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



DUAL LANGUAGE PROGRAMME

MATHEMATICS MATEMATIK YEAR 4 TEXTBOOK

WRITERS

EDITORS

• CHAN YOOK LEAN • RAMLAH MAJID • KHADIJAH NOORDIN

• MARIATI JOSEPHA MUSTAFA • ASMAHANIM AB RAHMAN

TRANSLATOR • SUGARA ABDUL LATIF

GRAPHIC DESIGNER • AINI ABD. HAMID ILLUSTRATOR • MOHAMAD SHARIF MOHD YASIN

Dewan Bahasa dan Pustaka Kuala Lumpur 2016

ACKNOWLEDGEMENTS

Serial No.: 0194 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.

CONTENTS 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 ................................. 1 7 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

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 .... 1 09

SELF-TEST

.................................. 113

iii

10 MONEY ........................................11 7 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 .....................1 29 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 .....................1 71 Subtraction of length .................1 74 Multiplication of length ..............1 76 Division of length .......................1 78 Solve the problems ....................180

iv

13 MASS ..................................187 Addition and subtraction of mass ................................187 Multiplication and division of mass ...............................190 Solve the problems ..............1 93 14 VOLUME OF LIQUID ..........1 97 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 ..............................21 7 16 COORDINATES ...................221 Recognise position ..............221 Determine the position .........226 17 RATE Rates

...................................229 ..................................229

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

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



ANSWERS

............................249

INTRODUCTION 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 StandardBased 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

FUNCTIONS OF ICONS IN TEXTBOOK

2

ADDITION

TOPIC Topic based on learning area.

Enrichment activity.

SUBTOPIC Mathematical skills to be acquired.

Encourage critical and creative thinking.

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

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

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

10.1 (i)

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

INFORMATION Key information in learning activities.

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

Summative exercise.

INFORMATION

Revision exercises to enhance pupils’ understanding.

TEACHER’S NOTES

ANSWERS

Additional activity guidance.

Lists of answers for Mind Booster and Self-Test.

Suggested websites.

Writers

vi

1

School

NUMBERS UP TO 100 000 Recognise number 1

Zone A purchased twenty thousand and four hundred boxes.



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

What is the purchase quantity of Zone C?

49 562 Forty-nine thousand five hundred and sixty-two

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

What is the purchase quantity of Zone D and Zone E? Say the numbers written on this board.

1.1 (i)

81 104 93 006 64 205 17 017

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

1

2 Seventeen thousand eight hundred and one.

17 801

Eighty-three thousand and fifteen.

83 015

3 AT A GLANCE

AT A GLANCE

On 15th Oktober 2012

Felix Baumgartner On 15th Oktober 2012

Felix Baumgartner from Australia succeeded in breaking the

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

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.

Thirty-nine thousand and forty-four

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.

Source: Utusan Malaysia. 8th December 2012

sa

ou th

y ne rt ni hi T nd tya en tw

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

nd

4

2

1.1 (i)

Say and write numbers from various sources including the Internet. TEACHER’S " NOTES http://www.ixl.com/math/grade-6/place-values-in-whole-numbers

5 42 009

Which card matches the number word?

8

2 0

1 0

40 029

40 209

Forty thousand and twenty-nine

Create six 5-digit numbers starting with 8 . The two 0 digits must be next to each other. Say and write the numbers.

1 Complete the table. Number Words 69 810 Ninety-five thousand and ninety-one 44 007 Fifty thousand and thirty-four 17 602 2 Write the numbers in words and numerals. a b

Ten Thousands Hundreds Tens thousands

1.1 (i)

Ones

Ten Thousands Hundreds Tens Ones thousands

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

3

Numbers explore Place value and digit value Every digit in a number has a place value and digit value.

1

19 365 Ten Thousands Hundreds Tens thousands

Nineteen thousand three hundred and sixty-five

Ones

The Number 19 365 Digit

9

1

Place value

3

6

5

ten thousands hundreds tens ones thousands

Digit value

9 000

10 000

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

300

60

5

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

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

2

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

Digit

95 702

1.1 (ii)

5

7

0

700

0

thousands

Place value Digit value

4

9

90 000

TEACHER’S " Use number cards to identify and write the place value and the digit value. NOTES

2

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

1

ten thousands thousands 7



Place value partitioning Digit value partitioning

3

hundreds

5

tens

1

ones

9

73 519 = 7 ten thousands + 3 thousands + 5 hundreds + 1 tens + 9 ones 73 519 = 70 000 + 3 000 + 500 + 10 + 9

Partition 40 609 into place value and digit value.

