Match.

2 Write in decimals.
 a       72        b    13   46        c    48   81         d    25 903      e    60     5
       1 000                1 000                 1 000                 1 000                 1 000

3 Write in fraction of the thousandths.
 a    0.037     b    1.815           c    5.203          d    39.040      e    17.9

Carry out activities like matching fraction cards to decimals number cards.

http://www.onlinemathlearning.com/decimals-to-fraction.html8.2 (i)

ones

1

tenths

0

hundredths

7

thousandths

6•

9     1
   1 000

9     17
   1 000

7    9
   1 000

197
1 000

19
1 000

7.009 9.017

9.0010.0190.197

1.076 is 1 ones,
0 tenths,
7 hundredths and
6 thousandths.

93

7   × 10
=

70

100 × 10      1 000

Change
  7

to
        100
equivalent fraction.

1 = 1 000            0.076 =    76
        1 000                         1 000

93
94

TEACHER’S
NOTES

Compare decimal numbers using number line.

http://www.mathsisfun.com/numbers/ordering-game.php?m=Dec-Tricky

The more the
coloured parts, the
larger the value.

8.2 (ii)

1   Which is the larger value, 1.023 or 0.97?

1.023             0.97

1.023 is larger than 0.97

2   Compare    2.168   with   2.45  .

2.168 is less than 2.45

2.45                                  2.168

8                            P  Q                                                R   9

Which letters have the values of 8.3 and 8.35 on the number
 line above? Explain.

Look at the ones
digits first. Then,
compare other
digits.

In which place value does the digit 6 in
6.666 has the largest value? Explain.

Compare decimals

ones

2

2

hundredths

6

5

thousandths

8

0

tenths

1

4

same value

1 is less than  4

94

•

•

•
95

TEACHER’S
NOTES

Do various exercises and activities using flash cards.

3

1 Write the decimal numbers on the number line. Fill in the blanks
 with more than or less than.

0         0.05       0.1                      0.2                      0.3                       0.4

a   0.08                           0.11         b    0.27                             0.3

c    0.31                            0.13        d    0.4                               0.04

2 Match.

0.26                43.01                2.06                4.310                 2.6

2.060                 4.31                43.010              2.600               0.260

3 State more than, less than or equals.

a    0.12               0.121          b    1.6                             1.06

c    2.08                        2.080         d    4.953                        4.95

8.2 (ii)

Can you add zero
after 8? Is the value
the same?

0.8 2.410
3.09

Can you drop
the zero?
Discuss.

Is the value of 3.9 and
3.09 the same when
you drop the zero?

95

Compare the value of 0 in each
decimal number above. Explain.

9595
96

TEACHER’S
NOTES

Use addition of decimals involving measurements without conversion of units.

http://interactive.onlinemathlearning.com/dec_addition.php?action=generate&
 numDigits0=2&numDigits1=2&numProblems=10

1  Fatin bought 2 ribbons.
  What is the total length of the two ribbons?

0.2 m  +  0.5 m  =             m

0.2        0.5

0.2 m + 0.5 m =   0.7  m

The total length of the two ribbons is  0.7  m.

2  Calculate the total volume of water in the two containers.

1.056 ℓ + 2.98 ℓ  =

1      1
                      1 . 0 5 6
                    + 2 . 9 8 0

4 . 0 3 6

1.056 ℓ + 2.980 ℓ =   4.036  ℓ

The total volume of water is 4.036 ℓ.

0.2 m

0.5 m

Arrange the numbers
so that the decimal
points are lined up in
the same column.

8.3 (i)

Is the answer correct?
Discuss.

Addition of decimals

1.056 ℓ 2.98 ℓ

Add the tenths:

2 tenths + 5 tenths = 7 tenths

Add the ones:
0 ones + 0 ones = 0 ones

+

ones
        0

0

0

tenths

2

5

7

•

•

•

96

3.17 + 5.238 =
              1

3.1  7
         + 5 . 2 3 8

5 . 5 5 5
97

TEACHER’S
NOTES

Emphasise to pupils that adding decimal numbers is the same as adding whole
numbers.

http://www.math-play.com/soccer-math-adding-decimals-game/adding-
 decimals-game.html

1.6

1.4

1.8

2.0

1.6

1.4

1.8

2.0

1.6

1.4

1.8

2.0

8.3 (i)
97

3  RM4.72  +              =  RM10.05

9    10

10 . 05
                 –  4 . 72

5 . 33

RM4.72  +   RM5.33   =  RM10.05

Fill in the blanks. The total of two numbers are outside the boxes. Each
decimal number filled in the box can be repeated.

1 Complete the following.
 a    0.29 + 3.48 =                          b    8.07 + 6.493 =

c    2.4 + 6.36  =                           d    4.209 + 8.874 =

e             + 3.08 = 9.154   f     26.459 +          = 60.7

2 Solve.
 a    What is 1.5 more than 39.05?

b    4 thousandths more than 5.79 is         .

3 Find the total of the largest and the smallest values.

0.87 8.07 8.7 7.080.780 7.8008.070.87 0.780 8.7 7.08 7.800

97

Relate addition
to subtraction.

RM4.00 +       = RM10.00
                       = RM10.00 – RM4.00

0.61.3

0.9
98

TEACHER’S
NOTES

1  What is the distance from National Monument to Perdana Lake Gardens?

3.7 km – 2.1 km =              km

Subtract the tenths:
     7 tenths  – 1 tenths  = 6 tenths
         Subtract the ones:
     3 ones – 2 ones = 1 ones

3.7 km – 2.1 km =  1.6   km

The distance from National Monument to Perdana Lake Gardens is  1.6   km.

2  17.9 kg – 6.85 kg =            kg

17.9 kg – 6.85 kg =   11.05  kg

Carry out simulation activities of subtracting decimals using paper strips to reinforce
the concept of subtraction.

http://www.math-play.com/subtracting-decimals-game/subtracting-decimals-
 game.html

8.4 (i)

3 . 7
–  2 . 1

1 . 6

Subtraction of decimals

Regroup because
0 hundredths is not
enough to subtract
5 hundredths.

–

tens

1

1

ones

    7

6

1

tenths
8

9

8

0

hundredths
10

0

5

5

•

•

•

98

Perdana Lake GardensNational MonumentMerdeka Square

3.7 km

2.1 km
99

TEACHER’S
NOTES

Guide pupils to subtract using partitioning or counting down.

http://interactive.onlinemathlearning.com/dec_subtraction.php?action=generate&
 numDigits0=2&numDigits1=2&numProblems=10

3              – 8.342 = 15.67

1  1    1

1 5 . 6 7 0
                +    8 . 3 4 2

2 4 . 0 1 2

24.012  – 8.342 = 15.67

Fill in the blanks.

1 Complete the following.
 a    10.7 – 0.3 =   b    9.211  –  4.37  =
 c    2.15 – 1.6 =   d    34.46 – 5.182 =
 e    50.81 –          = 7.293          f              – 17.94 = 80.6

2 Solve.
 a    How much less is 0.09 from 3.7?
 b    Find the difference between 40.2 and 18.56.
 c    How much must be subtracted from 30.2 to get 9.065?

3 Find the word by solving the questions.
 Take off my skin, I won’t cry, but you will! What am I?

0.625    1.13       0.715      0.625        1.13

a    3.3 – 2.17 = N   b    7.125 – 6.5 = O
 c     8.4 – 7.685 = I

8.4 (i)

–                .    9
            6    .

99

–  1  =  2

3  =  2  +  1

3   –  1  =  2

9999
100

TEACHER’S
NOTES

1  What is the total volume of water
    in the two beakers?

2 × 0.9 ℓ  =

2 × 0.9 ℓ =   1.8   ℓ

The total volume of water is    1.8   ℓ.

2  6 × 3.28 =    3 7 × 19.403 =

1     4               6  2         2

3 . 2 8             1  9 . 4 0 3
  ×             6     ×                    7

1 9 . 6 8          1 3 5 . 8 2 1

6 × 3.28 =   19.68   7 × 19.403 =  135.821

Emphasise that multiplying decimals is the same as multiplying whole numbers.

http://interactive.onlinemathlearning.com/dec_multbywhole.php?action=generate&
     numDigits0=1&numDigits1=2&numDigits2=1&numProblems=10

8.5 (i)

Multiplication of decimals

1 000 mℓ
900

800

700

600

500

400

300

200

100

1 000 mℓ
900

800

700

600

500

400

300

200

100

0.9 ℓ 0.9 ℓ

1

0 . 9
×      2

1 . 8

Multiply the tenths:
2 × 9 tenths = 18 tenths
18 tenths is 1 ones and 8 tenths.
Multiply the ones:
2 × 0 ones = 0 ones
0 ones + 1 ones = 1 ones

Put the decimal point in
the answer based on the
number of decimal places in
the question.

INFORMATION
101

TEACHER’S
NOTES

Explain the multiplication pattern of a decimal number by 10, 100 and 1 000.

8.5 (ii)

4  10 × 0.5 =

10 × 0.5 =   5.0

5  100 × 7.214 =          6       9.08 × 1 000 =

7.2 1 4 × 100 = 721.4      9.08
                                   ×       1 000

100 × 7.214 =   721.4      9 080.00

9.08 × 1 000 =   9 080

The answers in red are the products of
 the two numbers in each row. Complete
 the numbers.

1 Complete the following.
 a   8 × 3.7 =    b   4 × 2.64 =
 c    5 × 0.219 =          d   9 × 15.036 =
 e   100 × 1.5 =                               f   6 × 43.278 =

2 Solve.
 a   Given 3 × 3.85 = 11.55. What is 9 × 3.85?
 b   2 × 5.03 =          × 10. What is the number in the empty box?

Talk about the multiplication pattern of
a decimal number by 10, 100 and 1 000.

1.68 10.0

4.2 5.0

10 × 0.5  = 5.0

0.5
× 1  0

5.0

When multiplying a number
by 10, move the decimal point
one place to the right.

INFORMATION
102

TEACHER’S
NOTES

Emphasise that decimal points must be aligned in the same column in division.

Afif’s house

The post office is
located in the middle
of Afif’s house and
the school.

8.6
(i), (ii)

School

I poured 1.6 ℓ of water into 10
cups. Calculate the volume of
a cup of water.

1.6 ÷ 10 = 0.16

1

0.86 km

What is the distance from Afif’s house to the post office?

0.86 km ÷ 2 =            km

0.86 km ÷ 2 =    0.43   km

The distance from Afif’s house to the post office is   0.43  km.

2  1.6 ℓ  ÷ 10 =            ℓ

0. 1  6
  1 0 ) 1 .6 0
       – 0
          1 6
       – 1 0
    6 0
          – 6 0
       0

1.6 ℓ ÷ 10 =    0.16  ℓ

Divide the ones:
0 ones ÷ 2 = 0 ones
Divide the tenths:
8 tenths ÷ 2 = 4 tenths
Divide the hundredths:
6 hundredths ÷ 2 = 3 hundredths

When dividing a number
by 10, move the decimal
point one place to the left.

0 . 4 3
2 ) 0 . 8 6
 –  0
      0   8
 –       8
           0 6
       –     6
              0

INFORMATION

Division of decimals
103

TEACHER’S
NOTES

3  12.9 ÷ 100 =

0.1 2 9
  1 0 0 ) 1 2.9 0 0
         –  0
             1 2 9
          – 1 0 0
               2 9 0
            – 2 0 0
         9 0 0
               – 9 0 0
               0

12.9 ÷ 100 =   0.129

5             ÷ 6 = 72.415

1  2         3

7 2 . 4  1 5
    ×                    6

4 3 4 . 4 9 0

434.490  ÷ 6 = 72.415

1 Complete the following.

a    9.4 ÷ 2 =    b    3.27 ÷ 3 =

c    17.25 ÷ 5 =   d    36.108 ÷ 9 =

e            ÷ 8 = 5.634    f             ÷ 10 = 0.76

g            = 60.9 ÷ 100  h    2.803 =          ÷ 1 000

2 Find the quotient of 13.5 divided by 6.

Carry out quiz or mental calculation.

http://interactive.onlinemathlearning.com/dec_divbywhole.php?action=generate
 &numDigits0=1&numDigits1=3&numDigits2=1&numProblems=10

8.6 (i), (ii)

How do you
divide? Explain.

4  57.0 ÷ 1 000 =

0.0 5 7
  1 0 0 0 ) 5 7.0 0 0
             – 0
      5 7 0
             –       0
      5 7 0 0
             – 5 0 0 0
         7 0 0 0
       – 7 0 0 0
          0

57 ÷ 1 000 =   0.057

64.0  ÷  10  =  6.4

64.0  ÷  100  =  0.64

64.0  ÷  1 000  =
104

TEACHER’S
NOTES

1                               Malaysia Sports XV Pahang 2012
           7 – 16 July 2012
        Rhythmic Gymnastics

Source: Printed by SUKMA XV Pahang on 3.8.2012

Shok Yuki’s score 0.341 more than Izzah’s score. What is
 Izzah’s score?

Given           Shok Yuki’s score: 0.341 more than Izzah’s score.

Find           Izzah’s score.

Operation      Subtraction.

Solve           23.191 – 0.341 =

Check                                         2     11

2 3 . 1 9 1
                                           –     0 . 3 4 1

2 2 . 8 5 0

23.191 – 0.341 =   22.850

Izzah's score is  22.850.

Guide pupils to solve problems using mantic reasoning.

8.7 (i)

Contingent

Wilayah Persekutuan

Selangor

Selangor

Names of Gymnast

Tai Qing Tong

Shok Yuki

Izzah binti Azman

Placing

1

2

3

Izzah’s score must
be less than Shok
Yuki’s score.

Solve the problems

Final Score

24.225

23.191

?

1

2 2 . 8 5 0
+    0 . 3 4 1

2 3 .  1  9 1

Calculate the total score for the first and the
third placing. Check by estimation.

Malaysia Sport
105

TEACHER’S
NOTES8.7 (i)

2  In conjuction with the Recycle Campaign, Year 4
  Anggerik collected 9 piles of old newspapers.
  The mass of each pile was 8.5 kg. Calculate the
  total mass of the newspapers collected.

There were 9 piles of newspapers. The mass

of each pile was 8.5 kg. Calculate the

total mass of 9 piles of newspapers collected.

9 × 8.5 kg =

4
                           8 . 5
              ×         9

7 6 . 5

9 × 8.5 kg =  76.5 kg

The total mass of newspapers collected was 76.5 kg.

Volumes of drinks bought

Calculate the total volume of each type of drinks bought.

Check the answer using repeated addition.

Draw a diagram.

Guide pupils to solve the problems using a method from the simpler case first.
       Inculcate moral values during discussion.

8.5

8.5

8.5

8.5

8.5

8.5

8.5

8.5

8.5

If there are 100 piles of newspapers, what
is the total mass? Calculate mentally.

3.5 ℓ
3

1.25 ℓ
8

0.325 ℓ
9

Volumes of
each container (ℓ)

Number of containers

JUICE

ORANGE

MILK

RECYCLE
CAMPAIGN
106

TEACHER’S
NOTES8.7 (i)

3    Puan Nurin has 2.52 m of lace. The length of the
    lace is enough for 6 pairs of L-sized shirts or
  8 pairs of M-sized shirts. How many metres of lace
  is used for one pair of L-sized shirt?

Given         Length of lace:  2.52 m
            Number of L-sized shirts: 6

Find            Length of lace for one
           L-sized shirt.

Operation      Division

Solve

2.52 m ÷ 6 =

0 . 4 2
              6 ) 2 . 5 2
               –  0
                      2   5
                  –  2   4
                         1  2
                     –  1  2
                           0

2.52 m ÷ 6 =   0.42   m

0. 42 m of lace is used for one pair of L-sized shirt.

Check with
multiplication.

Solve problems using paper strips or simulation activities.

1
    0 . 4 2
×         6

2 . 5 2

2.52 m

?

Calculate the length of lace for
one pair of M-sized shirt.
107

TEACHER’S
NOTES

Materials    Newspapers, catalogues, magazines or pictures from the
        Internet, scissors, glue, A4 paper.

Steps

1 Gather information on prices, lengths, masses, volumes of liquid
 involving decimal points from magazines or the Internet.

2 Cut and paste pictures on A4 paper.

3 Create situations involving addition, subtraction, multiplication or
 division and solve them.
 Example:

Intan and her two sisters share the cost of
 RM120.90 of a handbag for their mother. How
 much money does each person contribute?

4 Teacher checks on pupils᾽ work.

5 Display the best work.

Solve.

a Shima bought 3 items.
  i   Calculate the total cost of the most expensive and the cheapest items.
  ii  Shima and her 2 friends shared an amount of money equally to

buy a dictionary. How much money did each person pay?
 iii   Calculate the total cost of 4 similar bags.

b Miss Lim bought 12.6 m of fabric to make 8 pieces of table cloths.
Calculate the length of fabric for each table cloth.

c     The diagram shows the metre reading of
     Encik Jasni’s car after travelling a distance of
     45.7 km. What is the original metre reading of
     his car?

RM
48.50

107

RM27.90

RM12.60

451.4
 72835

STUDENT᾽SDICTIONARY
108

TEACHER’S
NOTES

108

1 Calculate.

a   3.6 + 25.49 =     b   48 – 5.07 =               c   6 × 7.082 =

d   5.8  ×  10  =             e   70.4 ÷ 100 =               f   0.981 ÷ 9 =
g         ÷ 8 = 23.44       h   51.42 +      = 80.065        i   68.391 =        –  21.609

2 How much more is 0.9 than 0.75?

3 Add  1
   17

and 0.54. State the total in decimal.
         1 000

4                           Which estimation is the most accurate for the
      answer? Explain.

a   1 300 to 1 350                b   1 351 to 1 400

5 Solve the problems.

a    The mass of a blue chest is 13.805 kg. The mass of a red chest is
     2 times the mass of the blue chest. The mass of a red chest is 5

time the mass of the black chest.

i    Calculate the mass of a red chest.

ii    What is the mass of the black chest?

b    A length of wire which measures 4.2 m is cut into 6 equal parts.

What is the length of each part of the wire?

c                The volume of water in the pail is 15.8 ℓ
     less than the volume of water in the
              container. What is the volume of water

in the pail?

d    The incomplete table below shows the result of 100 m running event.

i The difference time recorded between

the first winner and the second was
       0.12 seconds. What was the time recorded
                                               by Usain Bolt?

ii   Usain Bolt was 0.16 seconds faster than
                  Justin Gatlin. Calculate the time recorded

by Justin Gatlin.
Source: http://www.london2012.
             com/athletics/event/men-
             100m/indx.html

13.95 × 99

The result of 100 m (M)
Running Olympic 2012

Usain Bolt

Yohan Blake

Justin Gatlin

?

9.75 s

?

27.04 ℓ
109

TEACHER’S
NOTES

Tell stories about situation involving percentages in everyday life.
 Emphasise the relationship between hundredths fractions and percentages using

hundred squares.

9.1 (i)

Sekolah9

Method 2

0.73 = 0.73 × 100%
  = 73%

Method 1

0.73 =  73
    100
   = 73%

1   Write 95% in decimal.       2   State 4% in decimal.

95% =        4% =

95% = 95       4% =   4
            100                 100

=  95 ÷ 100            =    4. ÷ 100

= 0.04

95% =   0.95      4% =  0.04

3   Convert 0.73
   to percentage.

0.73 =

PERCENTAGEPERCENTAGE

0.73 =   73%

109

CEREAL CEREAL

4%
-

4%
0%

0%
9%

9%

0 . 9 5
1 0 0 ) 9 5 . 0 0
       – 9 0   0
             5   0 0
           – 5   0 0
                     0

MARCH
     EXAMINATION

BAHASA
    MALAYSIA

Name: Chin WeiClass: 4 Arif
Marks: 95%

I got 95%.

NUTRIENT VALUE INFORMATION

Serving size: 30 g           Serving Per Container: 9

AMOUNT PER SERVING
            Total Energy : 111 kcal

30 g per serving        %AKG*

Protein

2.1 g

4%

Total Fat

0.2 g                       0%

Cholesterol

0.0 mg
           0%

Total Carbohydrate                     25.5 g
           9%

Dietary Fiber

0.9 g                      4%

Sugar

2.1 g

-

Nitrate

200.0 mg
           9%

Relationship between percentages and decimals
110

TEACHER’S
NOTES

Expose the easiest way to convert decimals to percentages by multipling decimals
with 100%.

http://www.superteacherworksheets.com/percents/converting-fraction-decimals-
 percents_EASIE.pdf

4   State 0.9 in percentage.

0.9 =

0.9 =  9 × 10
                10 × 10

=  90
                 100

= 90%

0.9 =  90%

A   +   B  =  80%
  10      10

The value of A is less than the value of B. The difference of A and B is 2.
What is the value of A and B?

1 Convert to decimal numbers.

a    9%           b    12%           c    47%           d    65%           e    80%

2 Complete the table.

Decimal number    Percentage      Decimal number     Percentage

73%                     35%

0.29                       0.5

8%                     61%

0.7                       0.03

3 State the values of P and Q in percentages.

9.1 (i)

0.10 0.2 0.3 0.4 0.5

State 0.01 in percentage.

10
100

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

20
100

30
100

40
100

50
100

60
100

80
100

90
100

100
100

70
100

P Q
111

TEACHER’S
NOTES

Prepare answer cards according to the number of pupils. Recreate activity according
to pupils’ abilities.

http://www.mathgoodies.com/lessons/vol4/decimals_to_percents.html
9.1 (i)

Materials

Answer card, pen,
coloured pencils/crayons.

Steps

1 Teacher prepares
 answer card.

2 Write the values of the decimals or
 percentages next to the values
 of the decimals or percentages stated.

3 Colour the matching values of the decimals or percentages with the
same colour.

4 Display your work in the Mathematics corner.

1 Create a greeting card for your
 friend’s birthday.

2 Create your greeting using ̔ percentages
 and decimal codes᾽.
3 Decorate your greeting card.

4 Email the
 code
 breaker
 table
 to your
 friend.

0.7

5%
6%

0.51

48%

0.11

82%

0.98

29%

30%

Find the matching

Secret Gree  tin
g Card

number and replace
decimal or percentage

them with the alphabet.

40%

CODE BREAKER TABLE

C
90%

L
0.32

S
0.02

P
7%

F
99%

O
0.5

Y
1.0

T
65%

R
0.25

A
70%

I
0.85

H
10%

U
0.4

D
0.11

B
0.2

E
48%

Answer card

0.48  2%  0.07   0.48  0.9    85%  0.7  32%  32%   100%

0.99     50%      25%
   0.7    25%     8

5%     3
2%

0.1 0.7  0.07  0.07  100% 20% 85% 25%  0.65  0.1  11
% 0.7 100%
112

TEACHER’S
NOTES9.1 (i)

1 Write the decimal number and percentage for the shaded parts.

a                           b                           c                           d

2 Complete the decimal number and percentage on the number line.

3 Fill in the blanks.

a    0.11 =        b    0.2 =          × 100%           c    38% =
         =          %
            =   %                  =

4 Convert to percentage or decimal.

a   0.7              b   42%              c   0.6              d   30%              e   0.05
  f   0.84           g   9%       h   0.23            i   17%      j   100%

5 Fahmi shaded 8 parts out of 100 squares. State the percentage of  the
parts not shaded.

6          Based on the diagram on the left, state
          the percentage for:

a                        b                        c

0 0.5 1

8%

112

0.03

3%
113

A Answer the following questions.