Partitioning number is to write number in expanded form according to the place value or digit value. INFORMATION

Place value partitioning Digit value partitioning

40 609 = 4 0

+ 0 thousands + 6 hundreds + +9

40 609 = 40 000 +

+

+

+

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

2

What is the number for this expanded form?

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. Ten Thousands Hundreds Tens Ones thousands

1.1 (iii)

50 762

TEACHER’S " Discuss the difference between partitioning into place value and digit value. NOTES http://www.ixl.com/math/grade-6/place-values-in-whole-numbers

5

3

hundred ten thousands hundreds tens ones thousands thousands



10 ten thousands

equals 1 hundred thousands.

10



0

0

0

0

10 ten thousands = 100 000 hundred ten thousands hundreds tens ones thousands thousands



1

0

0

0

0

0

1 hundred thousands = 100 000 Are 17 thousands and 170 hundreds have the same value? Explain.



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

4 7

c =

1

8 9 6

4 5 1 2 0

÷ x

3 – .

Write the place value and digit value of 6 in each number. a 11 261 b 38 617 c 61 582 d 96 453

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 6

1.1 (iii)

TEACHER’S NOTES



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

Numbers value 1



Sales

ZEES 12 600 units

AKI 11 800 units

MOMO 12 200 units

BLING 13 400 units

Which bicycle has the highest and the lowest sale? Arrange these numbers on the number line.

Aki

Momo

Zees

Bling

11 600 11 800 12 200 12 400 12 600 12 800 13 200 13 400 12 000 13 000 Bling is the highest in sale. Aki is the lowest in sale. The arrangement of the numbers above is in ascending order. The value of numbers increases from left to right.

Ascending order

11 800, 12 200, 12 600, 13 400

Descending order

13 400, 12 600, 12 200, 11 800

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

1.1 (iv)

Compare the value of numbers using the spike abacus or abacus. TEACHER’S " NOTES

7

2 Arrange these numbers in ascending and descending order. 26 105 Step 1

30 469

26 115

Find the smallest value. ten thousands hundreds tens ones thousands

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

Step 2

3 078

2

6

1

0

5

3

0

4

6

9

2

6

1

1

5

3

0

7

8

Find the largest value.

ten thousands hundreds tens ones thousands

2

6

1

0

5

3

0

4

6

9

2

6

1

1

5

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

ten The value of digits in the thousands hundreds tens ones ten thousands, thousands thousands and hundreds places are 5 2 1 6 0 the same. So, look at the digits in the tens places. 5 2 1 6 1 The value of digit 1 is more than 0. So, 26 115 is more than 26 105.

Ascending order Descending order

8

1.1 (iv)

, 26 105, 30 469, 26 115,

Compare and arrange numbers using flash cards. TEACHER’S " NOTES

, ,

9 Materials Number wheel, pen, A4 Paper.

Players

4 pupils

1 2 3 4 5 6 7

Determine each player᾽s turn. Spin the wheel 5 times according to the player᾽s turn. Record the numbers on a piece of paper. All 4 players compare their numbers. Arrange the 4 numbers in ascending order. Repeat steps 2 to 5. Then arrange the numbers in descending order.

1

Say the smallest number. a 72 210, 82 118, 74 450 c 28 976, 27 312, 29 115

8

2

7

3

b 13 622, 13 066, 13 226 d 70 629, 76 431, 62 725

2 What is the largest number? a b 40 049 11 642 49 032 11 634 40 900 11 694



1

6 5 4

Steps

3

0

c

93 820 93 208 9 1 330

Arrange the groups of numbers in: a Ascending order i 76 732, 71 845, 76 855, 78 237 94 001, 83 109, 42 870, 67 237, 74 324 ii b Descending order i ii

1.1 (iv)

3 065, 28 165, 3 402, 29 892 14 321, 29 109, 18 001, 27 237, 14 324 Use the numbers created by pupils in Number Tracking activity to reinforce TEACHER’S " the skills of comparing values of numbers. NOTES http://www.ixl.com/math/grade-3/put-numbers-in-order

9

Estimate quantity Jar A consists of 400 pieces of chocolates.

1

Almost half of jar B is filled with chocolates.

A



B

Estimate the number of chocolates in jar B.

A



The chocolates in jar B is less than 400 pieces.

B

400 pieces

The number of chocolates in jar B is about 200 pieces. 2

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

The beads in jar Q is more than 150 pieces.

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



P 150 pieces

10

1.2 (i)

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

Discuss the importance of estimation in everyday life. TEACHER’S " NOTES

3 Estimate the volume of water in tank Y.

Y

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

x

20 litres



litres

The estimated volume of water in tank Y is about 60 litres. How do you determine the estimated volume of water in tank Y is reasonable? Discuss.

Complete the reasonable estimates of quantities. 60 kg

a

b 150 pieces

-------c

d --------

600 cm

--------

1.2 (i)

60 mm

-----

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

11

Number patterns

1

What about these two sets of number cards?

How do Zeti and Johan classify their number sequences? In these two sets of number cards, the patterns increase by fours. +4

+4

+4

20 153 20 157 20 161 20 165 +4

+4

+4

17 028 17 032 17 036 17 040 Group the number sequence based on its pattern.

The patterns for these two sets of number cards decrease by tens. – 10

– 10

– 10

11 242 11 232 11 222 11 212 – 10

– 10

– 10

66 137 66 127 66 117 66 107

5 600 5 800 6 100 6 500 12 742 12 542 12 342 12 142 9 000 8 800 8 600 8 400 16 066 16 266 16 566 16 966

12

1.3 (i)

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

2 What are the following numbers in this number pattern? – 23

This number pattern is minus 23.

a 10 201

10 178

10 155

+2

b

25 003

+3

25 005

25 012

1

1

2

3

5

This is Fibonacci number sequence.

8 13 21 34

INFORMATION



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

1

Group the number sequence according to the same pattern. a b 26 007, 26 507, 27 507, 28 007 17 845, 17 835, 17 827, 17 821 80 000, 79 550, 79 100, 78 650 11 077, 11 143, 11 209, 11 275 11 350, 11 850, 12 850, 13 350 54 306, 54 372, 54 438, 54 504 10 001, 9 991, 9 983, 9 977 15 050, 14 600, 14 150, 13 700

2

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



b

3

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

1.3 (ii)

907, 892, 877,

, 847,

, ,

TEACHER’S " Find information about the speciality of Fibonacci sequence by surfing the related websites. NOTES

13

Round off numbers What is the quantity of detergent bought in January? Jimat Supe

rmarket Pu rchase of Jumbo De tergent

Month January February March

Quantity 19 862 11 257 12 999

About 19 900 boxes.

1 Round off the quantity of Jumbo detergent bought in January to the nearest ten. 1 862 is nearer to 1 860.

19 862 19 860 19 870 19 865 19 862 rounded off to the nearest ten is 19 860. Round off the quantity of detergent Jumbo bought in the month of February to the nearest thousand.

2 Round off 32 716 to the nearest ten thousand. ten thousands hundreds tens ones thousands

3 • • • •

14

2

7

1

6

Group  

Digit 0, 1, 2, 3, 4 5, 6, 7, 8,

• If the digit on the right is in Group  , 3 0 0 0 0 retain the digit to be rounded. Look at the digit to the right of • If the digit on the right is in Group , add 1 to the digit to be rounded. ten thousands place. • Then change all digits on the right The digit 2 is in Group  . to 0. Retain the digit in ten thousands place. Change the digits in ones, tens, hundreds INFORMATION and thousands place to 0. 32 716 rounded off to the nearest ten thousand is 30 000.

1.4 (i)

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



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

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

Source: Malaysia Population Census 2010

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

30 000

35 000 -------------- 40 000

49 506

--------

40 637 43 011 36 192 38 471 44 999 45 000 ------------

50 000

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

1 Round off the following numbers to: Number

Nearest Nearest Nearest Nearest ten hundred thousand ten thousand

67 369 10 065 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? 1.4 (i),(ii)

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

15

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. a b

13 000 mℓ

150 books

6 Group these numbers according to the patterns. 13 116 13 136 13 156 13 176 125

375

1 125 3 375

1 041

3 123 9 369 28 107

64 109 64 129 64 149 64 169

7 2 000 , 20 , 1 990 , 30 , 1 980 , , , Which number group completes the number pattern above? a c b 40, 1 970, 50 50, 1 970, 60 1 970, 40, 1 960 8 Which of these numbers becomes 60 000 when rounded off to the nearest ten thousand? 61 033

58 600

TEACHER’S NOTES

16

54 600

62 000

67 114

55 321

2

School

ADDITION WELCOME TO

Addition

RESERVED FOREST In June, 5 806 local tourists visited this place.

VISIT MALAYSIA YEAR

Foreign tourists were 21 345.

1 What is the total number of tourists in June? 5 806 + 21 345 = ten thousands thousands hundreds tens ones 1

1 5 7

2 + 2

1

1

3 8 1

4 0 5

5 6 1

+

2 1 5 2 7

1

3 4 5 8 0 6 1 5 1

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.

2.1 (i)

TEACHER’S NOTES

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

17

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

Central Zone

East Zone

21 407 sheets

15 854 sheets

893 sheets

Calculate the number of all leaflets. 21 407 + 15 854 + 893 = 2

21 15 + 38

1 1

407 854 893 154

Add the 10 addends and add the same digits.