1. Write 64 013 in words.

2. State the place value for the
digit 8 in the number 82 750.

3. Partition 95 107 according to the
digit value.

4. Write the numerals for eighty-
one thousand and four.

5. What is the value of P on the
number line below?

6. Add 9 043, 62 319 and 127.
Round off the answer to the
nearest ten thousand.

7.    52 009 – 628 + 4 745 =

8. Convert       to improper

fraction.

9. Convert                to decimal

number.

10. What is the value of  0.02
 less than 43.015?

11. 36 402 is 9 000 less than            .

12. Subtract 49 hundreds from
 7 ten thousands.

13. Write the mixed numbers that
represents the shaded parts of
the whole diagram.

14.    7 . 02              13 . 467

Find the difference in value for
the two underlined digits on the
cards above.

15.  21 780 ÷ 36 =

16.

PQR is a straight road as shown
in the diagram above. Find the
distance of PQ in km.

17.  2   +   1   +  4   =
  5        5       5

 Give answer in the form of

mixed number.

18. 8 ten thousands  + 17 hundreds
+ 6 ones =

19. How many hundreds are there in
90 000?

1
3

7

15
19

1 000

23 189 23 339 23 789P
P RQ

5.28 km

2.7 km
114

20.

What number is represented
by the spike abacus above?

21.  12.36 ÷ 4 =

22.

One number is left out in the

number pattern above. What is
the number?

23.  827 × 64 =

24. What must be added to 45 769
to become 90 000?

25.

State the shaded parts in
decimal.

26.

State the value of P in percentage.

27.

Form a number by adding the
digit values of the underlined
digits on the number cards above.

28.  20 120 × 4 ÷ 8 =

29. Subtract 5.9 from 60.12.

30.          ÷ 4 = 3.75
 What is the missing number in

the empty space?

31.  3  +   1   –   1   =
  5      10       2

Give answer in the simplest
form.

32. Find the difference between

and     .

33. Given 1 058 × 9 = 9 522,
 therefore, 1 058 × 63 =

34. Solve.
 54 768 –          = 9 317

35. Convert 1.101 to fraction.

36. Complete the following.

a.            × 1.58 = 1 580

b.   42.9 ÷         = 0.429

37. State 3% in decimal.

38.    1   +   1   +   5   =
  4       2        8

Give answer in mixed numbers.

41 900 43 900

42 90039 900

7
9

2
3

32 804 81 750 64 018

P 0.5 0.7

Ten
thousands

Thousands Hundreds Tens Ones
115

39.

State the digit in the
thousandths place in this
number card.

40. The product of 1 207 and 48,
divided by 16 is          .

B Solve the following problems.

1.

The table shows the number of
two model of cars produced by
a factory. Calculate the total of
the two models produced.

2. There were 50 421 male voters
at a polling station. The number
of female voters is 9 827 less
than the male voters.  What
is the number of the female
voters?

3. A basket can be filled with 45
oranges. Calculate the number
of baskets needed to fill 13 500
oranges.

4. A blue ribbon is 3 times the
 length of the red ribbon as in the

above diagram. Find the length of
the blue ribbon.

5. Faiz uses    ℓ of blue paint and

ℓ of white paint to paint the living

room of his house. What is the

total volume of paint used?

6. Chew cycles a distance of     km

on Saturday and     km on

Sunday. Find the difference in

the distance he cycles.

7. The total mass of 6 bars of
chocolate is 1.5 kg. What is  the
mass of a bar of  chocolate

in kg?

8. 400 m Running Event Result

The table shows 400 m Running
 Event result. The time difference

between the two winners is
0.8 minute. Calculate the time
taken by the runner up.

9.

The total of three numbers in
each row is the same as shown
in the diagram. Find the total of P
and Q.

5
8

1
8

3
4

7
8

2.04

11.69

P

28.6

9.43

Q5

Champion

Runner Up

9.281

9.12 m

Model

Number

Myvi

28 407

Proton

25 964

2.1 minutes

?
116

10. Encik Rosli delivers 985
newspapers each day. How

many newspapers does he
deliver in two weeks?

11.

The table above shows the

number of vehicles passing

through a toll plaza on a certain
day. Find the number of lorries
passing through the toll plaza.

12.

Miss Sim bought 5 boxes
of buttons as shown in the
diagram above. There are
white, black, red and yellow
buttons of the same number.
Find the number of the yellow
buttons.

13. The diagram shows
 Nathan’s height. Suli’s
 height is 0.19 m less
 than Nathan’s. How
 tall is Suli in metres?

14.

The diagram above shows the
locations of towns A, B and C.
Calculate the total distance
from A to C through B in km.

15.

Calculate the total mass
of vegetables bought by
Puan Intan.

16. A container holds     ℓ of water.

Ai Lin drinks    ℓ  of the water.

What fraction, of the water is

left in ℓ?

17.

The diagram above shows the
 number of biscuits in a tin.

Radin bought 15 tins of biscuits
and repacked them into
30-piece packets. How many
packets did he make?

Cucumber

1
kg

4

Cabbage

7
kg

10

Long Bean

2
kg

5

Vehicle

Car

Bus

Lorry

Total

Number

28 109

15 486

?

61 027

5.8 km
A

B

C

12.706 km

1 280 buttons
 1
2

1
5

140
pieces

Nathan
1.4 m

140
pieces
117

TEACHER’S
NOTES

Relate the usage of combination of money in everyday life involving the usage of
deposit slips. Inculcate moral values such as cautious and trustworthy.

"

10.1 (i)

School10

RM12 560

1  What is the total amount of money deposited?

RM5 000      RM5 000      RM2 000       RM560

50 pieces 100 pieces 100 pieces  56 pieces

Combination of money

Notes

RM100

RM50

RM20

RM10

Number of
pieces

50
100
100
56

Value
(RM)

5 000
5 000
2 000
560

Total
(RM)

12 560

Sir, this is my
money and form.

The total amount of money deposited is   RM12 560 .

MONEYMONEY

Counter 2

Twelve thousand five hundred and sixty ringgit
118

TEACHER’S
NOTES

Carry out simulation activities using play money. "

10.1 (i)

2

Price of car  = (300 × RM100) + (150 × RM50) + (4 × RM20) +
         (3 × RM5) +  (6 × RM1)
     = RM30 000 + RM7 500 + RM80 + RM15 + RM6
                    = RM37 601

Zairi has RM2 000 in his wallet. He wants to change all his money
    to RM20 and RM5 notes with the same number of notes. What
    is the number of RM20 and RM5 notes?

1    State the value for the following combination of money.
     a

b

2    Complete the combinations of money for RM70 362.

500 p
ie

ce
s

200 p
ie

ce
s

5
0 p

ie
ce

s

300 p
ie

ce
s

15
0 p

ie
ce

s

4 p
ie

ce
s

50 p
iece

s

50 p
iece

s

10
0 p

iece
s

10
0 p

iece
s

6
 p

ie
ce

s
Sp

ecim
en

3 p
ie

ce
s

RM ?
Count the amount of money
to find the price of the car.

600

Value of money

Combination 1

Combination 2

RM100  RM50    RM20    RM10     RM5     RM1

700

RM100 RM50 RM20 RM10 RM5 RM1

600
119

TEACHER’S
NOTES

Encourage pupils to relate the usage of rounding off in daily situations. "

10.2 (i)

RM30.20 is close to RM30.

RM30.20 rounded off to the nearest ringgit is   RM30  .

Round off RM30.95 to the nearest ringgit.

RM30.95 is close to RM31.

RM30.95 rounded off to the nearest ringgit is  RM31 .

1 The total is RM30.20.
You can just pay RM30.

a

RM30 RM30.50    RM31

RM30.20

b

RM30.95

RM30.50    RM31RM30

What is the value of RM30.50 when
rounded off to the nearest ringgit?

119

Round off values of money

How much
is our food?
120

TEACHER’S
NOTES

RM600.49

Educate pupils to make an estimation before spending.
 Discuss the importance of rounding off to make an estimation.
"
"

10.2 (i)

RM599.50 RM600.50

--
--

-

--
--

--
-

RM599.80
RM600.45RM599.95

RM600.05

Value of money

RM316.50

RM284.30

RM5 274.90

RM21 061.45

RM55 780.80

RM84 299.50

Round off to the nearest ringgit

RM 600

2   State five values of money when rounded off to the nearest ringgit
  become RM600.

The five values of money when rounded off to the nearest ringgit

become RM600 are  RM599.50 ,  RM599.80 ,  RM599.95 ,

RM600.05  and  RM600.45 .

1 Complete the table.

2 State three values of money when rounded off to the nearest ringgit
become:

a    RM1 692                 b   RM72 100             c   RM93 995

Why is RM600.50 not rounded off to
RM600? Discuss.
121

TEACHER’S
NOTES

Carry out addition operations using sales brochures, price tags and picture cards.

"

10.3 (i)

1  a   Calculate the total cost of a computer set and a broadcasting set.

RM7 430 + RM6 135 =

RM7 430 + RM6 135 =  RM13 565

b    What is the total cost of all the items above?

RM7 430 + RM6 135 + RM410.90 =

RM7 430 + RM6 135 + RM410.90 =  RM13 975.90

R

RM  7  4 3 0

RM  6  1 3 5

RM 13  5 6 5

+

RM 1 3  5 6 5 . 0 0

RM     4 1 0 . 9 0

RM 1 3   9 7 5 . 9 0

+
RM   7 4 3 0

RM  6  1 3 5

RM 1 3   5 6 5

+

RM7 430 RM6 135 RM410.90

Addition of money

Adding money is the same
as adding whole numbers.

The total cost of a computer set and a broadcasting set
is  RM13 565.

The total cost of all the items is RM13 975.90.

Align the dots that
separate the ringgit
and the sen.

INFORMATION
122

TEACHER’S
NOTES

Remind pupils of common mistakes made when the dot separating ringgit and sen
is not aligned in the same column.

10.3 (i)

"

2  RM517.85  +  RM6 809.50  +  RM21 043.20  =

RM517.85  +  RM6 809.50  +  RM21 043.20  =   RM28 370.55

3  RM32 451  +              +  RM23 041. 30  =  RM89 793 .95

RM32 451  +   RM34 301.65  +  RM23 041.30  =  RM89 793.95

1     Add.
  a   RM9 202.30  +  RM31 058  =

b   RM60 112  +  RM3 504  +  RM29 037  =

c    RM74 000  +  RM120.75  +  RM8 350.25  =

2 Complete the following.

a      +  RM42 632  =  RM64 120.25

b   RM59 783  +  RM4 000.90  +          =  RM83 115.80

c             +  RM23 455.40  +  RM60 090.30 = RM100 000

RM          5 1 7 . 8 5

RM   6  8 0 9 . 5 0

RM  2 1  0 4 3 .  2 0

RM  2 8  3 7 0 . 5 5

+

1

RM 3 2  4 5 1 . 0 0

RM 2 3  0 4 1 . 3 0

RM 5 5  4 9 2. 3 0

+

RM 8 9  7 9 3 . 9 5

RM 5 5  4 9 2 . 3 0

RM 3 4  3 0 1 . 6 5

–

2

RM55 492.30  +            =  RM89 793.95

=  RM89 793.95 – RM55 492.30

1

Simplify the case
3 +       + 2 = 8
      5 +        = 8
                  = 8 – 5
123

TEACHER’S
NOTES

Use business or sale catalogues to compare prices."

10.4 (i)

1  The diagrams show the price of a living room
  set and a bedroom set. Find the difference
  of the cost for the two sets.

RM38 715 – RM11 400 =

2

RM100 000 – RM88 400  =        RM100 000 – RM87 350 =

RM100 000 – RM88 400 = RM11 600     RM100 000 – RM87 350 =  RM12 650

I will choose Wasaki motorcycle so that the balance in my saving is more
than RM12 000.

RM 38 7 1 5

RM 1 1  4 0 0

RM 2 7  3 1 5

–

RM87 350

RM38 715

Subtraction of money

RM 1 0 0  0 0 0

RM    8 8  4 0 0

RM      1 1  6 0 0

–

9   10   10
9

RM 1 0 0  0 0 0

RM    8 7  3 5 0

RM      1 2  6 5 0

–

9   10   10
9

10
9

RM11 400

RM88 400

RM38 715 – RM11 400 =   RM27 315

The difference of the cost for the two sets is RM27 315.

Wasaki
Yama

My saving is RM100 000. Which
motorcycle should I choose so
that my balance in saving is more
than RM12 000?
124

TEACHER’S
NOTES

Emphasise on identifying the key words which mean subtraction in questions such
as balance, difference and compare.

"

10.4 (i)

3  Below is Miss Sim’s record of her withdrawal.

Miss Sim made two withdrawals for her children’s registration to
  university. Calculate the balance in her account on 2nd May 2014.

RM18 754.17 – RM1 500  –  RM2 400 =

RM18 754.17 –  RM1 500  –  RM2 400 =  RM14 854.17

4  RM39 257 –             = RM16 304.12

RM39 257 –  RM22 952.88  = RM16 304.12

1 Subtract.

a   RM76 452  –  RM50 210  =

b   RM50 825.80 –  RM43 500.20  –  RM5 674  =

c   RM98 045 –           =  RM31 721.55

2    a   Calculate the difference between RM24 500.10 and RM75 320.
        b  What must be reduced from RM91 008.75 to get RM63 122.40?

Date

16/02/2014

27/03/2014

02/05/2014

Withdrawal (RM)

600

1 500

2 400

Balance (RM)

18 754.17

RM 1 8  7 5 4 . 1 7

RM    1  5 0 0 . 0 0

RM  1 7  2 5 4 . 1 7

–
RM 1 7  2 5 4 . 1 7

RM    2  4 0 0 . 0 0

RM  1 4  8 5 4 . 1 7

–

6 12

RM 3 9  2 5 7 . 0 0

RM 1 6 3 0 4. 1 2

RM  2 2  9 5 2 . 8 8

–

8 12 6 100

The balance in Miss Sim’s account on 2nd May 2014 is RM14 854.17.
125

TEACHER’S
NOTES

Encourage pupils to plan and record their expenditure."

10.5 (i)

1

Calculate the balance.

RM68 047.35 + RM9 500 – RM3 470  =

RM68 047.35 + RM9 500 – RM3 470  =  RM74 077.35

2 Based on the table below, what is the balance in Encik Akid’s saving
 account?

RM80 000 – RM12 500 + RM23 864  =

RM80 000 – RM12 500 + RM23 864 =  RM91 364

Find other ways to
get the answer.

RM 6 8  0 4 7 . 3 5

RM    9  5 0 0 . 0 0

RM  7 7  5 4 7 . 3 5

+
RM 7 7  5 4 7 . 3 5

RM    3  4 7 0 . 0 0

RM  7 4  0 7 7 . 3 5

–

1 4 14

Hasnah made a record of income and expenditure of her layered
cake business in June.

Addition and subtraction of money

Savings

RM80 000

Business
profit

RM23 864

Balance of
saving account

?

Donation to Lahad
Datu victims

RM12 500

RM 6 7  5 0 0

RM 2 3  86 4

RM 9 1  3 6 4

+

1  1

RM 8 0  0 0 0

RM 1 2  50 0

RM  6 7  5 0 0

–

10107
9

The balance is RM74 077.35.

The balance in Encik Akid’s savings account is RM91 364.

Income                         (RM)

Money in bank          68 047.35

Layered cakes sold     9 500.00

Expenditure                (RM)

Cake ingredients bought   3 470.00
126

TEACHER’S
NOTES

http://www.dadsworld.com/v1/worksheets/moneywordproblems/
Money_WordProblems_Four_Add_Subtract_V2.html

10.5 (i)

Encik Kamal has RM50 893.55 in his savings account. He withdraws
 an amount of money to repair some damages of his house. Then  Encik

Kamal receives an investment dividend of RM16 000. Now, he has
 RM45 714.10. Calculate the cost of repairing his house.

RM50 893.55  –             +  RM16 000  =  RM45 714.10

RM50 893.55 –  RM21 179.45  + RM16 000  =  RM45 714.10

1     Calculate.

a    RM63 750 + RM2 840 – RM30 128  =

b    RM76 835.40  –  RM21 096.55 + RM38 415.75 =

c    RM63 502.70  +          – RM52 321.15 = RM22 066.55

d             – RM23 179 + RM56 005 = RM70 142.80

2   Solve.
      a    Find the difference between the sum of RM62 463 and RM30 179
    to RM25 408.

b    Reduce RM57 659.80 from the sum of  RM26 377 and RM45 831.20.

c    How much to reduce from the sum of RM59 082 and RM37 264
   to get RM50 000?

3

RM 6 6  8 9 3 . 5 5

RM 4 5  7 1 4 . 1 0

RM 2 1  1 7 9 . 4 5

–

138

RM 5 0  8 9 3 . 5 5

RM 1 6  0 0 0 . 0 0

RM  6 6  8 9 3 . 5 5

+

The cost of repairing Encik Kamal’s house is RM21 179.45.
127

TEACHER’S
NOTES10.6 (i)

Emphasise that multiplying the value of money is the same as multiplying whole
numbers. The difference is the dot separating the ringgit and sen.
"

Calculate the total cost of jerseys.

a Calculate the total payment for encyclopedias.

62  ×  RM174.50  =

62  ×  RM174.50  =  RM10 819

The total payment for encyclopedias is RM10 819.

b Calculate the total cost of sports shoes.

100 × RM218.90 =

100 × RM218.90 = RM21 890

100 × RM218.90  =   RM21 890

The total cost of sports shoes is RM21 890.

RM       1 7 4 . 5 0

×                 6 2

3 4 9   0 0

+   1 0  4 7 0   0 0

RM1 0  8 1 9 . 0 0

Description

Encyclopedia

Sports shoes

Jersey

Quantity

62

100

1 000

No.

1

2

3

Total (RM)Price per unit (RM)

174.50

218.90

12.60

Total

Date : 11.5.2014

No. 3343Harmony Company  Sdn. Bhd ( MA109877)

Multiplication of money
10.6 (i)

Given   x 3 = RM2 520

x             = RM25 200          Find the value of       and            .

1   Multiply.

a  3 × RM9 143 =                    b    12 × RM880 =

c    40 × RM607.45 =                   d    100 × RM532.60 =

e    1 000 × RM78.15 =                      f              × RM909 = RM90 900

g             × RM47.20 = RM47 200    h    1 000 ×          =  RM55  030

2   a  Calculate the cost of    b   What is the cost for 27
   8 bicycles.                                      cupboards?

3        Miss Chew’s salary for 1 working day is  RM61.70.
                 is a holiday. Use the calender to calculate
        Miss Chew’s salary for January 2014.

4   Complete the table below.

RM14 210      RM658

128

Item

Skate board

Skating shoes

Quantity

95

34

Price per unit (RM)

117

143.90

Total cost (RM)
129

TEACHER’S
NOTES

Innovation Champion

2014

RINGGIT MALAYSIA

FORTY-FIVE THOUSAND

RM45 000

1       Eight pupils shared equally a winning prize after becoming the
   champion of 2014 Innovation Competition. What was the value

of money received by each pupil?

RM45 000  ÷  8  =

RM     5 6 2 5
        8  RM 4 5 0 0 0
              –  4 0
                      5 0
                    4 8
                            2 0
                          1  6
                               4 0
                    4  0
             0

RM45 000 ÷ 8 =   RM5 625

2 Based on the situation shown, calculate the donation received by each
 orphan on Hari Raya celebration gathering.

  RM30 000 ÷ 50 =

RM 30 000   = RM600
                50

RM30 000 ÷ 50 =  RM600

6   0  0

1

Remind pupils to put the dot separating the ringgit and sen correctly when dividing
money involving ringgit and sen.
"

10.7 (i)

–

–

– How much will each pupil get if
there are 10 pupils in a group?

Division of money

Each pupil received RM5 625.

Each orphan receives RM600.

The donation of RM30 000 is for
50 orphans.

129
130

TEACHER’S
NOTES

"

10.7 (i)

3  RM74 580 ÷ 100 =

                RM74 5 8 0. ÷ 100 = RM745.80

RM74 580 ÷ 100 =   RM745. 80

4                   ÷ 1 000 = RM96

RM96 000  ÷ 1 000 = RM96

1   Divide.

a    RM10 347 ÷  6  =                         b    RM74 129.60 ÷ 8 =

c    RM52 710 ÷ 42 =                         d    RM30 708 ÷ 60 =

e    RM81 700 ÷          =  RM817         f              ÷ 1 000 = RM92

2

3  Calculate the price of each unit.

RM 9 6

1  0 0 0

RM 9 6 0 0 0

×

Show pupils the easy way to divide an amount of money by 100 and 1 000 .

6 siblings share an amount of money equally
to buy a car for their mother. How much money
must each person pay?

The inverse of division
is multiplication.

Quantity

30

1 000

Item

Air conditioner

Iron

Price per unit (RM) Total Cost (RM)

37 227

54 900

RM 42 900
131

TEACHER’S
NOTES10.8 (i)

1  Zek Supermarket gains a profit of  RM14 270.35  in August and

RM16 381.60 in September. Calculate the profit made in August

and September.

Given     Profit in August  RM14 270.35          Find      Total profit in
                         Profit in September RM16 381.60                 August and
              September

Operation   Addition

RM14 270.35 + RM16 381.60 =

RM14 270.35  + RM16 381.60 =   RM30 651.95

The total profit in August and September

is  RM30 651.95.

Solve Check

+

R M 1 4  2 7 0. 3 5

R M 1 6  3 8 1 . 6 0

R M 30  6 5 1 . 9 5

1            1           –

RM 3 0  6 5 1 . 9 5

RM 1 6      3 8 1 . 6 0

RM 1 4    2 7 0. 3 5

2 10 5 15

Solve the problems

August

September

Total

RM14 270.35

RM16 381.60

?

The profit made in October is RM12 843.10.
What is the difference of profit between
September and October?

Use ῾drawing a diagram᾽ method or modelling to solve problems."
132

TEACHER’S
NOTES

Introduce various strategies to solve problems such as drawing pictures, finding
patterns, trial and error and mantic reasoning.

10.8 (i)

"

2 Puan Sumarni bought a house and a car at a promotion price as
 shown in the pictures. The normal price of the house is RM98 750

while the normal price of the car is RM64 300. Calculate the difference
between the normal price and the promotion price of the two assets.

Given

Find   The differences in prices for the house and the car.

Operation  Subtraction

Solve   Difference in price: RM98 750 – RM88 640 =
    for the house

RM98 750 – RM88 640 =  RM10 110

The difference between the normal price and the
  promotion price for the terrace house is  RM10 110.

Difference in price: RM64 300 – RM59 020 =
     for the car

RM64 300 – RM59 020 =  RM5 280

The difference between the normal price and

the promotion price for the car is RM5 280.

–
RM 6 4  3 0 0

RM 5 9  0 2 0

RM   5  2 8 0

5 214 10

How do you check the answer? Discuss.

Asset

Terrace house

Car

Promotion price

RM88 640

RM59 020

Normal price

RM98 750

RM64 300

–

RM 9 8  7 5 0

RM 8 8  6 4 0

RM 1 0  1 1 0

DAMAI INDAH
TERRACE HOUSE

Promotion
Price

RM88 640

Promotion
Price

RM55 020
133

TEACHER’S
NOTES

3  Encik Zaid organised a Family Day. He rented 12 chalets with the

payment of  RM4 320 a day. How much is the rental for 3 days?

 Given  Rental for  1 day  is  RM4 320 .

  Find  Rental for  3 days .

  Operation Multiply

Solve  3 × RM4 320 =

3 × RM4 320 =  RM12 960

The amount of rental to be paid for 3 days is RM12 960.