Which is faster, 8 + 8 or 2 × 8? Why?

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 1 3 40 000 + 2 000 + 300 905 900 6 450 + 6 000 + 400 40 000 + 8 000 + 1 600

+ 10 + 3 + 0 + 5 + 50 + 0 + 60 + 8

Partition numbers according to the digit value and add up.

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.

18

2.1 (i)

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

4 Calculate the total number of souvenirs sold as shown. 53 139 + 2 481 + 27 641 = 53 1 39 the answer 2 481 Estimate by rounding off to the + 27 641 nearest thousand.

Key chain 53 139

53 000 2 000 + 28 000 83 000

Magnet 27 641

Postcard 2 481

11 1 1

53 1 39 2 481 + 27 641 83 261

Then, add up.

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

5 Add 41 045, 89, 3 955 and 24 011. 41 045 + 89 + 3 955 + 24 011 = Method 1 Method 2 1 1 1 1 1 4 1 045 24 0 1 1 + 3 955 + 89 4 5 000 24 1 00 Add up the two subtotals.

2.1 (i)

45 0 00 + 24 1 00 69 1 00

4 1 045 24 01 1 3 955 + 89 20 1 1 80 1 900 8 000 +6 0 000 6 9 1 00

41 045 + 89 + 3 955 + 24 011 = 69 100 TEACHER’S NOTES

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

19

6

Interesting places in Sabah Number of tourists Pulau Sipadan

3 5 00

Gunung Kinabalu

?

Kolam Air Panas Poring

8 211

Pasar Kraf Tangan Kota Kinabalu

20 0 1 5

Jumlah

38 219



Calculate the number of tourists in Gunung Kinabalu.



3 500 +

+ 8 211 + 20 015 = 38 219

1 2 0 0 1 5 8 2 1 1 + 3 500 3 1 726

1

1

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



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.

20

2.1 (i)

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.

Materials Cards, pen. +

Steps 1 2 3 4 5 6 7

Choose a leader. Leader says the numbers 0 to 9 randomly 14 times. Numbers can be repeated. Each player writes the numbers in the blank square cards. The numbers written cannot be erased. Each player adds up their numbers respectively. The largest answer is given 2 marks. Repeat five times the steps 2 to 5. 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 2.1 (i)

14 650 P 14 950 15 100 Q R Find the total value of P, Q and R based on the number line above. TEACHER’S NOTES

21

Pulau Layang-Layang

Solve the problems 1

Countries Singapore Japan China

Tanjung Aru

Pulau Tiga

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

Pulau Langkayan

Kudat

Gunung Kinabalu Orang Utan Sepilok

Kota Kinabalu

Number of tourists 10 127 8 839 71 152

Taman Laut Pulau Penyu

S A B A H

Batu Punggul

Gua Gomantong

Taman Bukit Tawau

Tawau Pulau Sipadan Pulau Mabul

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 Find

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

Operation

Addition.

Solve

10 127 + 8 839 + 71 152 = 1 1 11

7 1 152 10 127 + 8 839 90 1 18

Check



Check the answer by estimating to the nearest thousand.

10 1 27 10 000 8 839 9 000 7 1 188 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.

Calculate the total number of tourists from Singapore and China.

22

2.2 (i)

TEACHER’S NOTES

Gua Madai

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 Madai

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? Construct a table. Container

10 385, 10 485, 10 585. Number of Beads 10 285

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

300 more than blue container ? Total

29 420

10 285 + 10 585 + 1 2 1 1 0 2 8 5 1 0 5 8 5 + 8 550 29 420

Is there a different way to check the answer?

= 29 420 Check 1 1

13 8 3 12

1 0 2 8 5 29 420 + 1 0 585 –20 870 2 0 8 7 0 8 550

10 285 + 10 585 + 8 550 = 29 420 The number of beads in the green container is 8 550. The total number of beads in the yellow and green containers is calculated this way. Is it correct? Explain.

1 1 0 585 +85 50 96 085 2.2 (i)

TEACHER’S NOTES

Use the simplifying method to solve more complex problems.

23

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

Post office Number of cards

Seri Setia 42 317

Seri Aman 3 682 more than Seri Setia

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

Number of cartons b Find the total sale of: January February March i orange juice ii apple juice 13 631 Orange 10 527 8 745 in 3 months. 7 239 Apple 9 368 12 689 Juice

4

The number of visitors to Computer Gadgets Carnival Day Number of visitors

First 25 708

Second 41 320

Third 16 420

Fourth 15 612



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.

?

24

2.2 (i)

TEACHER’S NOTES

39 480

27 852

Unknown in addition 1

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.

Unknown means a quantity that is not known. INFORMATION

Can I write this way?

9 add up to a certain number of pages is 20 9 plus how many is 20 9+

9+

✩ = 20

= 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.

70 piec

es

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

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

2.3 (i) 2.4 (i)

TEACHER’S NOTES

Carry out simulation activities to identify the unknowns.

25

3 382 boys and girls took part in the Malaysia aerobic exercise. What are the unknowns for the sentence above? Write the number sentence.

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

B + G = 382

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.

26

2.3 (i) 2.4 (i)

TEACHER’S Create worksheets using math.com. NOTES http://www.mathdrills.com/algebra.shtml

Materials

Question card

Question card, MS Excel software. Steps 1 Execute MS Excel.

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

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. TEACHER’S NOTES

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

27

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 0 1 6 3 8 Use the same number cards to create the largest and the smallest numbers. Find the total. 3 62 475

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 20 960

21 060

P

Q

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. Day Number of visitors



First 21 382

Second 20 407

Third 27 639

Fourth

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. TEACHER’S NOTES

28

3

School

SUBTRACTION I N F O R M AT I O N TECHNOLOGY CARNIVAL 2014

Subtraction 1

Total: 12 654 units Sold: 2 664 units a How many black tablets left? 12 654 – 2 664 =

Total: 24 396 units

ten thousands hundreds tens ones thousands



0

1

– b

11 1

15 5

2 2 9

6 6 9

15

5 6 9

4 4 0

12 654 – 2 664 = 9 990 The number of black tablets left is 9 990 units.

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



24 396 – 9 990 = 1 13 13

24 396 – 9 990 1 4 406

3.1 (i)

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. TEACHER’S NOTES

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.

29

7

Materials

0 6

1 2

5 0

9 2

3

1

8 6

7 4

MS Word, 4 sets of digit groups. 3

Steps

0

6 8

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

1 Create empty boxes using MS Word.

–

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.

7 0 1 Example: 6 2 2 7 6 2 1 0 – 1 0 2 6 7 6 5 9 4 3 3

1 Subtract. a 72 684 – 1 506 = c 85 734 – 5 744 =

6 + 5 + 9 + 4 + 3 = 27

b 54 231 – 6 918 = 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? 30

3.1 (i)

TEACHER’S NOTES

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

Subtract consecutively 1 Sale of mobile phones at Pintar Company Initial amount January Sale February Sale

27 436 10 365 3 002

How many mobile phones left? 27 436 – 10 365 – 3 002 = Method 1 12 3 2 16 1 0 3 6 5 27 436 + 3 0 0 2 – 1 3 36 7 1 3 3 6 7 1 4 069 Method 2







3 13

2 7 4 3 6 – 1 0 3 6 5 1 7 0 7 1

17 071 – 3 002 = 3 000 2

1 7 0 7 1 – 3 000 1 4 0 7 1

14 069

14 070 –1

14 071 –1

27 436 – 10 365 – 3 002 = 14 069 The mobile phones that are not yet sold is 14 069 units. 27 436 – 3 002

3.2 (i)

– 1 0 36 5

Try to solve. Is the answer the same?

TEACHER’S Encourage pupils to subtract numbers without regrouping before subtracting using suitable strategies. NOTES http://interactive.onlinemathlearning.com/subtraction.php?addition=generate& numDigits0=1&numDigits1=5&numProblem=

31

2 47 504 – 12 996 – 31 500 =

47 504 – 31 500



16 004

16 004 – 12 996 = +4 +4 16 008 – 13 000 = 3 008

47 054 – 12 996 – 31 500 = 3 008 3

84 125 – 12 950 – 29 760 = Estimate the answer.

Round off the numbers to the nearest thousand.



84 125 1 2 950 29 760

84 000 1 3 000 30 000

Calculate the actual answer.

3

8 4 0 0 0 – 1 3 0 0 0 7 1 0 0 0

10 0 12

7 1 000 – 30 000 4 1 000

10 6 0 11

8 4 1 2 5 – 1 2 950

71 1 75 –29 760

71 1 75

41 4 15

41 415 is close to 41 000. The answer is reasonable. 84 125 – 12 950 – 29 760 = 41 415

32

3.2 (i)

TEACHER’S NOTES

Carry out simulation activities involving consecutive subtraction using smaller numbers.

4



– 53 712 – 8 435 = 27 904 1 1

1 1

2 7 9 0 4 + 8 4 3 5

1

10 – 5 – 3 = 2 10 = 2 + 3 + 5

36 339 +53 7 1 2

3 6 3 3 9

90 05 1

90 051 – 53 712 – 8 435 = 27 904 Can 8 435 be subtracted from 53 712 first, then added to 27 904? Discuss.

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?