4  Kumar plans to open a car workshop with the cost of  RM18 000. He
 saves RM600 every month. How many months must he save money?

Given Cost to open workshop is RM18 000,
  Monthly saving is RM600.

Find Number of months  to save money.         Operation    Division

Solve RM18 000 ÷          = RM600
       RM600 ×    = RM18 000

RM18 000 ÷  30  = RM600

Kumar must save his money for 30 months.

Carry out group activities using story cards, for example tourism activity or picnic.

"

10.8 (i)

Mark the
key words.

RM         6 0 0

3 0

R M 1 8  0 0 0

×

×

RM    4  3 2 0

3

RM 1 2  9 6 0

How to check the answer?

RM4 320 RM4 320 RM4 320

First
Day

Second
Day

Third
Day

RM18 000
RM600

= 30

3   0

1

Check
134

TEACHER’S
NOTES

http://www.flickr.com/photos/dylwalters/509076089/

10.8 (i)

5   Encik Fong and 14 friends took a tour
   package to Langkawi to experience the
   amazing hanging bridge. The total cost of
   the package is RM28 500. What is the cost
   for each participant?

   Given     The number of participants is 15.
       The total cost of package is RM28 500.

Find     The cost for each participant.

Operation    Division

Solve     RM28 500 ÷ 15 =     Check

RM28 500 ÷ 15 =   RM1 900

The cost of each participant is RM1 900.

1 9 0 0

1 5

9 5 0 0

1 9 0 0 0

28 5 0 0

×

+

1

4

1 participant  RM?

RM28 500

R M   1 9 0 0

R M 2  8 5 0 0

–  1  5

1  3 5

–  1  3 5

0 0

–   0

0 0

–  0

0

15
135

TEACHER’S
NOTES

135

Solve.

a

b Nur Ain paid RM14 000 for a kitchen set which costs RM13 899.90.
    What is her balance?

c A book rack in a library costs RM1 105. What is the cost of 14 similar
          book racks?

d A scholarship of  RM20 865 was distributed equally to 5 students.
   What was the value received by each student?

e Encik Farid attended a meeting overseas. The following is his
 expenditure for a day.

i   What is Encik Farid’s total daily expenditure?
  ii  What is his total expenditure for 10 days?

f The price of entrance ticket to the zoo is RM12. The total amount
  collected from sales of tickets is RM22 368. Calculate the number of
  visitors to the zoo.

RM896 RM1 734.90

135

The picture shows the price of
an electric oven and a water
purifier. Find the total cost of
both items.

Food and
drinks

RM200

Hotel
accomodation

RM587

Transport

RM100
136

TEACHER’S
NOTES

136

Materials   Brochures from supermarkets, bookshops and shopping malls,
                       expenditure record form.

Steps

1 Prepare a record form as above.

2 Refer to the supermarket brochures. Choose and calculate the price
of items and complete the total expenditure of RM1 000. Use basic
operations to get the total.

3 Complete the form and give it to a friend to check.

4 Do a new record form to make a total expenditure of RM5 000.

5 Keep all records that have been checked in Mathematics file or
Mathematics exercise book.

136

No.         Item Price Per Unit    Total Cost  (RM)Quantity

Name: ..............................  Class: ..............
                               Record of Expenditure

Total                   RM1 000
137

TEACHER’S
NOTES

Peta menunjukkan negara-negara Anggota ASEAN.

C H I N A

INDONESIA

LAOS

BRUNEI

SINGAPORE

PHILIPPINES

MALAYSIA

CAMBODIA
VIETNAM

MYANMAR

Carry out an activity on guessing the names of ASEAN countries currencies at
 random and describe their characteristics using flash cards.
 ASEAN: The Association of Southeast Asian Nations.

"

10.9 (i)

Recognise foreign currency

THAILAND
Baht

Rupiah

Dollar

Peso

Riel

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Ringgit

ASEAN Countries

Dollar

Sp
ecim

en Kip

Dong

Brunei   Cambodia  Indonesia    Malaysia   Myanmar  Philippines  Singapore   Thailand   Vietnam     Laos

Sp
ecim

en Kyat
138

TEACHER’S
NOTES

Carry out an activity to make scrapbooks of the currencies ASEAN countries and
world leading nations.

http://www.jepbanknotes.com/index.

"

10.9 (i)

Dollar          Dollar                  Pound

Dollar                        Yen

Swiss Franc               Dollar

Rupee            Taka            Naira

Renminbi                  Won

United States
of America

Canada Great Britain

Switzerland                            Hong Kong

China               Korea

India     Bangladesh       Nigeria

Australia              Japan

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

These are some of
the currencies we
should know.

Which country
uses Euro?
139

TEACHER’S
NOTES

Copy the word maze. Answer the questions and colour the answers.

Complete the table below.

1 The currency used in  buying and
 selling in Singapore is          .

5 The Phillipines is famous for
 her          .

6 What is Cambodia’s currency?

7 Malaysian northern neighbour
 uses          .

8 This ASEAN country uses the
 same currency as Singapore.

2 Indonesia’s currency is          .

3 Kyat is the currency used in         .

4 Chinese Athletes uses          in
 their country.

10.9 (i)

Countries           Laos        Brunei          India

Currency                     Dong       Swiss                    Yen                     Taka
                  Franc

N

X

N

G

O

R

W

N

R

K

I

E

N

U

R

B

E

C

U

B

D

P

R

A

N

E

H

Y

E

I

X

H

M

T

P

G

B

A

M

T

I

D

Q

D

O

H

K

O

N

W

O

S

C

J

H

Z

B

H

E

L

R

K

L

W

I

P

A

G

L

J

E

R

Z

T

P

I

H

A

I

Y

M

Y

A

N

M

A

R

M

139
140

TEACHER’S
NOTES

http://www.coinmill.com/MYR_calculator.

10.9 (ii)

The value of foreign currency

1     State the currencies of ASEAN countries.

2 State the values of the following currencies compared to RM1.
 a   Korea     b   Singapore      c   China         d   Great Britain

3 Choose and state 3 currencies that are frequently traded in
 Malaysia. Why?

Country

Singapore

Thailand

Brunei

Philipines

Indonesia

Vietnam

Laos

Cambodia

Myanmar

United States

Great Britain

China

Japan

Korea

Saudi Arabia

Bangladesh

Nigeria

The value of foreign currency
compared to RM1

0.40 dollar

9.68 bahts

0.40 dollar

13.56 pesos

3 093.35 rupiah

6 513.73 dong

2 370.47 kip

1 287.59 riel

294.82 kyatt

0.31 dollar

0.20 pound

1.94 renminbi

30.49 yen

361.31 won

1.17 riyal

23.90 taka

49.71 naira

Source: Forex Trading Malaysia: Currency Converter , 26th June 2013 08.35:07 hour
141

TEACHER’S
NOTES10.10 (i)

Payment instruments

Pay bills

Discuss the usage and safety of card as an instrument of payment.
 Pupils use their creativity to create payment card with safety features.
"

Buy shoes

I pay RM20 for
2 tickets.

Methods of payment

Is payment by cash suitable for a big
expenditure? Discuss.

Father pays with debit card.
They pay with cash.

Pay for petrol

Charge the
cost of shoes
from my debit
card.

The total payment
is RM107.45.

Debit
Card

SHOES

Buy tickets

Cash
Money

Sp
ecim

en
142

TEACHER’S
NOTES

Pay tolls

Carry out activities to create a suitable payment instrument based on
 pupils’ creativity.
"

10.10 (i)

Donation

Please accept our donation
for the land slide victims.

Cheque

Bank Kita                                                                                STAMP DUTY PAID

Tarikh
                                                                     Date

D       D       M       M       Y       Y
BAYAR/
PAY                                                               ATAU PEMBAWA/OR BEARER

RINGGIT
MALAYSIA

JANGAN TANDA TANGAN DI BAWAH GARISAN/NO SIGNATURE BELOW THIS LINE

CHEQUE NO.                                                                                AC NO.

AC PAYEE
ONLY

B
A

N
K

K
IT

A
 B

ER
H

A
D

Write a suitable situation for the usage of these payment instruments.

Ride a monorail

Cash money
Debit card
Prepaid card
Credit card
Cheque

Situation 1

Buy fish at the market

Situation 2

Pay taxi fare

instrument
Payment

RM60

Talk about each
activity in the
picture.

Prepaid
Card

Sir, please sign
here to endorse
the payment.

Credit
Card

Bank Kita

RM40 000

2 4 1 0 1 4

Forty thousand only

Yayasan Budiman
143

TEACHER’S
NOTES

1 Total up the value of money.

2 Round off the following values of money to the nearest ringgit.

a   RM4 786.65                    b   RM64 093.40              c   RM90 999.50

3 State 3 values of money when rounded off to the nearest ringgit
 become:

a   RM400             b  RM7 653                 c    RM71 042

4 Add RM14 631.25, RM7 419.20 and RM10 291.15.

5 Calculate.

a  RM92 950 + RM7 005 – RM4 000 =

b  RM82 004 – RM53 760 + RM9 112 =

c   RM71 439.05 –          = RM56 372.50

d   RM850 ÷          = RM0.85

e           ÷ 1000 = RM12.50

6 Solve.
 a    The table shows the total bill that
     Encik Hashim has to pay. He pays with
        an amount of RM200. Calculate his balance.

b    Puan Nyonya wants to buy 2 washing
          machines and 3 refrigerators for her new
     restaurants. Puan Nyonya pays with 104
        pieces of RM50 notes. Calculate her balance.

RM10 000

RM150 RM6

RM10 000 RM10 000

RM1 000

Total

RM75.20

RM21.80

RM84.70

Bil

Electric

Water

Telephone

143

RM715.90 RM1 243.75

Specim
en

Specim
en

Specim
en

Specim
en

Specim
en
144

TEACHER’S
NOTES

7 State the currency and country for the following notes.

a                                        b                                      c

d                                       e                                        f

8 Name the country that uses the following currencies.

9 Which payment instrument is suitable to use for each situation?

144

Daily situations

Buying fish and vegetables at the market.

Using card to call a friend.

Buying airline ticket to go on a tour.

Giving donation to fire victims.

Buying electrical items at a supermarket.

Payment
instrument

a   Pound Sterling

d   Naira

g   Baht

b   Won

e   Rupiah

h   Kyat

c    Renminbi

f    Riel

i    Peso

144

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en

Sp
ecim

en
145

TEACHER’S
NOTES

Infuse the elements of EMK in exploring the history of time.

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/time/
 index.htm.

"

11.1 (i)
a

School11

TIMETIME

Recognise time

Day and hour

1

1 day = 24 hours

2 days is equal to
how many hours?





Day and night

Direction of
rotationSun rays

Axis

Day

Night

2 days =          hours

2 days = 24 hours + 24 hours
       = 48 hours

2 days =   48   hours

Analogue
Clock

Hourglass

Ancient people used
various instruments to
determine the time.

Sundial Water Clock

Yes, the complete
rotation takes
24 hours.

--
--

--
--

--
--

--
--

--
--

--
--

--
--

--
--

--
--

--
--

--
--

--
--

--
--

The earth rotates
on its axis in 1 day.
146

TEACHER’S
NOTES

Relate days and hours based on the situation given.

"

11.1 (i)
a

2

3 days =          hours

24 hours   24 hours   24 hours

3 days =  72   hours

3  96 hours =          days

4     6 days 7 hours =         hours

6 days 7 hours   = 6 days + 7 hours
                         = 144 hours + 7 hours
                                   = 151 hours

6 days 7 hours =  151  hours
How many days and hours in
100 hours? Explain.

2 4  9 6
   9 6
    0

–

4

How many hours
in 5 days?

0      1      2          3

2 4  h o u r s
   3

7 2  h o u r s

×

1

96 hours =   4   days

•  Convert 6 days to hours.

6 × 24 hours = 144 hours

In a year, the Rafflesia blooms for 3
to 5 days only. State 3 days in hours.

96 ÷ 24 =           days

x 24

÷ 24

day             hour

INFORMATION
147

TEACHER’S
NOTES

Relate weeks and days based on the life cycle of insects such as the cockroach, the
fly and others.

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/time/
 index.htm

"

11.1 (i) b

1  The Patriotic Month is celebrated for 4 weeks.
  How many days are there in 4 weeks?

4 weeks =      days

4 weeks =   28    days

2  Aisyah and her family went for a holiday in a village for 41 days.
 How many weeks and days were they there?

41 days =      weeks       days

41 days =     5     weeks    6     days

They were in the village for 5 weeks 6 days.

In the life cycle process of a butterfly,        takes about

10 days to transform into                 . State the time in

weeks and days.
  Source: http://www.butterfly-insect.com/diy.book.php

4 × 7 = 28

7   4 1
 –  3 5
   6

5

4  ×  7 days =         days

National Day

31

Week and day

Remember the
7 times table.

There are 28 days in 4 weeks.

week            day
       × 7

÷ 7

INFORMATION
148

TEACHER’S
NOTES

Emphasise that leap year and normal year have the same number of months, but
different number of days.

Guide pupils to identify the leap years.

http://www.sheppardsoftware.com/mathgames/time/TimeConversions.htm

"

"11.1 (i) c

1  Study Kak Ngah’s family chart.
  How old is Usu in months?

5 years =          months

5 years =    60    months

2  187 months =          years          months

185 months =    15    years      7     months

Time taken by planets to make one
                   complete rotation around the sun.

State the time, in months, taken by Uranus.

Source: http://www.thestar.com.my./20130401/world/ploto-is-a-
                     planet-again.asp

Father
45 years 6 months

Mother
42 years

Kak Long
15 years
7 months Kak Ngah

10 years
5 months

Abang Chik
8 years

3 months
Usu

5 years

1 2
   5
 6 0

×

1 5
12  1 8 7
 –  1 2
        6 7
  6 0
   7

–

Year and month

Usu’s age in months is 60 months.

Whose age is the same
as 504 months? Explain.

Jupiter         12 years

Uranus    7 times the time taken by Jupiter

× 12

÷ 12

year           month

INFORMATION
149

TEACHER’S
NOTES

Prepare a few sets of time cards for enrichment activity.
  Game like “Happy Family” is encouraged.

11.1 (i)
a,b,c

"

Players   4 persons      Materials     21 pieces of time cards

(10 pairs of cards, 1 piece of stork card)

Steps

1     Distribute 21 pieces of cards to all players.

2    Determine the players turn. The player with the most

cards gets the first turn.

3    Pull out a card from each player according to turns.

4    If there are matching cards, the 2 cards are taken out.

5    Repeat steps 3 to 4 until all matching cards are

taken out.

6  The player who gets the stork card wins the game.

1 Convert.

2                                           How many weeks and days are

there in May 2014?

3     The first Prime Minister of Malaysia, the late Tunku Abdul

Rahman Putra Al-Haj served for about 13 years.

State his term of service in months.

3

4

149

a    9 days =           hours

i    How many hours in 7 days?

b    8 days 5 hours  =            hours

d   6 weeks  =          days

f    84 days =          weeks

g   10 years 3 months =         months

c     37 hours =         days         hours

e   2 weeks 4 days =          days

h   9 years  =          months

j   State 14 months in years
 and months.
150

TEACHER’S
NOTES

Use time line for addition operation.
 Emphasise the conversion of units from hour to day.

11.2 (i) a
"
"

1      a   The picture shows the
     handicraft products of the
        disabled. Find the total time
     taken to finish the baskets
     and shell crafts.

1 day 9 hours + 1 day 8 hours =          days          hours

1 day 9 hours + 1 day 8 hours =     2    days   17    hours

The total time taken to finish the baskets and shell crafts
        is 2 days 17 hours.

b    How many hours does it take to finish all the handicraft
        products above?

1 day 9 hours + 1 day 8 hours + 2 days 16 hours =           hours

1 day 9 hours + 1 day 8 hours + 2 days 16 hours = 129   hours

The time taken to finish all the handicraft products above
        is 129 hours.

1 day 9 hours

2 days 16 hours

1 day 8 hours

4 days = 4 x 24 hours

= 96 hours

4 days 33 hours  = 96 hours + 33 hours
                      = 129 hours

day    hour

1        9
  1          8

2       1 7

+

day     hour

1         9
  1    8

2       1 6

4         33

+

2

Addition of time
151

TEACHER’S
NOTES

Emphasise the conversion of units from day to week.
 Encourage pupils to talk about their school activities in weeks and days like
 Reading Campaign and sports practice.

11.2 (i) b

a   Calculate the time taken for shooting films at Pulau Redang
    and Belum Rainforest.

4 weeks 2 days + 6 weeks 1 day  =     weeks         days

4 weeks 2 days + 6 weeks 1 day =    10    weeks     3    days

The time taken for shooting films at Pulau Redang and
      Belum Rainforest is 10 weeks 3 days.

b    Calculate the duration taken for filming at the three locations.
        4 weeks 2 days + 6 weeks 1 day + 1 week 5 days

=          weeks         days

4 weeks 2 days + 6 weeks 1 day + 1 week 5 days

=   12   weeks    1    day

The duration taken at the three locations is 12 weeks 1 day.

"
"

FRIM
1 week 5 days

State 2 locations which take 42 days for filming.

Belum Rainforest
6 weeks 1 day

Pulau Redang
4 weeks 2 days

2

The photography association shot films at the locations above.

week     day

4        2
  6        1

1        5

11      8
+

11 weeks    8 days

1        –  7

12 weeks     1 day

+

week     day

4    2
  6             1

1 0    3

+
152

TEACHER’S
NOTES

3  Calculate the duration of service for
  Cikgu Sarah at the three schools based
  on the service record.

4 years 9 months + 3 years

8 months + 10 years 4 months

4 years 9 months + 3 years 8 months
 + 10 years 4 months =   18     years     9     months

The duration of service for Cikgu Sarah at the three schools is
 18 years 9 months.

Interview a few teachers at your school. Record their durations of service at
your school and others. Create an appreciation card for their contributions
and state the durations of service at your school.

1 Add.

a  3 days 7 hours + 2 days 6 hours =          days           hours

b  12 years 1 month + 8 years + 20 months =          months

c  9 weeks 3 days + 5 weeks 6 days =         weeks          days

d  5 days 8 hours + 4 days 10 hours + 12 hours =          hours

2 Find the total of 40 weeks 2 days, 15 days and 8 weeks 4 days.

Give answer in weeks.

17 years 21 months = 17 years +  1 year + 9 months
                        = 18 years 9 months

Diversify questions using a calendar.

11.2 (i)
a, b, c

"

year     month

4    9
  3    8

10   4

1 7       2 1

+

2

Duration

4 years 9 months
   3 years 8 months

Name
of school

SK Baiduri
     SK Angkasa
    SK Aman

Service Record

21 months ÷ 12 = 1 year 9 months

=          years          months   10 years 4 months
153

TEACHER’S
NOTES

Find the difference by doing simulation activities.
 Do subtraction by counting down.

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/
maths/timetables/index.htm

"

11.3 (i) a
"

day     hour

4        1 7
  3            1 2

1    5

–

day    hour

5       5
  2          9

2      2 0

–

4     29
 day    hour

2       2 0
            1 4

2               6

–

1 10

Subtraction of time

4 days 17 hours

3 days 12
 hours

1

Calculate the difference in time taken by the rabbit and the
 tortoise to reach Sang Kancil’s house.

4 days 17 hours – 3 days 12 hours =         days          hours

4 days 17 hours – 3 days 12 hours =     1     day    5    hours

The difference in time taken by the rabbit and the tortoise to reach
 Sang Kancil’s house is 1 day 5 hours.

2 5 days 5 hours – 2 days 9 hours – 14 hours =            days            hours

• 9 hours can be subtracted

from 5 hours.

• Convert 1 day to 24 hours.

24 hours + 5 hours = 29 hours

5 days 5 hours – 2 days 9 hours – 14 hours =    2     days     6     hours

Add 2 days 9 hours and 14 hours. Then, subtract the sum from
5 days 5 hours. Is the answer the same? Explain.
154

TEACHER’S
NOTES

Do subtraction by counting down.

"

11.3 (i)
b

week      day

2    6
  1             5

1   1

–

Mural A
2 weeks 6 days

Mural B
1 week 5 days

The difference in time to complete mural A and mural B is 1 week 1 day.

Assume 1 month = 4 weeks.
Calculate the time difference in
days for the growth of this chick.

3 weeks            3 months

Solve by changing the unit from week
to day first. Is the answer the same?

3  What is the difference, in weeks and
  days to complete mural A and mural B?

2 weeks 6 days  – 1 week 5 days

=          weeks          days

2 weeks 6 days – 1 week 5 days  =    1   week   1    day

4  19 weeks – 4 weeks 3 days – 6 days  =          weeks         days

19 weeks – 4 weeks 3 days – 6 days =    13    weeks    5    days

week   day

1 9    0
  4      3

14    4

–

18   7
                    /

week   day

1 4    4
       6

1 3    5

–

13             11
                    /
155

TEACHER’S
NOTES11.3 (i) c

Carry out activities to find difference in age amongst friends and relatives.

"

year     month
  4 5   3
  3 0   2

1 5   1

–

5   Find the difference of life span
           between the orang-utan and the
  panda. Give answer in months.

45 years 3 months – 30 years 2 months =         months

45 years 3 months – 30 years 2 months =  181  months

6      14 years 7 months  – 8 months – 2 years 3 months

=          years         months

14 years 7 months – 8 months – 2 years 3 months     11

=   11    years    8     months

1     Subtract.

a   8 days 3 hours – 5 days 2 hours =        days         hours

b    24 days  7  hours  –  10  days  15  hours  –  3  days  9  hours

=        days         hours

c   16 weeks 2 days – 6 weeks 5 days – 8 days =        weeks         days

d   31 years – 12 years 8 months  – 5 months =         years         months

2    Solve.
 a   Find the difference between 21 weeks 4 days and 13 weeks 3 days.
            Give answer in days.
 b   How many months more is 50 years than 23 years 9 months?

15 years 1 month = 180 months + 1 month
            = 181 months

30 years
2 months 45 years

3 months

The difference in time to complete mural A and mural B is 1 week 1 day.

The difference of life span is 181 months.

1 4 years  7 months
    2 years    3 months

1 2 years  4 months

–

1 2 years  4 months
         8 months

1 1 years  8 months

–

11             16
156

TEACHER’S
NOTES

Do multiplication using different suitable methods, like repeated addition.
Use schedules for school holidays and co-curriculum activities involving
multiplication of time.

"
"

1  How much time, in days and hours,
  is taken by Raden to do 5 similar
  wood carvings?

5 × 1 day 3 hours =         days          hours

5 × 1 day 3 hours  =     5    days    15    hours

Time taken to do 5 similar wood carvings is 5 days 15 hours.

2      a   Shah Indra attended computer courses.
            What is the total time of the two courses?
     Give answer in days.

2 × 2 weeks 4 days =          days

2 weeks 4 days  = 14 days +  4 days
                                      = 18 days

2 × 2 weeks 4 days =    36   days

This wood carving
is done in 1 day
3 hours.

day     hour

1    3
     5

5      1 5

×

1 8  days
     ×    2
       3  6   days

1

Estimate the number of wood carvings that
can be done in 11 days. Discuss.

2 weeks 4 days

Multiplication of time

11.4 (i)
a, b

The total time of the two courses
is 36 days.
157

TEACHER’S
NOTES

Guide pupils to build conversion of units chart.

"

11.4 (i)
b, c

3 × 2 weeks 4 days =         weeks         days

3 × 2 weeks 4 days=     7     weeks     5     days

3   4 × 10 years 7 months =         years          months

4  × 10 years 7 months =   42   years     4     months

year   month
 1 0       7
             4

40       2 8

×

2 weeks         4 days
                      3

6       12

+  1           –   7

7 weeks     5 days

×

40 years 28 months = 40 years + 24 months + 4 months
        = 40 years + 2 years + 4 months
                                   = 42 years + 4 months

The duration of the three courses is  7 weeks 5 days.

I attended the third course
for the same duration.

12 days = 7 days + 5 days
              = 1 week + 5 days

b

Calculate the duration of
the three courses. State the
answer in weeks and days.
158

TEACHER’S
NOTES

Relate multiplication of time in everyday life.
Inculcate moral values such as valueing time during group activity.

"
"11.3 (i) c

11.4 (i)
a,b, c

Players       4 to 6 persons.

Materials    Pupil’s register book, question cards.

Steps

1 Teacher retrieves information about pupil’s age
 from the register book and give the data to pupils.
2 Distribute question cards to each group.

3 Pupils answer the questions in the allocated time.

4 The group that answers all the questions correctly

in the shortest time wins the game.

5 The group that makes mistakes needs to
 make corrections.

1  Multiply.

a    7 × 8 days 2 hours =          days          hours

b    6 × 6 years 4 months =          years

c     3 × 9 weeks 5 days =          weeks          days

d    8 × 3 days 4 hours =          hours

e    4 × 5 weeks 3 days =          days

f     5 × 4 years 7 months =          years          months

2  Solve.

a    Multiply 6 by 4 days 8 hours. Give answer in days.

b  9 × 8 weeks 4 days =          days

Show the simplest method.

c    Calculate the product for 8 and 10 years 9 months.

Question Card

1. Find a pair of pupils

with the total age of

21 years.

2. The difference in age

of 2 pupils is 3 months.

3. 3 × 10 years 4 months

= ____ years.
159

TEACHER’S
NOTES

Guide pupils to divide units of time by subtracting consecutively.

"

11.5 (i) a

1 a  Based on the table, how long
   does it take to complete a
   model of a single-storey
    house?

6 days 15 hours ÷ 3 =          days         hours

2  days      5  hours

3   6  days    1 5  hours

–  6     –  1 5

0            0

6 days 15 hours ÷ 3 =     2    days     5     hours

b  Calculate the time taken to complete a model of a double-storey
  house. State the answer in hours.

9 days 4 hours ÷ 4 =         hours

2  days        7 hours

4    9  days        4 hours

– 8          +  2 4

1     2 8

–  2 8
                                      0

9 days 4 hours ÷ 4 =    55   hours

5 workers can paint a house in 10 hours. Can a worker
paint the house in 2 hours? Discuss.

Quantity

3 units

4 units

Type of house

Single-storey

Double-storey

Duration

of completion

6 days 15 hours

9 days 4 hours

Division of time

The time taken to complete the model of a single-storey house is
2 days 5 hours.

The time taken to complete a model of a double-storey house is
55 hours.

Welcome

159

2 days 7 hours = 24 hours + 24 hours + 7 hours

= 48 hours + 7 hours

= 55 hours
160

TEACHER’S
NOTES11.5 (i)

b, c

Expose various calculation and conversion of units strategies to pupils."

2  14 weeks 4 days ÷ 6 =          weeks         days

2  weeks          3  days

6  1 4  weeks          4  days

–  1 2         +  1 4

2             1 8

–  1 8

0

14 weeks 4 days ÷ 6 =     2    weeks     3    days

3 12 years ÷ 9 =          months

12 years ÷ 9 =   16    months

1     Divide.

a    2  18 days 20 hours   b   8   9 weeks 1 day

c    4   13 years 8 months   d   5    22 days 7 hours

e    20 weeks 4 days ÷ 6 =         weeks          days

f    45 days 12 hours ÷ 7 =   days          hours

2 Divide 30 years 9 months by 9. Give answer in months.

1 year 4 months = 12 months + 4 months
                          = 16 months

1  year          4  months

9    1 2  years        0  months

–    9              3 6

3                3 6

–  3 6

0

+

Convert the remainder
2 weeks to 14 days.
161

TEACHER’S
NOTES

Solve daily problems by drawing diagrams or making tables.      "

11.6 (i)

1 The table below shows the duration of operation times for two
multipurpose shops. Find the difference in time the two shops operate.

Given       Duration of operation of Era is whole day or 1 day.

Duration of operation of Kota is 8 hours.

Find      Difference in time

   Operation  Subtraction

  Solve      1 day – 8 hours =           hours

16 hours + 8 hours = 24 hours

1 day – 8 hours =  16  hours      Beza masa
kedua-dua

The difference in time the two shops operate is 16 hours.

Solve the problems

Check

Multipurpose shop      Duration of operation

Era                                 Whole day

Kota                               8 hours

2 4  hours

8  hours

1 6  hours

141

–

If another multipurpose shop operates 2 hours more
than Kota, calculate the duration the shop operates.

24 hours – 8 hours =        hours

1 day = 24 hours
162

TEACHER’S
NOTES11.6 (i)

Underline the key information before solving the problem."

2 In a year, a book exhibition is held in 3 stages. Each stage is held for
 1 week  4 days. Calculate the total time for the 3 stages of the exhibition.

3 × 1 week 4 days =          weeks          days

1 week         4 days

×                        3

3                    12

+  1                –    7

4                    5

3 × 1 week 4 days =  4 weeks 5 days

The total time for the 3 stages of the exhibition is 4 weeks 5 days.

3  Four similar phases of housing projects should be completed
in 9 years. Calculate the time in years and months to complete

one phase.

9 years ÷ 4 =          years         months

2 years      3 months

4    9 years      0 months

– 8           + 1 2

1               1 2

– 1 2

0

9 years ÷ 4 =  2 years 3 months

The time taken to complete one phase is 2 years 3 months.

1 week  4 days = 11 days

1 1  days

×  3

3 3  days

4

7   3 3

2 8

5

–

Total

1 week 4 days 1 week 4 days 1 week 4 days

weeks          days

Phase 1   Phase 2   Phase 3   Phase 4

9 years

?

How do you check the answer?
Explain.

Check.
163

TEACHER’S
NOTES

163163

Solve.
a    How much time boat A
 sails more than boat B as
 given in the information?

b A group of pupils made a study about the school history
for 3 weeks 4 days. The folio study was completed in

1 week 5 days. Find the total time taken by them.

c The table shows the duration
 of time taken by Fong to finish
 three projects. Find the total
 time needed to finish all the
 projects. Give your answer in
 days and hours.

d The life span of a jungle cat is about 5 years.
 While the life span of a tiger is 3 times a jungle
 cat. Calculate the life span, in months, of the tiger.

e  The table below shows the age of two pupils.

Pupil              Age

Alia                      13 years 6 months

Danisha         7 months younger than Alia

How old is Danisha?

f Kim attended a course in Putrajaya for 24 days. Calculate
 the duration of the course in weeks and days.

g GRAND PROMOTION
CHILDREN’S CLOTHINGS

18 July – 26 July 2014
Bukit Jalil Stadium

The poster shows the sale of children᾽s
clothings. The sale is held for 1 week 2 days.
The promotion is extended for 9 more days
because of good response. Calculate the time,
in weeks and days, the promotion is held.

2 days 9 hours

Project

History

Science

English

Duration

10 hours

9 hours

7 hours

A

B

1 day 3 hours
164

TEACHER’S
NOTES

164

1 Convert.

a    7 days =           hours           b   144 hours =           days

c    8 weeks 3 days =          days     d            days = 17 weeks

e   12 years =          months

f    92 months =          years          months

2 Solve.
 a   3 days 8 hours + 15 hours =          days           hours
 b   10 years 8 months – 2 years 9 months – 3 years 7 months
    =          years          months
 c   6 × 4 weeks 6 days =          weeks          days

d   11 days 6 hours ÷ 5 =          days         hours

3 Solve.

a    Change 8 days 10 hours to hours.

b           Which is the correct conversion of unit?
                   16 × 7 days   or  16 × 10 days

c   Multiply 4 by 7 weeks 2 days.
 d   28 years divided by 8. State the answer in months.

4 Solve the following problems.
 a   A writer takes 1 year 2 months to complete a novel.
  A collection of short stories is completed 4 months earlier
  compared to the novel. How long does it take to
  complete the collection of short stories?

b Nuriz did a scrapbook in 3 weeks 1 day. While Aziah
 took half the time taken by Nuriz. Calculate the time

taken by Aziah, in days.

c Mala is 8 years 9 months. The difference in age between
 Mala and her brother, Bala is 2 years 5 months.

Calculate Bala᾽s age.

16 weeks =         days

164
165

TEACHER’S
NOTES

12.1 (i)
a, b

What unit will you use to state:
(i) the thickness of a textbook?
(ii) the distance between Kota Bharu, Kelantan and Kangar,

Perlis? Explain.

Encourage pupils to explore the usage of mm and km in every day life.
 Use search engines and type the key word “location map” to retrieve various

information related to distance in kilometres.

1

2

School

LENGTHLENGTH

Recognise units of length

12

The length of the pencil
lead is 75 millimetres.

75 mm
Long

24
 pencil lead

5 mm
0.5 mm

Kilometre is used to state
the distance between two
places. The symbol is km.

Millimetre is used to state
the length of small and short
objects. The symbol is mm.

The distance from
Merdeka Square to
Petronas Twin Towers
KLCC is 3.5 kilometres.
166

TEACHER’S
NOTES

http://www.ixl.com.math/grade-3/compare-and-convert-metric-units-of-length

12.1 (ii)
a

1  6 cm =          mm     2     120 mm =         cm

6 cm  = 6 × 10 mm    120 mm  = (120 ÷ 10) cm

= 60 mm          = 12 cm

6 cm =   60   mm          120 mm =   12   cm

3  3 cm 7 mm =          mm    4     83 mm =          cm          mm

3 cm 7 mm    = 30 mm + 7 mm        83 mm = 80 mm + 3 mm

= 37 mm                = 8 cm + 3 mm

= 8 cm 3 mm

3 cm 7 mm =   37   mm   83 mm =   8    cm    3    mm

Complete the following.

a    152 mm =          cm 2 mm  b    631 mm = 63 cm          mm

c    4 cm          mm = 49 mm  d    71 mm =          cm          mm

e             cm 9 mm = 909 mm   f     34 mm = 3 cm          mm

The length of the blue
line is 1 cm or 10 mm.

1 cm

10 mm 1 cm = 10 mm

Relationship between centimetres and millimetres

10
cm

2 3 4 5

100
mm

20 30 40 50

Is 120 mm longer than 19 cm? Discuss.

cm       mm

× 10

÷ 10

INFORMATION
167

TEACHER’S
NOTES

Carry out activities at the school track or field for simulation distance of 1 000 m or
 1 km to reinforce pupils’ understanding.

http://www.math- Grills.com/measurement/matric_meters_kilometers_001.html
12.1 (ii)

b

1  8 km =          m      2     16 000 m =          km

8 km = 8 × 1 000 m    16 000 m   = (16 000 ÷ 1 000) km

= 8 000 m            = 16 km

8 km =   8 000  m            16 000 m =  16   km

3   71 km 900 m =                 m     4     25 300 m =          km          m

71 km 900 m = 71 000 m + 900 m         25 300 m   = 25 000 m + 300 m

= 71 900 m                     = 25 km + 300 m

= 25 km 300 m

71 km 900 m =    71 900   m            25 300 m =   25  km   300 m

Complete the following.

a    12 km =          m   b    78 000 m =          km

c    3 km  =          m            d    90 km =          m

e    8 km          m = 8 407 m   f    50 km          m = 50 021 m

Relationship between kilometres and metres

0 metre

1 km = 1 000 m

5 km 25 m equals to 5 250 m. Explain.

100 metres

So, Saiful will run a
distance of 1 000 m. This
distance is equal to 1 km.

Saiful will run 100 m back
and forth 5 times for
training today.      km       m

× 1 000

÷ 1 000

INFORMATION
168

TEACHER’S
NOTES

Carry out activities to estimate lengths of objects in mm and measure actual
lengths using measuring tape, thread, paper strip and ruler. Record the
measurements in a table.

http://www.vendian.org/mncharity/dir3/paper_rulers/

12.2 (i)

X

The thickness of the dictionary is           . The width of the bookmark is           .

1 What is the length of necklaces X, Y and Z?

2 Which necklace is the longest and which is the shortest?

3 What is your conclusion about the length of necklaces X and Y? Explain.

1 State the length of each object.
 a        b

mm
 i             mm    ii            mm

Y

Z

(i)

(ii)

Measure length of objects

Start measuring from 0 mm.
Read the measurement at
the other end.

30 mm

ERASER

1409050 150100 1308040 1207030 110602010
mm

0

The length of the
eraser is 30 mm.

D
IC

T
IO

N
A

R
Y

good
luck
169

TEACHER’S
NOTES

Create more questions on estimation of distances based on the above map.
 Discuss the importance of estimation in daily life.

12.2 (ii)

A digital library will be built within 3 km from the jetty.
Where is the suitable location? Explain.

X

Estimate distance

The estimated
distance is 2 times
more than 1 km.

169

X

1  What is the estimated distance
  from the chalet to the health centre?

Estimated distance = 2 km

The estimated distance from the chalet to the health centre is  about 2 km  .

2  State the place that is located almost 4 km from    .

The  health centre  is located almost 4 km from    .

3  What is the estimated distance from the jetty to the amusement centre?

Estimated distance = 5 km

The estimated distance from the jetty to the amusement centre is about 5 km .

The estimated
distance from
jetty to chalet is
about 1 km.

X

1 km

Chalet

Jetty

Amusements
Centre

Robotic
Museum

Health
Centre

Jetty

1 km
Jetty Chalet

Health CentreChalet

1 km

5 km

Jetty Amusement centreChalet
170

TEACHER’S
NOTES

Guide pupils to determine the estimated distances between two places based on
 a given reference.

12.2 (ii)

You and three friends found a treasure map
showing a treasure placed at X . The estimated
distance from the arrow to the cactus
area is 1 km. Complete the table below to
estimate the distance that you will pass
through.

Discuss the route that you have chosen and give reasons.

The diagram below shows the estimated distances from Nelly’s house
to a few surrounding places.

a Choose the correct answer.
  i    The distance from Nelly’s house to the school passing through
    the library is (more than, less than) 10 km.
  ii    Nelly wants to go to the library, the distance is
    (more than, less than) 5 km.
b What is the estimated distance from Nelly’s house to the Internet

Centre? Discuss and give reasons for your answer.

Route

Estimated
distance

(km)

A B C

X
A

B

1
km

C

1 km

Nelly’s
House

School

Bus Station

Library

Internet
Centre

Use thread to
measure the curved
route. Compare with
the given estimated
distance of 1 km.

Bus Station

L
ibrary
171

TEACHER’S
NOTES12.3 (i)

a

1  Based on the picture, what is the
  height of the seedling after 3 days?

5 mm + 2 cm 3 mm =         cm         mm

cm     mm
                    5
                   +  2         3

2      8

5 mm + 2 cm 3 mm =    2   cm    8   mm

The height of the seedling after 3 days is 2 cm 8 mm.

2    Add 32 cm 5 mm and 40 cm 9 mm.

32 cm 5 mm + 40 cm 9 mm =          cm          mm

cm     mm

3 2        5
                     +  4 0        9

1 4

Convert 14 mm to
              1 cm 4 mm.

cm      mm
                                                    1

3 2        5
                     +  4 0       9

7 3        4

32 cm 5 mm + 40 cm 9 mm =   73  cm    4   mm

http://www.k5learning.com/free-math-worksheets/fourth-grade-4/measurement

Addition of length

5 mm Increased by
2 cm 3 mm

After
3 days
172

TEACHER’S
NOTES

3  Calculate, in mm the total length of the ropes P, Q and R below.

18 cm 2 mm + 16 cm 5 mm + 17 cm 8 mm =         mm

cm     mm              cm     mm
                                                          2  1

1 8       2                 1 8       2
                    1 6       5         1 6       5
                +  1 7       8                   +  1  7        8

1 5         5 2       5

52 cm 5 mm = 520 mm + 5 mm
               = 525 mm

18 cm 2 mm + 16 cm 5 mm + 17 cm 8 mm =  525 mm

The total length of the ropes P, Q and R is 525 mm.

4

Calculate the total distance in the
  cycling competition for the two days.

76 km 433 m + 10 km 662 m =         km         m

km       m                     km      m
                                                                                1

7 6     4 3 3                   7 6    4 3 3
       +  1 0     6 6 2                +  1 0    6 6 2

1  0 9 5                   8 7    0 9 5

76 km 433 m + 10 km 662 m =  87 km   95  m

The total distance in the cycling competition is 87 km 95 m.

Drill pupils on conversion of units using flash cards.

12.3 (i)
a, b

P   18 cm 2 mm

Q   16 cm 5 mm

R   17 cm 8 mm

Distance of cycle

76 km 433 m

10 km 662 m

Day

First

Second
173

TEACHER’S
NOTES

Drill conversion of units using flash cards.

12.3 (i)
b

5  Add 8 km 240 m, 20 km 790 m and 5 km 125 m.
  Give the answer in m.

8 km 240 m + 20 km 790 m + 5 km 125 m =         m

km         m                  km       m
                                            1                                        1  1         1

8      2 4 0                      8     2 4 0
                     2 0      7 9 0                    2 0     7 9 0
                 +     5      1 2 5                +     5     1 2 5

1  1 5 5                    3 4     1 5 5

34 km 155 m = 34 000 m + 155 m
                      = 34 155 m

8 km 240 m + 20 km 790 m + 5 km 125 m =  34 155  m

1 Calculate.
 a    cm     mm         b    km     m         c    cm     mm         d    km     m
     34        7                  14     261              51        8                    3     128
   +  22        9             +  82     972             10        3                   1 1    492
               +  41        7              +    7    1 01

2 Add.
 a    12 cm 3 mm + 4 mm =          cm          mm

b    15 cm 4 mm + 7 mm + 21 cm 9 mm =          cm

c    65 km 28 m + 12 km 903 m =         km         m

d    25 km 114 m + 47 km 201 m + 665 m =         km          m

3 Solve.
 a    What is the total length, in cm and mm, when 125 mm

is added to 40 cm 8 mm?

b    The distance from Q to R is 642 m
     more than the distance from P to Q.
     What is the distance, in km and m, from P to R?

P
R

Q

7 200 m
174

TEACHER’S
NOTES

Encourage pupils to check the answers using addition.

12.4 (i)
a, b

1  What is the difference of length between the two keys shown in the
  pictures below?

5 cm 6 mm – 3 cm 2 mm =          cm         mm

cm     mm
    5         6
               –  3         2

2   4

 5 cm 6 mm – 3 cm 2 mm =    2    cm     4    mm

The difference of length between the two keys is 2 cm 4 mm.

2  28 cm 6 mm – 8 mm – 13 cm 5 mm =         mm

Method 1          Method 2

cm     mm          cm     mm
       2  7          16

2 8       6          2 7      8
      –               8            –  1 3      5

2 7       8               1 4      3

28 cm 6 mm – 8 mm – 13 cm 5 mm =  143 mm

3  78 km 607 m – 23 km 179 m =          km          m

78 km 607 m – 23 km 179 m =   55   km  428  m

7 16

2 8 6 mm       2 7 8 mm
 –         8 mm            –  1 3 5 mm

2 7 8 mm        1 4 3 mm

km       m
                        9
       5 10 17

7 8    6 0 7
–  2 3    1 7 9

5 5    4 2 8

Which method would you choose? Why?

Subtraction of length

14 cm 3 mm = 140 mm + 3 mm
    = 143 mm

5 cm 6 mm 3 cm 2 mm
175

TEACHER’S
NOTES12.4 (i)

b

4  12 km 742 m – 145 m – 3 km 415 m =         m

km       m       km      m
        13
                  6  3  12

1 2    7 4 2        1 2    5 9 7
         –           1 4 5    –    3    4 1  5

1 2    5 9 7                    9    1 8 2

12 km 742 m – 145 m – 3 km 415 m =  9 182  m

5

What is the distance from C to D based on the diagram above?

32 km 720 m – 8 km 950 m – 15 km 785 m =         km         m

km      m             km       m
         2  11       1612                 16 16 10
         3  1        17 2  0    2 2      17 7  0

3 2    7 2 0   2 3    7 7 0
   –     8    9 5 0         –  1 5    7 8 5

2 3    7 7 0                       7    9 8 5

  32 km 720 m – 8 km 950 m – 15 km 785 m =    7   km   985 m

The distance from C to D is 7 km 985 m.

Calculate.

a    94 cm 9 mm – 2 mm =          cm         mm

b    90 km 898 m – 47 km 288 m =         km         m

c     1 071 km – 67 km – 192 km =         km

d    76 cm 3 mm – 33 cm 5 mm – 7 mm =         mm

e    77 km 28 m – 9 km 35 m – 11 km 943 m =         m

http://www.bbc. uk/bitesize/ks2/maths/shape_space/measures/read/2/

Convert 1 km to 1 000 m.

First, add 8 km 950 m and 15 km 785 m. Then, subtract the
answer from 32 km 720 m. Is the answer the same?

9 km 182 m = 9 000 m + 182 m
   = 9 182 m

A B   C D

32 km 720 m

8 km 950 m 15 km 785 m
176

TEACHER’S
NOTES

Drill multiplication of length, with or without conversion of units.
 Carry out activities like quiz and cross number puzzle to reinforce pupils’

understanding. 12.5 (i)
a

1

The table above shows the lengths of ribbons for two
  types of bows.

  a   What is the length of ribbon needed to make 3 pink bows?

3 × 32 cm 2 mm =         cm         mm

cm    mm
        3 2      2
                    ×             3

9 6     6

   3 × 32 cm 2 mm =  96  cm    6   mm

The length of ribbon needed for 3 pink bows is 96 cm 6 mm.

b   Calculate the total length of ribbon, in cm, for 8 white bows.
          8 × 61 cm 5 mm =         cm

Method 1     Method 2
              cm      mm           cm       mm
              6 1        5              6 1         5
               ×                 8              ×                   8

4 8 8     4 0                      4 8 8     4 0
                 +         4  – 4 0   4 × 10 mm

4 9 2        0

8 × 61 cm 5 mm =   492  cm

The total length of ribbon, in cm, for 8 white bows is  492 cm.

488 cm 40 mm = 488 cm + 4 cm
        = 492 cm

Ribbon

Pink

White

Length

32 cm 2 mm

61 cm 5 mm

Multiplication of length
177

TEACHER’S
NOTES

Drill multiplication using flash cards and check the answers using calculator.

12.5 (i)
b

2  The distance of 1 round of go-kart circuit is 5 km 602 m. Calculate
  the distance covered in 4 rounds.

4 × 5 km 602 m =         km         m

km      m           km     m

2

5     6 0 2    5   6 0 2
  ×                4      ×                4

2 4 0 8          2 2   4 0 8

4 × 5 km 602 m =   22  km   408   m

The total distance covered in 4 rounds is  22 km 408 m.

3  6 × 8 km 278 m =         m
                                                             1     4  4

8 km 278 m = 8 000 m + 278 m            8   2 7 8 m
     = 8 278 m                       ×                 6

4 9   6 6 8 m

6 × 8 km 278 m =   49 668 m

Solve.

a    2 × 9 cm 3 mm =      cm      mm    b    6 × 36 cm 4 mm =       mm

c    5 × 18 cm 2 mm =      cm       mm    d    8 × 61 km 24 m =       km       m

e    3 × 4 km 118 m =       m               f     7 × 35 km 302 m =       km      m

g    Multiply 8 by 2 108 m. Give answer in km and m.