3.2 (i)

82 317 – 4 105 – 290 = 8 2 3 1 7 – 4 1 0 5 8 2 2 1 2

TEACHER’S NOTES



82 2 1 2 – 290 82 082

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

33

Solve the problems 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 11 330





13 580 – 2 250 =

Check

ten thousands hundreds thousands

tens

ones

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. Is there other ways to check the answer? Explain.

34

3.3 (i)

TEACHER’S NOTES

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

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?



Gather Informations



Option



A. B. C.

Level 1

Level 2

1 000 800 900

800 1 000 700

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.

I use the trial and error method.



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.

Why didn’t you choose C? Explain.

3.3 (i)

TEACHER’S NOTES

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

35

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. Desa Murni Desa Setia Desa Permai Name Number of 20 920 50 127 27 469 people

i

ii c d

Calculate the difference between the number of people in Desa Setia and Desa Permai. How many more people are there in Desa Permai compared to Desa Murni?

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? Calculate the number of fishling that must be added into the pond so that the total becomes 10 thousand. 1 265 fishlings

e P



36

Q 40 026

R

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.

3.2 (i)

TEACHER’S NOTES

Unknown in subtraction 1

Mother, I have collected 50 stamps of various countries.

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

Please give a few stamps to your brother.



What is the quantity that is not known? A few stamps. So, the unknown is a few stamps.



The number sentence is written as 50 –

Can you substitute

with

= 42

?

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

3.4 (i) 3.5 (i)

TEACHER’S NOTES

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

37

3

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



♦

–

✥



✤

– 192 =

= 192

★

Which number sentence is correct? Discuss.



The scale shown below is balance.



A B 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.

38

3.4 (i) 3.5 (i)

TEACHER’S NOTES

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.

Materials Players White laminated papers, marker pens, A4 papers, stopwatch and a duster.

2 pupils as players and one 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 7

The player who answers correctly in 30 seconds gets 5 marks. The player who answers correctly in more than 30 seconds gets 2 marks. Repeat steps 2 to 5 for five times.

8 The player with the highest mark is the winner.

3.1 (i)

TEACHER’S NOTES

Improvise activities according to pupils’ ability.

39

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 – – 9 056 h 30 thousand = 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. Hobby Surfing the Internet Number of pupils



i ii

Reading books 6 219

Calculate the number of pupils who like to surf the Internet. Find the difference in number of the two hobbies.

b Q P R 10 320 12 610

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. TEACHER’S NOTES

40

4

School

MULTIPLICATION Simple multiplication 1 ju book sho Ma p

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

What is the number of books supplied? Calculate by adding 3 × 2 120 = repeatedly and in + 2 120 standard written method. + 2 120

0

2 120

+ 2 120

4 240

6 360

2 1 20 × 3 6 360

3 × 2 120 = 6 360 The number of books supplied is 6 360. What is the number of books sent to 9 bookshops?

4.1 (i)

TEACHER’S NOTES

Relate the usage of multiplication with examples in daily life.

41

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

3

Method 2 2 485 = 2 000 + 400 + 80 + 5

5 3

2 485 × 7 1 7 395

Calculate by partitioning.

× 2 000 400 80 5 7 14 000 2 800 560 35 14 000 + 2 800 + 560 + 35 = 17 395 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 21 390 2 139 × 10 = 21 390 5 84 × 1 000 =

156 × 100 = 15 600 Complete and talk about the multiplication pattern of these numbers.

84 × 1 0 0 0 84 000

84 × 10 = 84 × = 8 400 × 1 000 = 84 000

84 × 1 000 = 84 000

42

4.1 (i), (iii), (iv)

TEACHER’S NOTES

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/



5 0 9 4 × 0 2 7 2 8 0

Fill in the blanks.

1 Multiply. a 4 123 × 2

b

6 012 × 5

c

6 576 × 7

d

8 025 × 9



e 3 × 4 822 =

f 4 × 9 051 =



h 7 × 5 463 =

i 8 × 7 006 =

g 6 × 9 730 = j 9 × 8 142 =

b 981 × 100 =

c 69 × 1 000 =

2 Calculate mentally. a 5 318 × 10 =

d 4 326 ×

= 43 260 e 570 ×

3 Fill in the blanks. a 9 60 1 × 3

b ×

08 003

7 000 300 60

5 35 000 TEACHER’S NOTES

f

8 260 6

× 100 = 99 000

c ×

40 500

4 Multiply. a 5 × 7 362 = ×

= 57 000

300 10

b 8×

9 7 3 0 7 33 807

= 73 160

× 8 72 000

100

5 320 40

43

Let's multiply

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

1



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

34 × 12 = Multiply the ones digit Multiply the tens digit 3 4 3 4 × 1 2 × 12 6 8 34 × 2 68 + 3 4 0 34 × 10