Multiply first. Then, convert km to m.
Is this method easier?
178

TEACHER’S
NOTES

Remind pupils to give answers in the required units.

12.6 (i)
a, b

1  What is the length of one part of the wood?

72 cm 9 mm ÷ 3 =         cm         mm

2 4 cm     3 mm
  3 ) 7 2 cm     9 mm
    –  6           –  9
          1 2             0
      –  1 2
          0

72 cm 9 mm ÷ 3 =   24   cm     3    mm

The length of one part of the wood is 24 cm 3 mm.

2  59 cm 4 mm ÷ 9 =         mm

6 cm        6 mm
  9 ) 5 9 cm        4 mm       6 cm 6 mm = 60 mm + 6 mm
           –  5 4       +  5 0         = 66 mm

5           5 4
                   –  5 4
                             0

59 cm 4 mm ÷ 9 =   66   mm

3  The total distance taken by Jane to music class for 7 days
  is 49 km 721 m. Calculate the distance taken by Jane in a day.

49 km 721 m ÷ 7 =         km         m

7 km     1 0 3 m
  7 ) 4 9 km     7 2 1 m
           –  4 9       –  7
          0            0 2
           –     0
        2  1
             –  2  1
           0        49 km 721 m ÷ 7 =    7   km   103  m

The distance taken by Jane in a day is 7 km 103 m.

First, convert 59 cm 4 mm
to mm. Then, divide by 9.
Is this method easier?

Division of length

A wood which is 72 cm 9 mm
long is cut into 3 equal parts.
179

TEACHER’S
NOTES

Prepare question cards for division and carry out a quiz activity in groups.

12.6 (i)
b

4

Murni Petrol Station is located
 between Sejahtera Supermarket
 and Mega Supermarket.
 What is the distance from Murni
 Petrol Station to Mega Supermarket?

79 km 464 m ÷ 2
 =         km         m

79 km 464 m ÷ 2 =   39  km   732  m

The distance from Murni Petrol Station to Mega Supermarket is
  39 km 732 m.

The distance from P to R is 60 km 600 m. The
distance from Q to R is 3 times the distance
from P to Q. What is the distance, in m, from P to Q?

Solve.

a   16 cm 8 mm ÷ 2 =         cm        mm     b   9 cm 2 mm ÷ 4 =        cm       mm

c    62 cm 5 mm ÷ 5 =        mm                  d   21 km 819 m ÷ 7 =       km         m

e    79 km 200 m ÷ 6 =        km       m       f    5 km 715 m ÷ 3 =        m

P Q R

60 km 600 m

79 km 464 m

MURNI
PETROL STATION

SEJAHTERA SUPERMARKET

MeGA SUPERMRKET

179

79 km 464 m ÷ 2 =         km         m

3 9 km         7 3 2 m
  2 ) 7 9 km         4 6 4 m
           –  6           +  1 0 0 0
       1  9             1 4 6 4
      –  1 8         –  1 4
          1                0 6
              –     6
            0 4
                           –     4
               0

How do you solve this problem
to give the answer in m?
180

TEACHER’S
NOTES

Guide pupils to solve problems using tables.

12.7 (i)

1  Zarul built 3 aeroplane models for Creativity
  Club. For models A, B and C, Zarul used
  cardboards  measuring 15 cm 2 mm,
  23 cm 5 mm and 13 cm 8 mm. Calculate
   the total length, in mm, the cardboards used.

Given     Cardboard A 15 cm 2 mm, Cardboard B 23 cm 5 mm,
       Cardboard C 13 cm 8 mm.

Find       Total length of cardboards in mm.

Operation    Addition

15 cm 2 mm          23 cm 5 mm          13 cm 8 mm

Solve              15 cm 2 mm + 23 cm 5 mm + 13 cm 8 mm =        mm

cm    mm
     1   1
      1  5       2
           2 3       5  52 cm 5 mm = 520 mm + 5 mm
                        +  1  3   8                                       = 525 mm

5 2       5

Check cm     mm                cm     mm
     5  1           15

5 2       5              3 8       7
                –  1  3       8          –  2 3       5

3 8   7              1 5       2

15 cm 2 mm + 23 cm 5 mm + 13 cm 8 mm =   525  mm

The total length of cardboards used is 525 mm.

Total length

Solve the problems

Draw a diagram.
181

TEACHER’S
NOTES12.7 (i)

2  The distance from Mr Jagdish’s house to the meeting venue is
  47 km 850 m. After driving for 998 m, he stops to fill petrol. He

continues his journey for another 35 km 810 m and stops again
 at a rest area. What is the remaining of his journey, in km and m?

Given    Distance from Mr Jagdish’s house to the meeting venue is
      47 km 850 m. Driving a distance of  998 m and stops
      to fill petrol. Driving 35km 810 m and stops at rest area.

Find       The remaining journey in km and m.

Operation   Subtraction

Solve    47 km 850 m – 998 m – 35 km 810 m =       km       m

km         m                      km         m
                               17 14 10
                4  6          18  5  0

4 7       8 5 0          4 6       8 5 2
                       –               9 9 8               –  3 5       8 1  0

4 6  8 5 2           1  1          4 2

Check     47 km 850 m            48 km
           998 m           1 km
        35 km 810 m             36 km
        48 km – 1 km – 36 km = 11 km

11 km 42 m is close to 11 km.
The answer is reasonable.

47 km 850 m – 998 m – 35 km 810 m =   11  km   42 m

The remaining distance of Mr Jagdish’s journey is  11 km 42 m.

998 m 35 km 810 m Remaining
distance

Total distance : 47 km 850 m

Estimate the
answer to the
nearest km.

Guide pupils to underline information or keywords based on the given problem and
 solve it with various strategies.

Meeting venue
182

TEACHER’S
NOTES

3  Encik Ismail needs strings to tie 6 similar parcels of the same size.
  Each parcel needs 60 cm 3 mm. What is the length of string, in

cm and mm, needed to tie all the parcels?

  Given     There are 6 parcels.
       60 cm 3 mm of string for 1 parcel.

  Find       Length of string needed for 6 parcels.

  Operation    Multiplication

Solve      6 × 60 cm 3 mm =         cm         mm

cm     mm
               6 0         3
             ×                    6

3 6 0      1 8

Check
             6 0 cm         3 mm
           6 ) 3 6 1 cm         8 mm
             – 3 6          + 1 0
                   0 1    1 8
        –    0        – 1 8
              1       0

6 × 60 cm 3 mm =   361  cm     8   mm

The length of string needed to tie all the parcels is 361 cm 8 mm.

Check your answer
by dividing it.

360 cm 18 mm = 360 cm + 10 mm + 8 mm
       = 360 cm + 1 cm + 8 mm

= 361 cm 8 mm

Guide pupils to solve problems by simulation using real objects.

12.7 (i)

60 cm 3 mm 60 cm 3 mm 60 cm 3 mm 60 cm 3 mm 60 cm 3 mm 60 cm 3 mm
183

TEACHER’S
NOTES

Ensure that pupils check the answers and explain the importance of checking them.

12.7 (i)

4  The Jalur Gemilang Run of 10 km 500 m will
  be held in conjuction with Hari Kemerdekaan.
  4 runners run in a relay, carrying the
  Jalur Gemilang. What is the distance, in m,
  of each runner?

Given           The distance is 10 km 500 m.
             There are 4 runners.

Find           The distance, in m, by each runner.

Operation   Division

Solve  10 km 500 m ÷ 4 =         m

2 km        6 2 5 m
   4 ) 1 0 km        5 0 0 m
    –     8        + 2 0 0 0
           2           2 5 0 0
           – 2 4
          1 0
              –    8
              2 0
        – 2 0
                     0

Check
     km        m
       2          1  2

2     6 2 5
          ×                  4

1 0      5 0 0

10 km 500 m ÷ 4 =   2 625  m

The distance of each runner is 2 625 m.

Check by multiplying
2 km 625 m by 4.

Runner 1 Runner 2 Runner 3 Runner 4

10 km 500 m

2 km 625 m = 2 000 m + 625 m
    = 2 625 m
184

TEACHER’S
NOTES

Solve.

a    Tarmizi draws three straight lines with the lengths of 12 cm 4 mm,
8 cm 6 mm and 15 cm 9 mm respectively. What is the total length of
the three straight lines?

b    Mei Chu recorded the measurements
 of leaves that she brought for Science
 experiment as shown in the picture.
 Calculate the total length of the leaves.

c

The diagram shows the distance between the office and the music
 class. The distance from Mr Singam’s house to the music class is
 3 km 120 m less than the distance from music class to the office.
 What is the distance from his house to the music class?

d    Rizal’s pencil is 12 cm long. Lily’s pencil is 3 cm 4 mm longer than
 Rizal’s pencil. What is the total length, in mm, of their pencils?

e    The table shows the distance to Taman Setia and Taman Anggerik
from Taman Kenanga.

The distance from Taman Kenanga to Taman Anggerik is 3 times the
distance from Taman Kenanga to Taman Setia. What is the distance,

in m, from Taman Kenanga to Taman Anggerik?

f The width of a book is 3 times Dahlia’s hand span. The width of the book
is 36 cm 3 mm. What is the length of Dahlia’s hand span?

12 km 18 m

Office

Mr Singam’s
HouseMusic Class

184

7
cm

7
 m

m

30
 m

m

41
 m

m

Place

Taman Setia

Taman Anggerik

Distance from Taman Kenanga

10 km 217 m

?
185

TEACHER’S
NOTES

Make enough copies of the location map for each group.

7.6 (i)

Materials     Ruler, pencil, pen and           Players    5 pupils in a group.
     location map.

Kesuma Jaya Town is a new town. Suggest the locations for a recreational
park, a school and a mini library based on the estimated distance of 1 km
in the plan and the rules given.

Rules

a The distance of the recreational park is 1 km less than the lake so that
 citizens can go fishing and cycling around the lake.
b The distance of the mini library is between 1 km to 2 km from the

community hall.
c The school is located between the recreational park and the mini

library with an estimated distance of 3 km.

Steps

1 Mark X at the suggested location. Draw the distance and label the
name of the location.

2 Add other necessary facilities. State why do you need the facilities.

3 Discuss the outcomes of your group work.

4 Display it at the Mathematics corner.

1 km

X

X

KESUMA JAYA TOWN PLAN

X

Community Hall

Lake

Multipurpose
Shop

Police Station

X
186

TEACHER’S
NOTES

186

1 Measure the length of each object. Write the measurement.

a             b

mm         cm          mm

2 Fill in the blanks.

a    62 mm =         cm         mm         b    2 576 m =           km          m

c              cm 5 mm = 85 mm             d             km 212 m = 16 212 m

3 The distance of X and Y is given. Estimate the distance from Y to Z.

1 km                           4 km
 a           b
    X       Y                                    Z           X                               Y              Z

4 Complete the following.

a    26 cm 8 mm – 8 cm 8 mm =           cm

b    18 cm 9 mm ÷ 9 =          cm          mm

c    14 cm 7 mm + 6 mm + 5 cm 5 mm =          mm

d    3 × 12 cm 8 mm =         cm          mm

e    7 × 6 km 404 m =           m

f    53 km 124 m ÷ 4 =          km          m

5 Solve.

a    The distance from Azrul’s house to school is 3 km 742 m.
    Calculate the total distance, in km and m, travelled by Azrul for
    3 days, back and forth to school.

b   A length of wire measuring 74 cm 5 mm, need to be cut into

5 equal parts. What is the length of one part of the wire in mm?

c The lengths of the lines X and Y
are less than the line PQ as
shown in the diagram. Calculate
the difference in length, in mm,
the lines X and Y.

P                                                Q
    25 cm

X
                  80 mm

Y
      120 mm
187

TEACHER’S
NOTES

Add and subtract masses based on situations and simulation activities.
 Explain that adding and subtracting units of masses is the same as adding
 and subtracting whole numbers.

"
"

13.1 (i)

School13

What is the total mass of the items bought?

2 kg + 400 g – 150 g =          kg          g

2 kg + 400 g – 150 g =    2     kg   250  g

The total mass of the items bought is 2 kg 250 g.

Oh, uncle you have over weighed the
beans! Can you make it 150 g lesser?

1 kg 900 g

MASSMASS

Addition and subtraction of mass

1

10 kg

100

200300

400

500
    gram

0

Crackers
2 kg

–

kg    g

2    0 0 0
   4 0 0
 2    4 0 0

+

kg    g

2    4 0 0
   1 5 0
 2    2 5 0

3            10

1 kg 900 g

Add the two masses of dodol. What is the
difference in mass between the dodol and the
crackers bought?

Azim, how many grams
do you want to buy?
188

TEACHER’S
NOTES

Pay attention on regrouping from g to kg.
 Emphasise on conversion for values more than 1 000 g.
"
"

13.1 (i)

2      10 kg 80 g – 3 kg 450 g + 2 kg 370 g =          kg

10 kg 80 g – 3 kg 450 g + 2 kg 370 g =    9    kg

3  26 kg + 8 760 g –          kg         g = 4 815 g

26 kg + 8 760 g –   29   kg  945  g = 4 815 g

Determine the 2 packets of biscuits that should be mixed first.
  Then, reduce 100 g so that the mass becomes 2 500 g.

1 kg 500 g 1 kg 550 g1 kg 50 g

P Q R

–

kg    g

1 0             8  0

3 4 5 0

6  6 3 0

10 kg 80 g = 9 kg + 1 000 g + 80 g

= 9 kg 1 080 g

+

2 6    0 0 0 g

8      7 6 0 g

3 4    7 6 0 g

1

–

3 4     7 6 0 g

4    8 1 5 g

2 9    9 4 5 g

5            3           10           2           17
13

kg   g

6   6 3 0

2      3 7 0

9   0 0 0

+

1           1

630 g + 370 g = 1 000 g
        = 1 kg

450 g connot be subtracted from 80 g.

29 945 g = 29 kg 945 g

Convert 26 kg
to 26 000 g.

9        1 080

× 1 000

÷ 1 000

kg            g

INFORMATION
189

TEACHER’S
NOTES

Diversify activities such as cross number puzzles, simulations and games to
 reinforce the concept of mixed operations.
"

13.1 (i)

Materials

Steps

1  The first pupil weighs a few pebbles and record its

mass.

2  The second pupil adds more pebbles and

record its mass. For example, add 600 g of pebbles.

3  The third pupil takes out some pebbles

and record the mass of pebbles left.

4 The fourth pupil writes the complete number

sentence involving addition and subtraction.

5  Discuss and solve the number sentence in groups.

1 Calculate.

a   4 kg 820 g + 5 kg 100 g – 1 kg 694 g =         kg          g

b   9 kg – 3 016 g + 1 kg 110 g =          kg          g

c   30 kg 60 g – 22 kg 445 g + 1 kg 32 g =          g

d   27 kg 510 g + 7 kg 390 g – 18 kg 900 g =          kg

e   16 kg 450 g – 9 480 g + 4 kg 30 g =          kg

f   10 kg + 6 kg 5 g – 2 080 g =         g

2 Subtract 3 510 g from the sum of 7 kg 30 g and 4 kg.

3     12 kg     9 kg 78 g    9 kg 200 g

Based on the cards above add the heaviest mass to the second
heavy mass. From the answer, subtract the lightest mass.

4 pupils in each group.

Weighing scale, pebbles, exercise book.

189

Players
190

TEACHER’S
NOTES

Guide pupils to multiply and divide units of mass through simulation or based on
given situation.
"

13.1 (ii)

1   2 0 0 g

3

3   6 0 0 g

×

4 5 0  g

8  3  6 0 0  g

3  2

4 0

–   4 0

0 0

–  0

0

–

1

Based on the picture,
 what is the mass of
 crisps in 1 small pack?

3 × 1 200 g ÷ 8 =         g

3 × 1 200 g ÷ 8 =  450  g

2   8 x 2 kg 500 g ÷ 4 =          kg

8 × 2 kg 500 g

4

8 × 2 kg 500 g ÷ 4 =     5    kg

Multiplication and division of mass

g
2     5 0 0
       2
4    1  0 0 0
1   – 1  0 0 0
5         0

+

×

kg

Why subtract 1 000 g
and add 1 kg? Explain.

crisps

The mass of crisps in 1 small pack is 450 g.

1

23

4

5
    kilogram

0

190

Hadi, please repack these
3 packs of crisps into 8
smaller packs.

2

1
191

TEACHER’S
NOTES

Expose various strategies involving multiplication and division to enhance
pupils’ understanding.

"

13.1 (ii)

Method 1

Method 2

3   18 kg 945 g ÷ 9 × 2 =          g

18 kg 945 g ÷ 9 × 2 =   4 210   g

4   31 kg ÷ 5 × 10 =          kg

31 kg × 10

5

31 kg ÷ 5 × 10 =   62    kg

2

First, multiply 9 by 2. Then, divide
18 kg 945 g by the product. Is the
answer the same?

2  kg   1 0 5  g
1 8  kg 9 4 5  g
1 8     –  9
 0         0 4
       –  0
          4 5
      –  4 5
        0

–
9

Which method do you
choose? Why?

kg    g

6   2 0 0

1 0

6 0    2 0 0 0

×

6  kg   2 0 0  g
 5  3 1  kg       0  g
  – 3 0   +  1  0 0 0
   1      1 0 0 0
         –  1  0
               0 0

–  0
              0 0
            –  0
               0

31 kg × 2   =

= 62 kg

191

4 kg 210 g = 4 000 g + 210 g
          = 4 210 g

60 kg 2 000 g = 60 kg + 2 kg
            = 62 kg

1

kg   g

2    1 0 5

2

4    2 1 0

×

1
192

TEACHER’S
NOTES

Diversify activities involving mass for mixed operations in co-curriculum such as
cooking competition.

13.1 (ii)

"

Each      has the same mass. What is the mass of          , in g?

Players   4 to 6 pupils.

Steps

1    Teacher prepares a few number cards, mass cards and symbol cards.
     Examples:

2   Keep 1 set of cards in an envelope.

3   Teacher gives an envelope filled with the same set of cards to
     each group.

4      Pupils arrange the cards to form a complete and correct number sentence.

5   The fastest group with the correct number sentence is given 5 marks. Other

groups are given 3 marks each.

6   Repeat steps 2 to 5 for different sets of cards.

7   The group that scores the highest mark is the winner.

Calculate.

a    5 × 8 kg 60 g ÷ 10 =      kg      g     b    4 × 6 kg 300 g ÷ 6 =      g

c    10 × 9 kg ÷ 12 =      kg       g          d    40 kg 500 g ÷ 9 × 10 =       kg

e    21 kg ÷ 5 × 3 =       kg       g            f     19 kg 110 g ÷ 7 × 8 =      g

2 770 g   –   =   6 kg 550 g   10 kg 480 g   +   6 kg 700 g  (set 1)

8 350 g  =    10 kg 20 g    6   ÷   ×     5  (set 2)

Materials  Mass cards, symbol cards,
        number cards, envelopes.

4 kg

200 g

192
193

TEACHER’S
NOTES

Guide pupils to solve problems by making tables or mantic reasoning."

13.2 (i)

2  kg  5 0 0  g

+  3  kg 0 0 0  g

5  kg  5 0 0  g

5  kg  5 0 0  g

–  1  kg 7 5 0  g

3  kg  7 5 0  g

4
14 10
 15 0  0

2  5 0 0  g

+  3  0 0 0  g

5  5 0 0  g

Solve the problems

Check

3 750 g = 3 kg 750 g

193

5  5 0 0  g

–  1  7 5 0  g

3  7 5 0  g

4             4
 14

10

I draw a diagram.
Then, I calculate.

?

Total

1 kg 750 g

2 kg 500 g 3 kg

Solve

The picture shows the mass of a bunch
of rambutans and a watermelon. The mass
of the bunch of rambutans is 2 kg 500 g. The
mass of the pomelo is 1 kg 750 g lighter than
the watermelon. Calculate the total mass of the
bunch of rambutans and the pomelo.

Given  A bunch of rambutans is 2 kg 500 g, the watermelon is 3 kg,
      the pomelo is 1 kg 750 g lighter than the watermelon

Find     Total mass of the bunch of rambutans and the pomelo

Operation   Addition and subtraction

2 kg 500 g + 3 kg – 1 kg 750 g =          kg          g

2 kg 500 g + 3 kg – 1 kg 750 g =   3 kg 750 g

The total mass of the bunch of rambutans and the pomelo is 3 kg 750 g.
194

TEACHER’S
NOTES

600 g

Guide pupils to solve problems by trying a simpler case and working backwards.
Simulation can be done in groups.

Expose various types of Higher Order Thinking Skills (HOTS) questions involving mass.

"

13.2 (i)

2  Nani’s mother bought 2 boxes of raisins. Nani gave
  the raisins equally to 12 friends. What is the mass of
  raisins each person got, in gram?

2 × 600 g ÷ 12 =  100 g

The mass of raisins for each person is 100 g.

An amount of 8 kg 400 g of flour is filled equally into 7 containers.

What is the mass of flour in 4 containers, in gram? Which number

sentence is correct?

a   8 kg 400 g × 7 ÷ 4 = 14 700 g     b   8 kg 400 g ÷ 7 × 4 = 4 800 g

Check2 × 600 g ÷ 12 =          g Solve

1 0 0 g

1 2   1  2 0 0  g

–  1  2

0  0

–   0

0 0

–   0

0

×

6 0 0 g

2

1 2 0 0 g

×

If Nani shares 1 200 g of raisins with 5 friends, what is
the mass of raisins will each of her friends get?

"

I draw a picture.

1 200 g

2

600

1

194

600 g 600 g

1 2

1 0 0 g

1  2 0 0  g
195

TEACHER’S
NOTES

1 kg 200 g

Beans
3 kg 620 g

Murukku
640 g

2 kg 50 g5 kg 280 g

Solve.

a Puan Hayati cooked 1 kg 400 g of the total mass of vegetables that she
bought. Calculate the vegetables left, in kg and g.

b A pupil brings 4 packets of green beans to do an experiment. The
mass of each packet is 250 g. The Science teacher then divided the
green beans equally to 10 pupils. What is the mass of green beans
each pupil gets?

c

The mass of cake P is 1 kg 100 g heavier than cake Q. While the mass
of cake R is 700 g lighter than cake P.

i   Choose the correct number sentence to find the mass of cake R.

1 kg 200 g + 1 kg 100 g – 700 g         1 kg 200 g – 1 kg 100 g + 700 g

ii   What is the mass of cake R in grams?

d Pak Kasim puts 5 boxes of biscuits of
 the same mass on a scale.
 Calculate the mass, in g,
 for 3 boxes of biscuits.

e A packet of flour weighs 980 g less than the
 total mass of the two items on the left.
 What is the mass of the flour?

2 kg

50 g

P
Q R

195
196

TEACHER’S
NOTES

1 Solve in standard written form.
 a   2 kg 400 g + 3 kg 690 g – 1 kg 286 g =        kg       g

b   8 kg 720 g + 5 kg 685 g – 2 kg 405 g =        kg
 c   17 kg 360 g – 9 kg 847 g + 8007 g =       g
 d   20 kg 50 g – 16 kg 700 g +       g = 9 kg
 e   4 × 6 kg 80 g ÷ 5 =       kg       g
 f   9 × 8 kg 240 g ÷ 6 =       g

2 a  Reduce 4 295 g from the sum of 5 kg 840 g and 6 kg 960 g.
  What is the mass, in gram?

b  Divide the product of 7 and 14 kg 240 g by 8.