Add up the products 34 × 12 1 68 + 340 408

34 × 12 = 408 The total number of books received is 408. 2 67 × 23 =

Multiply the ones digit





2

Multiply the tens digit 1 2

Add up the products 1 2



6 7 6 7 67 × 2 3 × 2 3 × 23 2 0 1 67 × 3 2 0 1 20 1 + 1 3 4 0 67 × 20 + 1 340 1 54 1

44

67 × 23 = 1 541 4.1 (ii)

TEACHER’S NOTES

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

3 182 × 45 = Method 1 Method 2 182 = 100 + 80 + 2

× 100 80 40 4 000 3 200 5 500 400 4 500 3 600

182 × 45 10 400 500 8 0 3 200 + 4 000 8 1 90

2 80 10 90

4 500 + 3 600 + 90 = 8 190

2× 5 80 × 5 100 × 5 2 × 40 80 × 40 100 × 40

182 × 45 = 8 190 4 603 × 52 = Round off 603 and 52 to the nearest

603 52



600 50

×

1

603 52 ten to estimate the 1 206 603 × 2 answer. 600 + 30 150 603 × 50 × 50 31 356 Actual 30 000 answer 31 356 is close to 30 000. The answer is reasonable. 603 × 52 = 31 356 5 548 × 73 = 5 13

4 0 4.1 (ii), (iv)

1

5 5

4 22

1

8 2

8 15

2

×

6

7

4

3

Next, solve using standard written method.

0 0 4 548 × 73 = 40 004

TEACHER’S Carry out quiz activity or mental calculation. NOTES http://www.superteacherworksheets.com

45

99 is 100 6 852 × 99 = 852 × 99 = 852 × 100 – 852 minus 1. = 85 200 – 852

852 × 100 = 85 200 852 × 1 = 852

11 9 4 12 10 10

85 200 – 852 84 348



852 × 99 = 84 348

× 80 = 58 160 7 727 7 × 8 = 56 8 ) 5 8 16 7 = 56 ÷ 8 – 56 2 1 58 160 Relate multiplication to division. – 16 80 56 × 80 = 58 160 – 56 = 58 160 ÷ 80 0 727 × 80 = 58 160

1 Complete the calculations. a 2 1 b 5 2 4 x 4 6 × 5 5 1 2 2 2 0 + + 6 2 0 6 28 20 2 Multiply. a 41 × 14 = d 487 × 62 =

b 36 × 25 = e 913 × 99 =

3 Calculate. a The product of 95 and 46. c Multiply 34 tens by 9 tens. 46

4.1 (ii), (iv)

TEACHER’S NOTES

c × +

c f

378 2 6 68 5 8

52 × 37 = × 70 = 98 490

b 5 hundreds multiply by 18. d 288 hundreds is multiply 10 tens.

http:www/.superteacherworksheets.com

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: 2 6 0 7 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. j c

h

l

a g

e

Complete the cross number puzzle. Down

Across a. b. c. d. e. f.

58 × 66 = 232 × 15 = 111 × 64 = 50 × 1 000 = × 100 = 43 300 275 × = 27 500

4.1 (i), (ii)

TEACHER’S NOTES

g. h. i. j. k. l.

1 360 × 9 = 466 × 2 = 72 × = 72 000 × 20 = 13 460 × 42 = 42 000 7× = 59 150

k b

i

d f

Do exercises or times table quiz to reinforce multiplication skill.

47

Solve the problems 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 8 280

Solve

8 280

8 280

8 280

8 280

8 280

6 × 8 280 = 1

4

8 280 × 6 49 680 Check

+ + + + +

8 8 16 8 24 8 33 8 41 8 49

280 280 560 280 840 280 1 20 280 400 280 680

Check your answer by adding repeatedly.

6 × 8 293 = 49 680 The total number of eggs ordered is 49 680.

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

48

4.2 (i)

TEACHER’S NOTES

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

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 = 5

9 2

7

1

5

0 0

×

0 3

2 0 0 0 0 0 0 0 8 5 0 0

Check 21

9 500 9 500 + 9 500 28 500 950 × 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? Source: Mark Carwardine. Animal Records. Page 35, 2008

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)

TEACHER’S NOTES

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

49

1 Multiply. a 6 021 × 4

b

2 Calculate. a 3 × 2 121 = d 42 × 33 = g 174 × 100 = × 1 000 = 92 000 j

8 433 × 6

b e h k

c

76 × 45

5 × 6 018 = 82 × 60 = 78 × 1 000 = 4× = 8 812

d

892 × 73

c 8 × 7 109 = f 664 × 94 = i 53 × = 53 000 l × 30 = 8 940

3 Find the product of the underlined digits on the cards below. 4 756 3 194 4 In the calculation on the right, the answer 4 344 is incorrect. Correct the mistake in the calculation.