3 How many grams more is 30 kg than the total mass of two objects
which are 13 kg 960 g and 15 kg 750 g.

4 Solve these problems.
 a

The above diagram shows the masses of a pair of twins.
    Their total mass is 4 kg 920 g more than their mother,

Puan Fazlin. What is the mass, in kg and g, of Puan Fazlin?

b   A worker buys 6 packets of powder detergent. He refills
   the powder detergent equally into 24 containers.
   What is the mass in g, for 1 container?

c Mother adds 50 g more of longans into the
basket. Calculate the total mass in kg and g,
of the longans if the basket weighs 350 g.

2 kg 80 g

30 kg 500 g                  29 kg 700 g                        Mother

9 kg

196
197

TEACHER’S
NOTES

Carry out simulation activities using liquid and measuring cylinders.

14.1 (i)

1 ℓ 200 mℓ
   Watermelon juice

1 ℓ 500 mℓ

Find the difference in
volume between the
watermelon juice and
the grape juice.

1 ℓ 500 mℓ

School14

3 ℓ
3 ℓ

2 ℓ 600 mℓ

1 ℓ 500 mℓ

197

1  Based on the pictures above, what is the volume of watermelon
 juice left in the jug?

2 ℓ 600 mℓ + 200 mℓ – 1 ℓ 500 mℓ =         ℓ           mℓ

2 ℓ  600 mℓ          2 ℓ  800 mℓ
   +        200 mℓ             –  1 ℓ  500 mℓ

2 ℓ  800 mℓ           1 ℓ   300 mℓ

2 ℓ 600 mℓ + 200 mℓ – 1 ℓ 500 mℓ =     1    ℓ   300  mℓ

The volume left in the jug is 1 ℓ 300 mℓ.

Watermelon juice
 365 mℓ

I add 200 mℓ
of watermelon
juice into the
jug.

Thank you, father.

Let me fill up this bottle
with watermelon juice.

VOLUME OF LIQUIDVOLUME OF LIQUID

Grape
Juice

Addition and subtraction of volume of liquid
198

TEACHER’S
NOTES

Guide pupils with mechanical questions in short sentences using vocabulary which
means add and subtract.

http://www.primaryresources.co.uk/maths/docs/Capacity_Problems_Y4.doc

14.1 (i)

2  49 ℓ – 13 ℓ 472 mℓ + 8 472 mℓ =           ℓ

4  8        10 0  0          1                 1   1

4 9 ℓ         0 mℓ       3 5 ℓ     5 2 8 mℓ
   –  1  3 ℓ   4 7 2 mℓ            +     8 ℓ    4 7 2 mℓ
      3 5 ℓ   5 2 8 mℓ       4 3 ℓ  1 0 0 0 mℓ

43 ℓ 1 000 mℓ = 43 ℓ + 1 ℓ
             = 44 ℓ

49 ℓ – 13 ℓ 472 mℓ + 8 472 mℓ =    44   ℓ

3  750 mℓ + 3 ℓ 900 mℓ – 260 mℓ =            mℓ
   1                                                                  5  15

3 ℓ   9 0 0 mℓ  4 ℓ   6 5 0 mℓ
 +          7 5 0 mℓ       –           2 6 0 mℓ
      4 ℓ   6 5 0 mℓ  4 ℓ   3 9 0 mℓ

750 mℓ + 3 ℓ 900 mℓ – 260 mℓ =    4 390  mℓ

How do you fill up 9 ℓ of water
            into the green container using

both the red and blue pails?
            Explain.

Convert 4 ℓ 390 mℓ
to mℓ.

Add 49 ℓ and 8 472 mℓ. Then, subtract  13 ℓ 472 mℓ
from the answer. Explain.

In the number sentence above, convert
3 ℓ 900 mℓ to mℓ. Then, solve it. Is the
answer the same?

198

12 ℓ 15 000 mℓ

9  9 10

litre   millilitre

× 1 000

÷ 1 000

INFORMATION
199

TEACHER’S
NOTES

Prepare enough sets of cards for each member of the group and add questions
on mixed operations.

14.1 (i)

Materials           Players

4 sets of volume cards, task cards,              4 pupils in a group.
A4 paper.

Steps

1 Determine each player’s turns.

2 Carry out the tasks based on the task cards. Show your
 calculation on an A4 paper.
 Example:

3 Discuss the task among members in the group.

4 Keep the task in Mathematics file.

1 Calculate.

a   5 ℓ  550 mℓ + 4 ℓ  340 mℓ – 1 ℓ  240 mℓ =         ℓ          mℓ
 b   6 ℓ  78 mℓ – 988 mℓ + 3 ℓ  885 mℓ =         mℓ
 c   368 mℓ + 17 ℓ  120 mℓ – 2 ℓ  388 mℓ =         ℓ
 d   12 ℓ  198 mℓ – 10 ℓ  662 mℓ + 22 ℓ  464 mℓ =          ℓ          mℓ

2 Reduce 36 712 mℓ from 86 ℓ. Then, add the answer to 712 mℓ.
State the answer in  ℓ.

C    650 mℓB    4 ℓ  300 mℓA    2 ℓ  720 mℓ

199

Pupil 1:
a. Add the volumes of Card A and Card B.
b. Subtract the volume of Card C from
     the answer in a.
c.  Write the number sentence and the answer.

Pupil 2:
a. Subtract the volume of Card A from Card B.
b. Add the answer in a to the volume of
 Card C.
c. Write the number sentence and the answer.

Pupil 4:
a. Subtract the volume of Card C from Card A.
b.  Add the answer in a to the volume of
 Card B.
c. Write the number sentence and the answer.

Pupil 3:
a. Add the volumes of Card B and Card C.
b. Subtract the volume of Card A from
 the answer in a.
c.  Write the number sentence and the answer.
200

TEACHER’S
NOTES

Emphasise that answers must be given in units required.
 Drill pupils with questions involving cancellation method.

14.1 (ii)

1

Multiplication and division of volume of liquid

1  What is the volume of honey in each small bottle based on the
  situation above?

3 × 1 500 mℓ ÷ 6 =           mℓ

1  500 mℓ
   ×         3

4 500 mℓ

3 × 1 500 mℓ ÷ 6 =  750  mℓ

The volume of honey in each small bottle is 750 mℓ.

2  5 × 12 ℓ  800 mℓ ÷ 4 =           ℓ
                                                                3   2 0 0

5 × 12 ℓ   800 mℓ   =   5 × 12 800 mℓ
     4         4

=   16 000 mℓ

5 × 12 ℓ  800 mℓ ÷ 4 =   16   ℓ

Convert 12 ℓ 800 mℓ
to mℓ.

1

750 mℓ
6 ) 4 500 mℓ
 –  4 2
        30
    –  30
     00
       –    0
    0

16 000 mℓ   =   16 ℓ
1 000

1  500 mℓ 1  500 mℓ 1  500 mℓ

Each bottle holds
1 500 mℓ of honey.

I transfer equally
into 6 small bottles.
201

TEACHER’S
NOTES

Get pupils to create stories based on division number sentences.

14.1 (ii)

3  Divide 87 ℓ 836 mℓ by 14, then multiply by 9.

87 ℓ   836 mℓ ÷ 14 × 9 =            mℓ

6 ℓ         274 mℓ
  14 ) 87 ℓ         836 mℓ
    –  84    +  3 000
        3         3 836
            –  2 8
            1 03
          –     98         54 ℓ  2 466 mℓ = 54 000 mℓ + 2 000 mℓ + 466 mℓ

56                = 56 466 mℓ
              –  56
           0

87 ℓ   836 mℓ ÷ 14 × 9 =   56 466   mℓ

4  827 ℓ ÷ 25 × 2 =           ℓ            mℓ

33 ℓ               80 mℓ
  25 ) 827 ℓ               0 mℓ
         –  75          +  2 000
                77      2 000
          –  75        –   2 00
            2           00
          –    0
                 0

827 ℓ ÷ 25 × 2 =   66   ℓ   160  mℓ

1

33 ℓ      80 mℓ
×                2

66 ℓ   160 mℓ

Does 33 ℓ 80 mℓ + 33 ℓ 80 mℓ
give the same answer? Discuss.

6 3

6 ℓ     274 mℓ
×                  9

54 ℓ  2 466 mℓ

Convert 87 ℓ 836 mℓ to mℓ
and solve. Is it easier?
202

TEACHER’S
NOTES

Find the volume of
              water in ℓ and mℓ
              in container B.

Answer the puzzle. Complete the answer with the matching letter in
the blanks below.

What object has a neck but no head?

1 Calculate.

a   2 × 7 ℓ 930 mℓ ÷ 5 =       ℓ       mℓ    b   8 ℓ 56 mℓ ÷ 8 × 9 =       mℓ
 c   5 × 2 ℓ 884 mℓ ÷ 14 =        mℓ             d   12 ℓ 640 mℓ ÷ 8 × 7 =        ℓ      mℓ
 e   3 × 7 ℓ 602 mℓ ÷ 9 =        mℓ               f    9 ℓ 100 mℓ ÷ 13 × 50 =       ℓ

2 a   Find the product of  10 322 mℓ and 7 divided by  2. State
    the answer in ℓ and mℓ.

b   What is the volume when divided by 5 and multiplied by 9 gives
   the answer  27 ℓ ?

Half the volume of C

14.1 (ii)

4 times the volume of A4 565 mℓ

3  ×  2 ℓ  115 mℓ  ÷  5 T 6  ×  12 ℓ  300 mℓ  ÷  2 E

8  ×  5 ℓ  45 mℓ  ÷  4 B

35 ℓ  280 mℓ  ÷  7  ×  9 O

70 ℓ  600 mℓ  ÷  10  ×  12 L

1 ℓ  269 mℓ 1 269 mℓ 84 ℓ  720 mℓ 36 900 mℓ10 090 mℓ 45 360 mℓ

Carry out simulation to help pupils answer challenging questions.
 Drill the conversion of units orally.

A
B

C
203

TEACHER’S
NOTES

520 mℓ remainder

The volume
of tea drank

1  The Pandu Puteri Tunas club prepared
  27 ℓ 850 mℓ of tea during a camping activity.
  By afternoon, 14 ℓ 600 mℓ of tea was added.
  At the end of the activity, 520 mℓ of tea remained.
  What is the volume, in ℓ and mℓ, of the tea drank?

Given  The volume of tea drank is 27 ℓ  850 mℓ.
    The volume of tea added is  14 ℓ 600 mℓ.
    The volume of tea remaining is  520 mℓ.

Find  The volume of tea drank.

Operation   Add, then subtract.

14 ℓ 600 mℓ

27 ℓ 850 mℓ

Solve

27 ℓ  850 mℓ  +  14 ℓ  600 mℓ  –  520 mℓ =            ℓ             mℓ
               1   1          4  1        1  450

2 7 ℓ  8 5 0 mℓ      4 2 ℓ  4 5 0 mℓ
          +  1 4 ℓ  6 0 0 mℓ  –            5 2 0 mℓ

4 2 ℓ  4 5 0 mℓ      4  1 ℓ  9 3 0 mℓ

1           4  1        1  450

Check          4 1 ℓ  9 3 0 mℓ      4 2 ℓ  4 5 0 mℓ
          +           5 2 0 mℓ  –  1  4 ℓ  6 0 0 mℓ

4 2 ℓ  4 5 0 mℓ      2 7 ℓ  8 5 0 mℓ

27 ℓ   850 mℓ  +  14 ℓ   600 mℓ  –  520 mℓ=    41   ℓ   930  mℓ

The volume of tea drank was 41ℓ 930 mℓ.

14.2 (i)

Guide pupils to draw tables to solve problems.
 Guide pupils to estimate the reasonable final answers.

Solve the problems
204

TEACHER’S
NOTES

2  Encik Lingam bought 3 bottles of goat milk with
  the volume of  2 ℓ 750 mℓ in each bottle. Then,
  he poured equally into 5 containers for his
  children. What is the volume of milk, in mℓ,
  for each container?

Given  Bought 3 bottles of goat milk.
    The volume of 1 bottle of goat milk is  2 ℓ  750 mℓ.
    Poured equally into 5 containers.

Find  The volume of goat milk for 1 container, in mℓ.

Operation   Multiply, then divide.

Solve   3  ×  2 ℓ  750 mℓ  ÷  5  =            mℓ

2       1

2 ℓ  750 mℓ
             ×             3

8 ℓ  250 mℓ

Check       3  2

1 650 mℓ
             ×        5

8 250 mℓ

3  ×  2 ℓ  750 mℓ  ÷  5  =   1 650  mℓ

The volume of milk in each container is 1 650 mℓ.

1  650 mℓ
5 ) 8 250 mℓ
 –  5
     3 2
 –  3 0
   25
    –  25
     00
       –    0
       0

Give other daily situation for problem solving involving division and multiplication.

14.2 (i)

2   7   5  0
     22 15

8  2 5 0 mℓ  =  2 750 mℓ
      3
         1

8 ℓ  250 mℓ  =  8 250 mℓ

Milk Milk Milk

2 ℓ  750 mℓ2 ℓ  750 mℓ2 ℓ  750 mℓ
205

TEACHER’S
NOTES

Solve.

a    Devaki and Lisa fill up  5 ℓ 350 mℓ and 8 ℓ 950 mℓ soya drink
respectively into a container. 3 500 mℓ soya drink is served to the
guests. What is the remainder, in  ℓ and mℓ , the volume of soya drink?

b Sayang Restaurant has 18 ℓ 50 mℓ olive oil. After consuming
 16 ℓ 180 mℓ, an amount of  12 ℓ  is added to the stock of oil. What is
 the volume of olive oil, in ℓ and mℓ, in the restaurant?

c
             Mak Jah gave 3 containers of

equal amount  of porridge to
             8 neighbours. Find the volume

of porridge, in mℓ, received by
            each neighbour.

d    A school provided 4 ℓ 720 mℓ cooking oil for a cooking competition.
The oil was given to 8 groups that were competing. Calculate the
volume of oil received by 5 groups. Choose the correct number

sentence and solve it.

4 ℓ 720 mℓ ÷ 5 × 8 =                     5 × 4 ℓ 720 mℓ ÷ 8 =

e The volume of paint from a container is poured in equal amount
 into 9 small tins. The volume of paint in 2 small tins is 2 ℓ 700 mℓ.

Calculate the volume of paint in the container at the beginning.

Give more standard UPSR questions involving volume of liquid.

3 ℓ 752 mℓ

3 ℓ 752 mℓ

3 ℓ 752 mℓ
206

TEACHER’S
NOTES

1 Calculate.

a    3 ℓ 201 mℓ + 54 ℓ  – 18 ℓ 127 mℓ =         ℓ          mℓ
 b    16 ℓ 672 mℓ – 998 mℓ + 44 ℓ 326 mℓ =         ℓ
 c    40 ℓ 765 mℓ + 13 ℓ 478 mℓ – 23 ℓ 499 mℓ =          ℓ          mℓ
 d    2 × 4 ℓ 210 mℓ ÷ 4 =         ℓ          mℓ

e    12 ℓ 105 mℓ ÷ 15 × 3 =         mℓ
  f     8 ℓ 75 mℓ ÷ 5 × 7 =          ℓ

2 Calculate.

a    Reduce 10 ℓ 326 mℓ from the sum of  674 mℓ and  18 ℓ 78 mℓ.
    Give answer in mℓ.

b    Divide 29 ℓ 848 mℓ by 8 then multiply by 7. Give your answer in ℓ and mℓ.

3 Solve.

a    Gobind buys 8 tins of diesel. The diesel is distributed
    equally among him and 8 workers for the lawn
    movers. What is the volume, in ℓ and mℓ,
    received by each person?

b    A total of  25 ℓ 500 mℓ milk from Bagus Farm and
    20 ℓ 880 mℓ from Jaya Farm was collected by Encik Bakri.

He sold 43 ℓ 150 mℓ of milk. Calculate the volume of milk left,
    in ℓ and mℓ.

c    3 jugs of orange juice with the volume of  2 ℓ 800 mℓ each is
      poured equally into 7 bottles. What is the volume of orange juice,
    in mℓ, for each bottle?

206

5 ℓ 130 mℓ
207

TEACHER’S
NOTES

Encourage pupils to recognise angles for basic shapes found at a preschool
playground or the reading corner.
"

15.1 (i)

Sekolah15

Recognise angles

SPACESPACE

2

Right angle

1

A right angle is
formed at the corner
of a rectangle.

An obtuse angle is bigger
than a right angle.

Right angle

Look at my arm.
What type of angle
is formed?

Obtuse angle

What types of angles are
there in the shapes above?

An acute angle is smaller
than a right angle.

A triangle has
3 sides and
3 angles.

A rectangle has 4 sides.
Corners are formed
when 2 sides meet.

There is an angle at each
corner. There are 4
angles in a rectangle.

Acute angle
208

TEACHER’S
NOTES

Use the Geoboard to form various basic shapes and relate them to angles.   "

15.1 (i)

1 2

4

3

Materials   A4 paper, pencil, ruler and scissors.

Steps

Fold a sheet of A4 paper
 into two equal parts.

1  How many angles are there in each diagram?

a                                         b                                        c

2  Name the angles found in the following shapes.

a     b     c

Mark the acute angle

and the obtuse angle

on both paper cuttings.

Label them.

5   Paste the paper cuttings

in your exercise book.

Mark the right

angle.

Draw a line as in the
 picture and cut it.

Can a right angle
be formed from this
paper? Explain.

Right
angle

Right
angle

Right
angle Acute

angle

Obtuse
angle
209

TEACHER’S
NOTES

" Encourage pupils to tell stories about objects or places which have a lot of
parallel lines.

15.2 (i)
a

Recognise lines

Look at side a and side b

which are opposites on the

white board. The distance

between the two is the

same. Both of these lines

are parallel lines.

Observe the railway tracks.
Why must they be parallel?
Discuss.

Diagrams A and B
show parallel lines.
Does diagram C show
parallel lines? Discuss.

B

A

Parallel lines

1.4 m The same distance 1.4 m

C

209

a

b

Both of these racks
show examples of
parallel lines.

30 cm

30 cm 30 cm 30 cm

30 cm 30 cm
 0.6 m

0.6 m
210

TEACHER’S
NOTES15.2 (i) b

• Look at line a and line b at the
 picture. The two straight lines
 which intersects at a right
 angle are perpendicular lines.

State 10 objects in the classroom that have perpendicular lines. "

Materials   Rulers and set square.

Aim     Use the knowledge of parallel lines and perpendicular lines to
      beautify the school.

Activity  Pupils draw lines using rulers and set square.

Perpendicular lines

Can you point to the
perpendicular lines in the
three pictures above?

Draw a flag                                  Draw hopscotch    Draw a draughtboard

a              b       c

Which parts of this door
are perpendicular lines?

a

b
211

TEACHER’S
NOTES

Prepare exercises as in questions 2(a) and (b) in the worksheets.

http://www/superteacherworksheets.com15.2 (i)

"

Name the pairs of straight lines
     that form parallel and perpendicular
     lines in the diagram.

1 Count the number of perpendicular lines in the following shapes.

a                   b       c

d          e                                     f

2 Redraw and mark:

a   red lines for parallel lines.          b   blue lines for perpendicular lines.

a b ed

g

h

fc
212

TEACHER’S
NOTES

http://www/superteacherworksheets.com/geometry/perimeter-3_TZFFD.pdf

15.3 (i)

Draw the shapes of a square, a rectangle and triangles with the
  perimeters of 12 cm.

1

2

Perimeter

Perimeter A:

4 cm + 6 cm + 4 cm + 6 cm =  20 cm

4 cm

6 cm A 3 cm

4 cm

5 cm
B

A is a rectangle
and B is a right
angled triangle.

Mummy, what is
the length of the
lace that you used?

I use the lace
according to the
length around the
pillow case.

3

3

3 3

+       +        =

Perimeter B:

3

Perimeter:

3 + 3 + 3 + 3 = 12 units

The length of the lace is
12 units. The 12 units is the
perimeter of the pillow case.
213

TEACHER’S
NOTES

Carry out hands-on activities to measure perimeters of triangular and four-sided
 objects in the school compound.

15.3 (i)

4

5                                                     6      Find the perimeter of the square.

Measure all the sides of the following objects using a ruler or measuring
tape. Record the measurements and calculate the perimeter of the objects.

a   Textbook cover   b    Blackboard                      c    A4 paper

d   Door                    e    The surface of a pupil’s desk         f     A tile

Find the perimeter.

a                                 b                          c                               d

Find the perimeter of the hexagon.
The length of each side is 3 cm.

Perimeter = 3 cm  + 3 cm  + 3 cm  + 3 cm + 3 cm  + 3 cm
         =  18 cm  18 cm

Can you calculate perimeter using
multiplication? Discuss.

6 cm
 10 cm

8 cm

Perimeter = 6 cm + 8 cm + 10 cm
                =  24 cm

The length of each
 side is 4 cm

The length of each
side is 5cm

Perimeter = 12 cm + 12 cm + 12 cm + 12 cm
       = 4 × 12 cm
        = 48 cm

12 cm

5 cm

13 cm 15 cm

8 cm
"

12 cm 12 cm

12 cm

12 cm
Multiplication
is repeated

addition.

INFORMATION
214

TEACHER’S
NOTES15.3 (ii)

" Carry out hands-on activities using grid book to measure areas of basic shapes.

http://www.superteacherworksheets.com/geometry/area-1_TWBDW.pd

3 cm

5 cm

Width

Length

Area

1

2 Find the area of the checkerboard.

1 unit

1 unit 1 unit2

The area of the checkerboard =      cm2

Area = 15 units2

The area of the orange square is 4 square units.
Area =  4 units2

The area of the red
rectangle is 6 square
units.
Area =  6 units2

Area = Length × Width
    = 5 cm × 3 cm

=  15 cm2

The area of 1 unit
square is 1 square
unit. It is written
as 1 unit2.

INFORMATION

The area of each square of
the checkerboard is 1 cm2.
215

TEACHER’S
NOTES

Emphasise that the height of a triangle must be measured from
    the base to the vertex of the triangle that has the right angle.

15.3 (ii)

"

Draw a line from
vertex to vertex.

5

4

1 square forms
two triangles of the
same size.

Area      = Length × Width

= 4 cm × 4 cm

= 16 cm2

4 cm

4 cm

Width

Length

The area of a triangle is half the area of a square.

4 cm

4 cm

3

Area       =  Area
        2
       =  16 cm2

2
       =  8 cm2

4 cm

3 cm

Area      =  Base × Height
            2
       =  6 cm × 8 cm
                               2
         =  48 cm2

2
       =  24 cm2

It is written as
 1 × Base × Height.
2

Area            =   1  × Base × Height
       2
           =   1  × 3 cm × 4 cm
       2
           =  12  cm2     =   6 cm2

2

6 cmBase

Height 8 cm
216

TEACHER’S
NOTES

The perimeter of a rectangle is 48 cm. This
           rectangle consists of two squares. What is the
           area of the rectangle?

1 Look at the diagrams in the squared grid. Answer the questions.

a  Find the areas of A, B, C and D.

b   State the shapes having the same areas.

2    Calculate the areas of the coloured diagrams.
         a      b    c

d               e    f

3

5 cm

8 cm

4 cm

10 cm

12 cm

9 cm

7 cm

16 cm

5 cm

--
--

--
--

15.3 (ii)
216

P is a square. Find the area,
in cm2, of the shaded part.

http://www.charliefrench.com/PDF/Gr4measure2PDF

7 cm

A B

C

D

1 unit

1 unit

5 cmP

13 cm

8 cm

6 cm
217

TEACHER’S
NOTES

Carry out the activity to find the volume of cube and cuboid using
unit cubes.

"

15.4 (i)

1

2

Volume

These small boxes
are cubes.

1 unit

1 unit

1 unit

1 cm

1 cm

1 cm

Volume of cube = 1 unit × 1 unit × 1 unit
                        = 1 unit3

Volume of cube = 1 cm × 1 cm × 1 cm
                           = 1 cm cube
          = 1 cm3

How many cubes are
needed to fill up the
space of the big box?

How do you count
the number of the
hidden cubes?

Volume  = 12 units3

12 cubes are needed
to fill up the big box.
This big box is a cuboid.

There are 8 unit cubes
Volume =  8 units3

There are 18 unit cubes
Volume =  18 units3

The volume of a cube is 1 unit
cube. It is written as 1 unit3. This
cube is known as cubic unit.

INFORMATION

The volume of a cuboid
can be determined by
counting the number of
cubes filled in it.
218

TEACHER’S
NOTES15.4 (i)

Encourage pupils to draw nets to differentiate areas and volumes.

"

Length    Width   Height  Volume
      (units3)
      4            2          4           32

Length    Width   Height  Volume
     (units3)
     3            3          3           27

Calculate the volume of the box.

Volume =  50 cm × 30 cm × 20 cm
      =  30 000  cm3

a                                             b

Volume  = 27 cubic units
       = 27 units3

Volume = 32 cubic units
      = 32 units3

height

width
length

1 cm
1 cm

50 cm
30 cm

20 cm

1 cm

Can volume be calculated by multiplying
the area of base by height? Discuss.

3

4

5

Try to use the formula of volume
of cube and cuboid to check the
anwers for 3   a    and 3   b  .

Volume = Length × Width × Height

= 5 cm × 2 cm × 3 cm

=  30 cm3

The formula for volume of cube or
cuboid is Length × Width × Height.

INFORMATION
219

TEACHER’S
NOTES15.4 (i)

Discuss.
      a   Can 2 boxes with the same base area produce different volume?
         Explain.

b   Can 2 boxes with different base area produce the same volume?
          Explain.

1    State the number of unit cubes. Calculate the volume of the diagrams.

a               b          c

2   Calculate the volume of the diagrams.

a                      b                             c                                 d

3 Calculate the volume of the cube and cuboid.

8 cm

3 cm

8 cm

2 cm

unit cubes.

Volume =         units3

unit cubes.

Volume =         units3

unit cubes.

Volume =         units3

http://www/superteacherworksheets.com/geometry/volume-cubes-1_TZWBB.pd.

4 cm

4 cm

4 cm

10 cm

10 cm

10 cm
15 cm

12 cm

4 cm

8 cm
10 cm5 cm

219
220

TEACHER’S
NOTES

220

a

1  Draw and mark the angle on the diagram. Fill in the blanks.

2  Copy and draw:

3  The perimeter of rectangle X is the same as the perimeter of square Y.

a    Find the perimeter of diagram X.
  b    Find the length of the sides of
     diagram Y.
  c    Find the areas of the diagrams
     X and Y.

4  The surface area of A is 48 cm2.
        Find the volume of this cuboid.

5     The perimeter of the surface B is 16 cm.
     Find the volume of this cube.

6  The length of the side of square B is 4 times
  of square A. How many times is the area
  of B compared to A?

parallel lines. perpendicular lines.b

Right angle      Acute angle    Obtuse angle

A

2 cm

B

A

3 cm

5 cm

X

3 cm

A

B

Y

A
221

TEACHER’S
NOTES

Discuss the positions of other objects. Encourage pupils to surf the Internet to see the
locations.

Tell the history of Rene Descartes (French Mathematics Expert) regarding the
 coordinate plane. Emphasise that there are 2 axis on coordinate grid.
 http://www.learningwave.com/wonline/algebra_section2/alg_coord.html

"

"16.1 (i)

School

Wong

Muaz

Nina

Farah Siva Ros

Ika Amit

Ain

Shah Joseph

IzamMay

AdamYee

1 6
COORDINATES COORDINATES

Recognise position

1    The picture shows the positions of pupils of 4 Bijak.

What is Yee’s position?
State the position of other pupils.

So, Siva sits in the second
column, third row.

What is Siva’s position?

Yes,
teacher.

Siva is at 2 tables to the right
and 3 tables to the back.

The pupil
in the fifth
column, row
two, are you
a new pupil?
222

TEACHER’S
NOTES16.1 (i)

The grid below shows the positions of the objects in the decor rack
        in Amin’s room.

The toy car is located 6 squares horizontally and 3 squares vertically.
   The ball is located at          .

Explain the positions
of the others object.

Use paper foldings, tiles or grids to create square grids to show the positions
 of the objects.
 Diversify the usage of vocabulary like north, south, east and west.

"

"

State the position of the storybook.

2

Explain the positions of the toy car and the ball.

The storybook is 4 squares to the right
and 5 squares to the top.
223

TEACHER’S
NOTES

Guide pupils to say locations at the horizontal axis first then at the vertical axis.
 Relate the locations of objects in daily life such as seatings in a cinema.
"

16.1 (ii)

The picture shows the positions of the chessmen.

is located at A4 and          is located at H3.

3

King Queen

Bishop Knight

Pawn Castle

The numbers 1 to 8 are located at the vertical axis.
This axis shows the locations at the row.

8

7

6

5

4

3

2

1

A  B  C  D  E  F  G  H

What can you see at E2, F4
and B7? Discuss.

The letters A to H are located at the horizontal axis.
This axis shows the locations at the column.

At the location C2, we can see the white bishop.
At G8, we can see the black knight.

The position of an
object is stated by
the column first
followed by the row.

INFORMATION
224

TEACHER’S
NOTES

Diversify exercises, activities or games to recognise the positions of
 objects in or outside the classroom.

"

Materials   MS Word    Players  4 pupils

Steps

1     Each group choose a theme.

2    Execute MS Word.

3    Choose Insert Table (4 × 5 table).
 Type the letters at the horizontal
 axis and numbers at the vertical axis.

4    Choose the graphics of animals from
      Clip Art. Copy and paste in the
 squares.

5    Create another table under the
 animal grid. Complete the table.

6    Print and check your work.
      Display at the Mathematics corner.

5

4

3

2

1
A  B  C  D

Position          Animal

16.1 (ii)

The princess wants
to find her shoe with
the condition that the
number of movements
at the horizontal axis
and the vertical axis are
the same. What is the
colour of her shoe?

1  2  3  4  5  6

6

5

4

3

2

1

0
225

TEACHER’S
NOTES

Complete.

a The Independence Memorial is located at the same row as             and            .

b The Crocodile Farm is located at the same column with          .

c At location B2 is the          .

d D2 is the location of a historical building called          .

e       is located at A4 and          is located at E3.

A     B      C     D          E

4

3

2

1

Tourist attraction places in Malacca

225225

Key:

Crocodile
Farm

Mini
Malaysia

A FamosaButterfly
Garden

Malacca
Zoo

Stadthuys
Building

Samudera
Museum

Independence
Memorial
226

TEACHER’S
NOTES

Relate the situation in the picture with the positions of the objects.
 Prepare grid papers and get pupils to draw objects and determine their positions.

"

16.2 (i)

The Strawberry Farm is located at C5 and the Cactus Valley

is at D2. The Vegetable Farm is located at          .

The Tea Plantation is located at         .

"

Determine the position

The location of the Flower Garden is 2E. The Museum
and Gallery is at 5D. Is it true? Discuss.

Where are the Strawberry Farm
and Cactus Valley located?

What is the location of the
Bee Apiary based on the
horizontal and vertical axes?

The Bee Apiary
is at A3.

Cameron Highlands

A     B      C     D          E

4

3

2

1

5 Tea
Plantation

Strawberry
Farm

Museum and
Gallery

Bee Apiary

Cactus
Valley Flower

Garden

Vegetable
Farm
227

TEACHER’S
NOTES

1   State the positions of the following
          f rui ts:
                                                  a   Ciku                b   Papaya

c   Durian            d   Guava

2   The squirrel does not like chillies and
                                                   bitter gourds. State the positions of
                                                  the chillies and bitter gourds.

Players      2 pupils in each group.

Materials   Letter Grid card (except x),
              questions on the position of letters
              using MS Word, A4 paper.

1     Distribute the letter grid
 card to each pair.

2 Teacher flashes the questions on the position of letters.
 Example:
                        B3      A4      C1      A2      D2
3 Write the letters on an A4 paper based on their positions.

4 Rearrange the letters to form a word.
 Example:    h      o         r         s        e
           C1     B3     A2      A4      D2
5 The fastest group with accurate answers is given 5 marks.

6 Repeat steps 2 to 5.

7 The group with the highest score wins.

Steps

Diversify game methods based on creativity.

"

16.2 (i)

The squirrel is searching for food at Pak Ali’s orchard.

5

4

3

2

1

A B C D E

j

s

d

r

p

c

k

o

a

m

f

q

g

i

h

n

b

v

e

y

t

z

l

w

u

Letter Grid Card

5

4

3

2

1

A B C D E
228

TEACHER’S
NOTES

228

1  Look at the positions of the shapes. Answer the questions.

a        is located 5 squares to          and
   2 squares to         .

b A to F is located at          axis.

c  1 to 4 is located at          axis.

d State the shapes seen at the
           locations:

i    B1   ii   D4     iii  A3

2  Answer these questions based on the grid.

a  Choose a method how you would
    explain the location of         .

i   First the digit 5 followed by the letter D.

ii  First the letter D, second the

digit 5.

b   State the location of         .

3    Look at the locations of the letters
      in the grid. Answer this riddle:

Which box cannot be lifted?

4        State the coordinates of these objects:

a                   b                   c

228

C3       F5      G2

E1      D6      B2       A6     D5     B4     G4

A B C D E F G

a

l

e

o

yt

p
n

b
x

6

5

4

3

2
1

A   B  C  D   E  F

5
4
3
2
1

1 2 3 4

4

3

2

1

0

A  B  C  D  E  F

4

3

2

1
229

TEACHER’S
NOTES

Carry out simulation activities like buying and selling. Inculcate
 moral values of being a prudent consumer.
 Emphasise that finding the value of an item (per unit) is the unitary method.

http://www.transum.org/software/SW/Starter_of_the_day/Students?unitary_
 Method.asp

17.1 (i)

1

The price of                    at Pintar Bookstore is cheaper,  RM3.60.

229

School

RATERATE

Rates

17

The price of a pen
is RM0.75.

The price of a pen
is RM0.60.

Kancil Bookstore

RM0.75
     2 ) RM1.50
           –  0
      1 5
           –  1 4
                  10
              –  10
           0

Price                       at
  Kancil Bookstore:

6 × RM0.75 =
    4  3

RM0.75
    ×            6

RM4.50

RM0.75 × 6 =  RM4.50

Pintar Bookstore

RM0.60
     3 ) RM    1 .80
           –  0
      1 8
           –  1 8
                  00
               –   0
           0

Price                        at
  Pintar Bookstore:

6 × RM0.60 =
    3
        RM0.60
    ×            6

RM3.60

RM0.60 × 6 =  RM3.60

I want to buy 6 pens.
Which is cheaper?

KANCIL BOOk  STORE SPECIAL OFFER

SPECIAL OFFER
PINTAR BOOKSTORE
230

TEACHER’S
NOTES

2 books
RM15.00

3 books
RM21.60

Diversify questions involving money, time and units of measurement.

http://www.wiziq.com/tutorial/49646-grade6-unitary-method

2 30 buses carry 1 320 passengers. Each bus carries the same number
 of passengers.
          a    What is the number of passengers carried by 6 buses?
     Number of passengers for                  Total number of passengers for

The number of passengers carried by 6 buses

is  264  persons.

b    How many buses are needed to carry 220 passengers?

44 passengers           1 bus
            220 passengers         220 ÷ 44

220 passengers         220 ÷ 44 =   5  buses

5  buses are needed to carry 220 passengers.

Fazlin wants to buy 12 storybooks for
             her friends. Help her to spend wisely.

17.1 (i)

How many buses are needed to carry
110 passengers? Discuss.

5
44 ) 220
    – 220
   0

6 × 44 =
    2 2

44
×      6

264

44
30 ) 1 320
    – 1 20
    120
  – 120
      0
231

TEACHER’S
NOTES

Guide pupils to find a value involving unitary. Pose various types of questions
 to reinforce the unitary concept.

3           Zarif puts 20 marbles of the same size
                   on the weighing scale. The total mass
                                          of the marbles is 100 g. Calculate the

mass of 7 marbles.

20 marbles        100 g
             1 marble          100 g ÷ 20

1 marble           5 g
           7 marbles        7 × 5 g = 35 g

The mass of  7 marbles is   35  g.

4

Encik Chong takes 2 hours to drive from Town A to Town B. He takes
  3 hours to drive from Town B to Town C with the same speed.
  Calculate the distance from Town B to Town C.

2 hours         180 km

1 hour                   km ÷          =          km

3 hours                  ×          km =          km

The distance from Town B to Town C is          km.

17.1 (i)

180 km

A B C

? km

5
20 ) 100
   – 100
   0

What is the mass, in g of 25 marbles of
the same size? Discuss.
232

TEACHER’S
NOTES

Prepare enough sets of cards for pupils. Customise activities according to pupils’
creativity and ability.

17.1 (i)

Materials         Players

Question card, A4 paper, pen.      2 pupils in a group.

Steps

1 Prepare 3 question cards for each group.
  Example:

2 Show the calculation steps to find the answers on an A4 paper.

3 Present. Discuss the answers with friends.

4 Keep your work in the Mathematics file.

Solve.

a Encik Rahman receives a wage of RM35 for 5 working hours.
 What is his wage for 8 working hours?

b What is the mass of 150 pieces of
 50 sen coins of the same size?

c A car can travel for a distance of 112 km by consuming 7 ℓ of petrol.
What distance can it travel with 10 ℓ of petrol?

d In an evening, the shadow of a 30 cm plant is 60 cm. What is the
length of the shadow of a 45 cm plant?

20 pieces          240 g

24 cm

Find the length of
5 similar squares.

What is the mass of
7 similar balls?

6 boxes      600 paper clips

4 boxes         ?
233

TEACHER’S
NOTES

233

Hasrul lost in a garden. Find the way out by colouring the answer for each
question in order.

Hasrul’s way out is at          .

a                      b                        c

10 units       RM1.50                 5 kg     RM17.50            12 m        3 pieces
     8 units                           9 kg                            40 m           pieces

d  15 minutes       420 words       e   120 stamps      6 envelopes
     7 minutes              words              100 stamps           envelopes

RM1.20

RM32.40RM31.50RM1.50

4 envelopes
5 envelopes

205 words
196 words 182 words

10 pieces

8
 p

ie
ce

s

9 pieces

2
 0

5
0

m
ℓ

2
 5

0
0

m
ℓ

250 mℓ

START

P Q

R

f    4 glasses       1  ℓ
    10 glasses             mℓ
234

TEACHER’S
NOTES

9.1 (i)

1 Solve.
 a                                   b                                     c

How much does    Find the mass of            Calculate the
    3 books cost?    7 packets.                       height of 4 boxes.

2 Solve.

a    8 children have 336 stamps. Each person has an equal number
       of stamps. Calculate the number of stamps for 9 children.

b    The total number of paper clips in 7 boxes is 455. Each box
    contains the same number of clips. How many paper clips are

there in 5 similar boxes?

c    A tank was filled with tap water at the rate of 90 ℓ per 15 minutes.
    Calculate the volume of water, in mℓ, filled in 2 hours.

d

A businessman wants to buy a printing machine. He chooses
   printing machine A with the reason that the machine prints more
   greeting cards. Is his reason right? Prove it.

e

Based on the diagram above, a piece of cloth is cut into 4 parts of
    equal length. Which number sentence is correct to find the

length of 3 parts of the cloth?

12 m ÷ 4 × 3         or    12 m ÷ 3 × 4

3 packets of sweets
weigh 900 g

4 books
cost RM30

234

45 cm

12 m

Printing Machine  A
1 hour produces

600 greeting cards

Printing Machine B

1
 1

hours produces 900 greeting cards
    2
235

TEACHER’S
NOTES

Emphasise that pictures must be appropriate with the title of the pictograph.

http://urbrainy.com/get/1507/interpreting-pictograms-6273

"

18.1 (i) a
18.2 (i) a

School

× =

18
DATA HANDLING DATA HANDLING

Recognise and compare information

PIE CHART
My Friends’ Storybooks

10

8

6

4

2

0
Akif   Hui Li   Sarjit  Ajol

-------

---------------------

----------------------------

--------------

Friends’ names

BAR CHART
My Friends’ Storybooks

represents 2 books

My Friends’ Storybooks

Key:

represents 2 books

PICTOGRAPH
My Friends’ Storybooks

N
u

m
b

e
r

o
f

b
o

o
ks

Title

Picture

Key

Key:

In a pictograph, pictures are
used to represent data.

Who has the most number
of storybooks?

Akif

Hui Li

Sarjit

Ajol

1

Akif has 8 storybooks.
2 + 2 + 2 +2 = 8
4 × 2 = 8

Hui Li has          storybooks.

Akif

Hui Li

Sarjit

Ajol

Pictograph

MATHEMATICS CORNER

Sarjit
30%

Hui Li
20%

Akif
40%

Ajol
10%

These are three methods
of presenting data.
236

TEACHER’S
NOTES

Use various types of pictographs to retrieve information and create questions.

http://urbrainy.com/get/2304/more-pictogrms-7825

"

18.1 (i) a
18.2 (i) a

2

The sales of mangosteens on Monday is 30.

The highest sale of mangosteens is on Tuesday, which is 50.

The sales of mangosteens on Monday and Wednesday is the same.

On Thursday, the sales of mangosteens is the lowest.

The difference of mangosteens sold on Tuesday
  and Thursday is 30.

50 – 20 = 30

The sales of mangosteens for four days is 130.

30 + 50 + 30 + 20 = 130

Key:        represents 10 mangosteens

The Sales of Mangosteens for 4 Days

On Friday, the number of mangosteens sold is 15
more than the sales on Thursday.

What are the other ways can you calculate the
total sales of mangosteens for four days?

Complete the table.

Does this picture represent
the number? Discuss.

Monday  Tuesday  Wednesday  Thursday

Day          Number of Mangosteen

Monday             3 × 10 = 30

Tuesday          5 × 10 = 50

Wednesday     3 × 10 =

Thursday         2 × 10 =
237

TEACHER’S
NOTES

Ensure the distance of each marking is the same. Relate questions to everyday life to
enhance pupils’ understanding.

http://urbrainy.com/get/1508/interpreting-bar-charts-6922

"

18.1 (i) b
18.2 (i) b

The horizontal axis shows the types of musical instruments.

The vertical axis shows         .

10 pupils like to play the flute, 16 like to play the drum,          like to play

the angklung and          like to play the piano.

The difference between the number of pupils who like to play the drum

and the piano is          .

The total number of pupils is          .

10 + 16 + 14 + 20 =

Vertical axis
Musical Instruments Played

by a Group of Pupils

Musical Instrument

-------------

Flute       Drum   Angklung   Piano

----------------------------------------------------

---------------------------------------

--------------------------

20

18

16

14

12

10

8

6

4

2

0

N
u

m
b

e
r

o
f

p
u

p
ils

Markings

Title

Horizontal axis

Bar chart

In a bar chart, bars are used to show data.

What is the most favourite musical instrument? Why?
238

TEACHER’S
NOTES

238

C
lu

b

0    5    10   15   20   25   30   35   40

--
--

--
--

--
--

--
--

--
--

--
--

--
--

--

--
--

--
--

--
--

--
--

--
--

--

--
--

--
-

Club Attendance of Year 4

Number of pupils

238

Taekwondo

Silat

Robotic

Cultural

4 Type the title and label the
 horizontal axis and the
 vertical axis.

5 Discuss the outcomes.

Reading             12
Swimming         5

Number of Pupils

Hobby

1

2 Key in data in MS Excel.

3    Highlight data, choose the
       menu Insert and click Column.
 Choose Chart Layout and
 click 2-D Column.

2

3

4

Hobbies of Pupils of 4 Cerdas

Hobbies of Pupils of 4 Cerdas

Hobbies of Pupils of 4 Cerdas

Hobbies of Pupils of 4 Cerdas

The bar chart shows the attendance of pupils in club activities.
 The total number of members in each club is 40. Calculate the
 absent members.

Materials   MS Excel, data set.                                 Players   In pairs.

1 Gather data on the hobbies
 of each friend in the class.
 Choose 4 types of
 hobbies.
239

TEACHER’S
NOTES

Relate the percentages of pie chart to fractions. Emphasise the total percentage of a
pie chart must be 100%.

Tell the history of the first pie chart created by William Player in 1801.
 http://www.superteacherworksheets.com/graphing/pie-graph-simple-
 2_TWNWR.pdf

"

"18.1 (i) c
18.2 (i) c

1

50% of Shida’s pocket money is spent on food.

Shida uses 20% of her pocket money for transport.

of her pocket money is saved.

2

The percentage of pupils who like to eat nasi lemak is 30%.

The most liked breakfast is bread which is          .

The least liked breakfast is         which is          .

Favourite Breakfast of 10 Pupils

Shida’s Pocket Money

Fried noodles
20%

Biscuits
10%

Nasi lemak
30%

Bread

40%

Food
50%

Savings
30%

Transport
20%

Pie chart

239

The total percentage
of a pie chart is 100%.

A pie chart represents data in circles.

INFORMATION
240

TEACHER’S
NOTES

240

1     Study the pictograph and complete the answers.

a       saves RM2.

b            saving is the most, which is          .

c   The difference between Faizal’s and

Sivam’s saving is          .

d   The total saving of the four pupils is          .

a   State the time taken to answer the

Mathematics test.

i    Ina    ii   Ho

iii   Ajay   iv  Dayang

b   Arrange the names in order of speed in

answering.

c   The difference in time taken between

and is 15 minutes.

a   The percentage of jasmine is          .

b   The          and the          have the same
           percentage.

c   The total percentage is          .

d   The percentage of the flowers, excluding

chrysanthemum is           .

Ina      Ho   Ajay Dayang

Time to Answer
Mathematics Test

Ti
m

e
 in

m
in

u
te

40

30

20

10

0

Name

-----------------
--------------------------

-----------------------------------
50

60

---------

Key:      represents 50 sen

Savings of 4
Pupils

2    Answer the questions based on the bar chart.

3    Look at the pie chart and answer the questions.

Faizal

Ai Lin

Sivam

Esha

Jasmine
50%

Ylang
20%

Types of Flowers in Painting

Chrysanthemum
20%

Rose
10%

240
241

TEACHER’S
NOTES

241

State the percentage of
 oxygen in the atmosphere.

Materials Pictograph, bar chart,       Players       4 groups of equal
          number of pupils.

Steps

1    Display pictograph, bar chart and pie chart using MS PowerPoint.
      Example:

2 Put the question cards on the magnetic board.

3   The group representative takes the numbered
     question card in turn and answer the question
     orally.

4   Pupil who answers correctly is given 5 marks.

5   The group with the highest score wins.

Gas in the Atmosphere
Other Gases

1%

Nitrogen
78%

Oxygen

pie chart,
numbered question cards.

241

Ways of Going to School

Bus
10%

Bicycle
30%

Car
20%

Walking
40%

24

20

16

12

8

4

0

Pupils’ Hobbies

Reading   Internet    Swimming   Singing
   surting

N
u

m
b

e
r

o
f

P
u

p
ils

Hobby

Pie Chart

What is the percentage

of the pupils walking

to school?

Pictograph

Who borrows the most
number of books from
the library?

Bar ChartFind the difference in

percentage between the

pupils who like to surf the

Internet and those who

like to read books.

-------------
--------------------------

Number of Books Borrowed

Key:        represents 10 books

Adam

Lily

Mira

Maria
242

TEACHER’S
NOTES

1    Study the pictograph and answer the following questions.

a    How many ice creams are sold on
   Sunday?

b    Calculate the total number of
          ice creams sold in 4 days.

c What is the difference in sales of the
  ice creams on Tuesday compared to

Sunday?

d      costs RM2. Calculate the sales

of the first two days.

2    Answer the questions based on the bar chart.

a Green Team collects           marks.

b The total score of           and

Teams is the same as the score
  of Red Team.

c Red Team needs           more

marks to equalise the marks
     of Green Team.

3    Look at the pie chart. Answer the questions below.

a The percentage of glass and

aluminium tins that are recycled

is            .

b The percentage of paper that is

recycled is          .

c      The difference in percentage

between the items most

recycled and the least is           .

Sales of Ice Cream for 4 Days

represents 20 ice creams

Sunday

Monday

Tuesday

Wednesday

242

Key:

Blue

Red

Green

Yellow

Scores of 4 Sport Teams

Mark
0      5       10     15    20    25    30

--
--

--
--

--
--

--
--

Sp
o
rt

T
e
a

m

242

Items Recycled

Paper
Aluminium

Tins
45%

Plastic
10%

Glass
25%
243

A Answer the following
questions.

1. Round off RM53 247.65 to the
nearest ringgit.

2. 63 days =          weeks

3. RM70 406.15 + RM16 319
 + RM782.90 =

4. Convert 11 days 4 hours
 to hours.

5. a.   Convert 9 050 m to
     km and m.
 b.   Calculate 8 km 40 m ÷ 8.
    Give answer in m.

6.

State the length of the needle,
in mm.

7.

Calculate the total value of

money.

8. Solve:

6 cm    9 mm
 ×    5

9.

State the pair of perpendicular
 lines.

10. RM19 620 – RM8 765 – RM437 =

11. 10 years  6 months ÷ 9
 =          years          months

12.

State all pairs of parallel lines
in the rectangle ABCD.

13. The price of  9 kg of rice is

RM22.50. What is the price of
 7 kg of rice?

14.

Find the perimeter, in cm.

15.

Calculate the volume of the
 cuboid, in cm3.

16. 5 ℓ 80 mℓ ÷ 4 × 3 =        ℓ        mℓ

Money

Number
(pieces)

RM100

100

RM50

80

RM20

7

5 sen

9

14 cm

7 cm

9 cm
5 cm

4 cm

C

A

B

A B

D C

0 1cm 2 3 4 5 6
244

17.      17 years 11 months
     +  9 years 10 months

18.  20 kg 840 g + 9 kg 176 g
  – 6 kg 24 g =          kg          g

19.  7 ℓ 680 mℓ  – 4 ℓ 250 mℓ
  + 5 ℓ 90 mℓ =          ℓ          mℓ

20.       – RM10 312.25 + RM948.75
= RM30 120. What is the value
in           ?

21. 6 × 1 600 g ÷ 8 =          g

22.

What is the perimeter, in cm, of
 the pentagon?

23.  30 days 8 hours – 29 hours
  – 4 days 14 hours =
     days       hours

24. Name the following angles.
 a.

b.

c.

25. The diagram below shows the
 height of 4 boxes of the same
 size.

Calculate the height, in cm, of
3 boxes.

26. 4 km 230 m =         – 2 km 865 m
 State the answer in m.

27.     years       months
  6  )  35 years

28 .

The diagram ABCD above is
a rectangle. Find the area, in
cm2, of the shaded part.

29. A square has the same
perimeter as its area. What is
the length of its side, in cm?

6 cm

A 8 cm

4 cm

D

B

C

60 cm
245

30. The grid below shows
 the positions of the shapes.

a.  State the positions of
   i.              ii.              iii.

b.  State the shapes in these
  positions.

i.  C4       ii.  B1         iii.  E5

31. State the currency of these
 countries:
 a. Malaysia       b. Singapore

c. China          d. Vietnam
 e. Indonesia   f.  Thailand

32. State the 3 instruments of
payments other than cash in
our daily life.

33. Which is less than 4 020 m?
 a.  40 km 2 m    b.  4 km 20 m
 c.   4 km 2 m

34.

The diagram above is a square.
 Calculate the:
 a.  Perimeter
 b.  Area

35.

The distance from X to Y is 3
 times the distance from Y to Z.

What  is the distance, in km and
m, from X to Y?

36. 5 weeks 6 days

+ 4 weeks 5 days + 9 days

=         weeks         days

37. RM4 138.50 – 725 sen =

38.      My Friends’ Stamps

Key:         represents 8 pieces

 Look at the pictograph above

and complete the answers.

a.  Lin has         stamps.

b.          has the most number
     of stamps, which is          .

c.  The difference of number
      between Aiza’s stamps and

Nitish’s is          .

d.  Lin and Zul have           stamps.

9 cm

9 cm

5

4

3

2

1

A B C D E

X ZY

1 km 700 m

Lin Aiza Zul Nitish
246

39.

The perimeter of the right angled
 triangle is 30 cm. Find the
 length of PR, in cm.

40. The bar chart shows the
Mathematics marks of 4 pupils.

Complete.
 a. Gurmit scored           marks in

the Mathematics test.

b.          and          got the
      same marks.

c.  Shireen gots         marks less
      than Gurmit.

41.

Calculate the area, in cm2, of the

triangle ABC.

42.       Favourite Sports of
   10 Pupils

a.          % of the pupils like
    to play football.

b.  The most liked sport is         .

c.  The difference in percentage
    between         and
    is 20%.

43.           The diagram shows
           a cuboid. The base

area is 9 cm2. Find
           the volume, in

cm3, of the cuboid.

44.

What is the mass, in kg and g,
 of 9 similar        ?

5 cm

P

Q  R
12 cm

1 kg

1 kg

500 g1 cm

1 cm

A

B

C

7 cm

Amy
Gurmit

Shireen

Mark

Mathematics Marks

N
a

m
e

Zamir

0 2010 60 70 8030 9040 50

Football
20%

Badminton
40%

Volleyball
30%

Table tennis

10%
247

B Solve the following
problems.

1.

Each vase has the same mass.
Calculate the mass of 7 vases,
in kg and g.

2. The total age of a pair of twins,
Aishah and Aizah, is 19 years
8 months. How old is Aizah?

3.

The diagram above shows the
 length of a ribbon. Hasnah

needs 7 ribbons of the same
length for decoration. Calculate
the total length, in cm and mm,
the ribbon needed.

4.

The table shows the prices of
 three items. What is the total
 cost?

5. Encik Ramu’s annual income
is RM51 840. Calculate his
monthly income.

6. A tailor takes 13 hours
 20 minutes to sew 8 similar
 dresses. How long does she

take to sew a dress?

7. Liza jogs 2 km 500 m. Marina
jogs 950 m more than Liza. How
far has Marina jogged?

8.

The diagram is a painting.

a.  Find the area, in cm2.
 b.  Find the perimeter, in cm.

9.

Mother bought 3 bottles of soya
 milk. She poured equally into

25 glasses. What was the
volume, in mℓ, for each glass?

Soya

1 ℓ  250 mℓ

9
 c

m

20 cm

30 cm 6 mm

Item

Television

Furniture

Camera

Price

RM3 499

RM10 520

RM2 880

MASS:

1.2
kg

MC MR M+
ALARM

ON
OFF

ZERO MODE TERA
248

10. The diagram shows 2 packets
of milk powder of different sizes.

a.  Puan Raihan bought both
  packets. She paid with a
   RM100 note. What was her
     balance?

b.  Puan Raihan used 850 g
      of the chocolate flavoured
   milk powder. Calculate the

balance, in g.

11.

The diagram shows the volume
of water in containers P and Q.
7ℓ 420 mℓ of water is poured out
from container P. The water from
container Q is then added into
container P. Calculate the volume
of water, in ℓ and mℓ, in container
P.

12.

The distance from Q to R is 950 m
 more than the distance from  P to

Q. Calculate the distance, in km and
m, from P to R passing through Q.

13.  Gopal bought a used car which
costs RM31 200. He pays the
car by installment for 5 years.
Calculate his monthly installment.

14. A roll of rope is cut into 8 equal
 parts. Each part measures
 12 cm 6 mm. Calculate the

original length of the rope, in
cm and mm.

15.

The diagram shows the locations
 of three cities. Encik Muaz drives

from City D to City F using the
 longest route and returns to

City D using the shortest route.
Calculate the total distance, in
km and m, he travelled.

15 ℓ  20 mℓ 940 mℓ

P
3 km 850 m

Q
R

50 km 180 m

17 km

D

E

F

34 km 840 m

40 km 920 m

QP

RM56.20RM30.90

Original
Flavour

Free 200 g
Chocolate
Flavour

Free 250 g

2 kg
1 kg
249

TOPIC 1: NUMBERS UP TO 100 000
Mind Stretcher (page 16)
1.   a. Twenty-eight thousand six hundred and three
     b. Fifty thousand nine hundred and one
     c. 47 011                         d. 80 025
2.  a. thousands , 5 000              b. ten thousands, 50 000
     c. hundreds , 500                  d. tens, 50
3.  a. 2 ten thousands + 6 thousands + 3 hundreds + 1 tens + 7 ones
         20 000 + 6 000 + 300 + 10 + 7
     b. 6 ten thousands + 2 thousands + 8 hundreds + 3 tens + 9 ones
          60 000 + 2 000 + 800+ 30 + 9
     c. 7 ten thousands + 0 thousands + 1 hundreds + 1 tens + 6 ones
         70 000 + 100 + 10 + 6
     d. 3 ten thousands + 4 thousands + 0 hundreds + 0 tens + 1 ones
         30 000 + 4 000 + 1
4.  a. Ascending order:    30 561, 34 461, 34 726, 39 562, 39 894
         Descending order:  39 894, 39 562, 34 726, 34 461, 30 561
     b. Ascending order:   87 201, 89 372, 90 425, 90 753, 97 281
         Descending order:  97 281, 90 753, 90 425, 89 372, 87 201
5.  a. 90 to 100 books            b. 6 500 mℓ to 7 000 mℓ
6.  Add  20

Multiply by 3

7.  40, 1 970, 50                  8.  61 033, 58 600, 62 000, 55 321

TOPIC 2: ADDITION
Mind Stretcher (page 28)
1.   a. 17 567    b. 84 222    c. 30 720    d. 58 710    e. 56 697     f. 10 098
2.  96 678                           3. a. 2 070  b. 22 425                        4.  84 540
5.  a. 26 179     b. i. 41 789  ii. 30 572
6.  a. A number of durian ice-creams. 40 +       = 260
     b. A number of chickens and ducks.        +       = 1 280

TOPIC 3: SUBTRACTION
Mind Stretcher (page 40)
1.   a. 10 130    b. 67 459    c. 63 199    d. 64 630   e. 34 115     f.  61 213
     g. 30 241    h. 39 056     i. 29 374     j. Accept any correct answers.
2.  a. 29 632   b. 90 294    3. a. i) 14 594          ii)  8 375             b. 2 280
4.  a. Non-fiction books.  750 –       = 380
     b. A total amount of coconuts.        – 13 690 = 5 862
     c. A number of fabrics sold. 10 000 –        = 400

TOPIC 4: MULTIPLICATION
Mind Stretcher (page 50)
1.   a. 24 084   b. 50 598    c.  3 420     d. 65 116
2.  a. 6 363     b. 30 090    c. 56 872    d. 1 386      e. 4 920       f.  62 416
     g. 17 400    h. 78 000     i.  1 000        j. 92          k. 2 203  l.  298
3.  63 000
                      2 1

4.            543    5. a. 3 000 reams
      ×           62         b. 39 630 passengers
             1 086        c.  25 000 pupils
      +  32 580       d. 20 supermarkets

33 666

1 041 3 123 9 369 28 107

125 375 1 125 3 375

64 109 64 129 64 149 64 169

13 116 13 136 13 156 13 176

249

TOPIC 5: DIVISION
Mind Stretcher (page 60)
1.  a. 97      b. 41 remainder 3     c. 93 000                    d. 100
2.  a. 4 115   b. 5 628                 c. 2 358 remainder 3    d. 872 remainder 1
     e. 428     f. 1 779 remainder 2      g. 1 414                    h. 8 597
      i.  368 remainder  1              j.  90
3.  974 remainder 9, 1 441, 81 280   4. a. 1 350 pieces   b. 165 flowers
                                                                        c. 568 boxes        d. 245 participants

TOPIC 6: MIXED OPERATION
Mind Stretcher (page 68)
1.   a. 2 578      b. 9 218             c. 83 636                d. 62 094
     e. 3 510      f .  4 280           g. 1 903                   h. 91 052
2.  a. 142         b. 808                c.  7                          d. 10
3.  a. 1 119        b. 300               c. 85 100
4.  a. 5 400 packets                 b. 5 504 km              c. 96 passengers
     d. 10 370 eggs

TOPIC 7: FRACTIONS
Mind Stretcher (page 88)
1.

2.  a.
 17

, 2
 5

b.
 13

, 3
 1

3.  1
 3

6       6         4      4                  10

4.  a.
 2

b.
 13

c. 1
 5

d.
 4

e.
 1

3                 15                       12                            7                        8

f.
  1

g. 1
 4

h.
  2

i.
5

5                   9                      3                             24

5.
  5

6. a.
 7

kg          b.
 1

kg
     8                         8                   10

TOPIC 8: DECIMALS
Mind Stretcher (page 108)
1.  a. 29.09      b. 42.93             c. 42.492                 d. 58               e. 0.704
       f.  0.109      g. 187.52           h. 28.645                   i. 90
2.  0.15             3. 1.557
4.  b. Estimate 13.95 to 14 and 99 to 100.
         The product is about 1 400.
5.  a. i. 27.61 kg  ii. 5.522 kg   b. 0.7 m                   c. 11.24 ℓ
     d. i. 9.63 seconds  ii. 9.79 seconds

TOPIC 9: PECRCENTAGE
Mind Stretcher (page 112)
1.   a. 0.08            b. 0.2, 20%           c. 0.36, 36%                 d.  0.24 , 24%

2.  0.03, 3%.     0.2, 20%.            0.35, 35%.                 0.68, 68%.
     0.82, 82%

3. a.
   11

, 11%  b. 0.2, 20%        c.
 38

, 0.38
         100                                         100
4.  a. 70%        b. 0.42               c. 60%                     d. 0.3                 e. 5%
      f. 84%        g. 0.09              h. 23%                      i. 0.17                 j. 1.0
5.  92%            6. a. 32%          b. 19%                      c. 49%

SELF-TEST
A (page 113)
1.   Sixty-four thousand and thirteen.
2.  Ten thousands  3.  90 000 + 5 000 + 100 + 7           4.  81 004

5.  23 639     6.  70 000         7.  56 126                8.
  10

7
 9.  15. 019        10. 42.995         11.  45 402               12. 65 100

13. 3
1

14. 6.993          15. 605                    16. 2.58 km
        4

17. 1
2

18. 81 706         19. 900                    20. 28 015
        5

21. 3.09           22. 40 900       23. 52 928              24. 44 231

25. 0.38          26. 30%            27. 80 808              28. 10 060

29. 54.22        30. 15.0             31.
1

32.
 1

5                              9

ANSWERS ANSWERS

3
 1

2
2

1
  2

1
 1

2

6
2

4
2

2
2
250

33. 66 654               34. 45 451            35. 1
   101

1 000

36. a. 1 000              b.   100                  37. 0.03                    38. 1
 3

8
39.  1                         40. 3 621

B (page 115)
1.  54 371 cars        2.  40 594 voters   3. 300 baskets             4.  27.36 m

5.
3

ℓ                       6.
  1

km                7.  0.25 kg                  8. 2.9 minutes     4                              8
9.   38.82                 10. 13 790 copies                               11. 17 432 lorries

12. 1 600 buttons      13. 1.21 m             14. 18.506 km           15. 1
  7

kg                            20

16.
 3

ℓ                      17. 70 packets     10

TOPIC 10: MONEY
Mind Stretcher (page 143)
1.  RM31 157.35         2. a. RM4 787        b. RM64 093            c. RM91 000
3. Choose 3 values of money between:
    a. RM399.50 to RM400.49        b. RM7 652.50 and RM7 653.49
    c. RM71 041.50 and RM71 042.49
4. RM32 341.60        5. a. RM95 955     b. RM37 356            c. RM15 066.55
                                      d. 1 000           e. RM12 500
6. a. RM18.30           b. RM36.95
7. a. Dong: Vietnam                              b. Rupiah: Indonesia
    c. Yen: Japan                                    d. Dollar: Singapore
    e. Dollar: America                     f. Peso: Philipines
8. a. Great Britain     b. Korea               c. China                    d. Nigeria
    e. Indonesia         f. Cambodia       g. Thailand               h. Myanmar
     i. Phillipines
9.  Accept any reasonable answers.

TOPIC 11: TIME
Mind Stretcher (page 164)
1.  a. 168                    b. 6                       c. 59                         d. 119
    e. 144                     f.   7, 8
2. a. 3 days 23 hours                            b. 4 years 4 months
    c. 29 weeks 1 day                            d. 2 days 6 hours
3. a. 202 hours         b. 16 x 7 days      c. 29 weeks 1 day    d. 42 months
4. a. 10 months        b. 11 days             c. 11 years 2 months

TOPIC 12: LENGTH
Mind Stretcher (page 186)
1. a. 55 m                 b. 3 cm 5 mm
2. a. 6 cm 2 mm      b. 2 km 576 m     c. 8 cm                      d. 16 km
3. a. more than 4 km                            b. less than 2 km
4. a. 18 cm                b. 2 cm 1 mm      c. 208 mm
    d. 38 cm 4 mm    e. 44 828 m         f. 13 km 281 m
5. a. 22 km 452 m     b. 14 cm 9 mm    c. 40 mm

TOPIC 13: MASS
Mind Stretcher (page 196)
1. a. 4 kg 804 g          b. 12 kg                c. 15 520 g               d. 5 650 g
    e. 4 kg 864 g          f.  12 360 g
2. a. 8 505 g            b. 12 kg 460 g      3. 290 g
4. a. 55 kg 280 g            b. 2 250 g            c. 2 kg 680 g

Topic 14: VOLUME OF LIQUID
Mind Stretcher (page 206)
1. a. 39 ℓ 74 mℓ           b. 60 ℓ                 c. 30 ℓ 744 mℓ           d. 2 ℓ 105 mℓ
    e. 2 421 mℓ            f. 11 ℓ 305 mℓ
2. a. 8 426 mℓ        b. 26 ℓ 117 mℓ
3. a. 4 ℓ 560 mℓ         b. 3 ℓ 230 mℓ  c. 1 200 mℓ

TOPIC 15: SPACE
Mind Stretcher (page 220)

1.    A          B  B  B          A

A    C  B         B   C    A

2. a. Accept any reasonable answers.
    b. Accept any reasonable answers.
3. a. 16 cm                b.   4 cm               c. Area of diagram X = 15 cm2,
           Area of diagram Y = 16 cm²
4. Area of B is 16 times area of A.       5. 64 cm³                    6. 144 cm³

TOPIC 16: COORDINATES
Mind Stretcher (page 228)
1. a. right, at the top (accept reasonable answers)
    b. horizontal        c.   vertical            d. i.            ii.             iii.
2. a. ii                        b. D5                    3. penalty box
4. a. (2, 1)                   b. (3, 3)                 c.  (1, 2)

TOPIC 17: RATE
Mind Stretcher (page 234)
1.  a. RM22.50           b. 2 100 g             c. 36 cm
2. a. 378 stamps        b. 325 paper clips     c. 720 ℓ
    d. No. The rate of both machines is the same.
    e. 12 m ÷ 4 x 3

TOPIC 18: DATA HANDLING
Mind Stretcher (page 242)
1.  a. 100                    b. 280                  c.  60                         d. RM360
2. a. 25                      b. yellow and blue                              c.  5
3. a. 70%                  b. 20%                 c. 35%

SELF-TEST
A (page 243)
1.    RM53 248           2.   9 weeks       3.   RM87 508.05      4.   268 hours
5.   a. 9 km 50 m      b.   1 005 m          6.   55 mm
7.   RM14 140.45       8.   34 cm 5 mm  9.   AB and BC          10.  RM10 418
11.  1 year 2 months                             12. AD and BC, AB and DC
13.  RM17.50              14.  42 cm
15.  180 cm³                 16.  3 ℓ 810 mℓ     17.  27 years 9 months
18.  23 kg 992 g        19.  8 ℓ 520 mℓ    20.  RM39 483.50
21.  1 200 g                22.  30 cm            23. 24 days 13 hours
24. a. right angle        b. acute angle    c.  obtuse angle        25. 45 cm
26. 7 095 m              27. 5 years 10 months                             28. 16 cm²
29. 4 cm                    30. a. i.  C2          ii.   A3                       iii.   E2
                                        b. i.  ii.                               iii.
31. a. ringgit           b. dollar              c. renminbi              d. dong
       e. rupiah              f. baht
32. credit card, debit card, cheque         33. c
34. a. 36 cm             b. 81 cm²             35. 5 km 100 m
36. 11 weeks 6 days                              37. RM4 131.25
38. a. 16                    b. Zul, 40             c.  8                          d. 56
39. 13 cm                  40. a. 90  b. Amy, Zamir           c.  10
41. 10 cm²                 42. a. 20%           b. badminton
                                  c. volleyball and table tennis/badminton and football
43. 63 cm³                44. 5 kg 625 g

B (page 247)
1.    2 kg 800 g          2.   9 years 10 months
3.   214 cm 2 mm      4.   RM16 899      5.   RM4 320
6.   1 hour 40 minutes     7.   3 km 450 m   8.   a. 180 cm²           b.   58 cm
9.   150 mℓ                10. a. RM12.90     b.   1 150 g
11.  8 ℓ 540 mℓ          12.  8 km 650 m   13.  RM520
14.  100 cm 8 mm     15.  92 km 760 m
Dengan ini, SAYA BERJANJI akan menjaga buku ini
dengan baiknya dan bertanggungjawab atas kehilangannya,

serta mengembalikannya kepada pihak sekolah pada
tarikh yang ditetapkan.

Nombor Perolehan: ______________________________

Tarikh Penerimaan: ______________________________

BUKU INI TIDAK BOLEH DIJUAL

Skim Pinjaman Buku Teks

Sekolah _______________________________________

Tahun Darjah Nama Penerima Tarikh
Terima
PRELIM

UNIT 1 NOMBOR

unit 2 tambah math tahun 4

unit 3 tolak math tahun 4

unit 4 darab math tahun 4

unit 5 bahagi math tahun 4

unit 6 operasi bergabung math tahun 4

unit 7 pecahan math tahun 4

unit 8 perpuluhan math tahun 4

unit 9 peratus math tahun 4

uji diri 1 math tahun 4 (letak selepas unit 9)

UNIT 10 WANG

UNIT 11 MASA DAN WAKTU

unit 12 panjang math tahun 4

UNIT 13 JISIM

unit 14 isi apdu cecair math tahun 4

UNIT 15 RUANG

UNIT 16 KOORDINAT

unit 17 kadaran math tahun 4

UNIT 18 PERWAKILAN DATA

uji diri 2 math tahun 4 (letak selepas unit 18)

jawapan terbaru2 math tahun 4 sk