543 × 62 1 086 + 3 288 4 344

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. Source: Airport Council International

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?

50

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. TEACHER’S Banyakkan latihan yang merangkumi pelbagai bentuk soalan untuk mengukuhkan 2.3 (i) 2.4 (i)

NOTES

kefahaman murid.

5

School

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

1

How many bags are distributed to each school bookshop? 39 630 ÷ 3 =



13 3)39 – 3 09 – 9 0 –

210 630

6 6 03 – 3 00 – 0 0



Division Guide 1. Divide ten thousands digit 2. Divide thousands digit 3. Divide hundreds digit 4. Divide tens digit 5. Divide ones digit INFORMATION

39 630 ÷ 3 = 13 210 The number of souvenir bags distributed to each school bookshop is 13 210. 5.1 (i)

TEACHER’S NOTES

Emphasise the steps of division in detail. http://fivejs.com/math-strategies-multiplication-division-video-tutorial

51

2 50 475 ÷ 6 =

3

78 600 ÷ 100 =

Remainder must 8 4 1 2 Method 1 be less than the 6 ) 5 0 4 7 5 divisor. – 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 – 12 Remainder 3 78 600 ÷ 100 = 786 50 475 ÷ 6 = 8 412 remainder 3

4 93 021 ÷ 1 000 = 93 1 000 ) 9 3 0 2 1 –9000 3021 –3000 2 1

Check

The inverse of division is multiplication.

93 021 ÷ 1 000 = 93 remainder 21 Multiply: 9 3 × 1 0 0 0 9 3 0 0 0

Add remainder: 93 000 + 21 93 02 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 g 87 006 ÷ 8 = e 37 465 ÷ 4 = f ÷ 1 000 = 91

2 Calculate mentally. a 54 210 ÷ 10 = b 73 200 ÷ 100 = d 76 700 ÷ = 767 e ÷ 100 = 543 f

52

5.1 (i)

TEACHER’S NOTES

c 5 6013 ÷ 1 000 = ÷ 1 000 = 91 remainder 5

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

Let's divide 1

F a r m o r s A s s o c i a t i on

752 durians are packed equally.





Build the 16 16 1 6 times table 1 06 16 based on 1 and 6 times tables. 2 12 32



16 baskets

752 ÷ 16 =

3 1 8 48 4 24 64 5 30 80 6 36 96 7 42 1 1 2 128 8 48 9 54 144

47 16 ) 7 5 2 – 64 1 12 – 1 12 0 752 ÷ 16 = 47

2 6 950 ÷ 30 = Partition 6 950 to

Method 1 6 000 + 900 + 50. Then, divide one

2 3 1 by one. 30 ) 6 9 5 0 – 6 0 9 5 – 90 50 – 30 20

Method 2 200 + 30 + 1 30 ) 6 000 + 900 + 50 – 6 000 – 900 – 30 0 0 20 remainder 200 + 30 + 1 = 231

6 950 ÷ 30 = 231 remainder 20 5.1 (i)

TEACHER’S NOTES

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

53

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

34 800 ÷ 25 =

5 25 5 25 = 5 × 5

6 5)34 – 30 4 – 4

1 5)6 – 5 1 – 1

960 800

392 960

9 5 46 – 45 10 – 10 0

8 5 30 – 30 00 – 0 0

34 800 ÷ 25 = 1 392 Each customer receives 1 392 quail eggs. 4 79 871 ÷ 79 =

Estimate the answer.

79 871 79 1

80 000 80

000

80 000 = 1 000 80 1



1 Add up the 10 quotients 1 000 79 ) 7 9 8 7 1 – 79 000 87 1 – 7 90 81 – 79 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

54

5.1 (i)

TEACHER’S NOTES

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

5 24 360 ÷ 12 =

45 155 ÷ 11 = 1 4 11 5

2 0 3 0 24 360 = 2 030 12

45 155 = 415 11

1

1

Where is the mistake? Discuss.

24 360 ÷ 12 = 2 030

6





÷ 52 = 431

The inverse of division is multiplication.

1

431 52

×

÷ 52 = 431 = 431 × 52



1

1

862 + 2 1 550 22 4 1 2

22 412 ÷ 52 = 431

6 400 ÷ =

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

Divide. a

15 ) 2 670

e

8 436 ÷ 12 =

f

26 514 ÷ 17 =

g

53 788 ÷ 29 =

h

72 009 ÷ 36 =

i

81 048 ÷ 49 =

j

96 324 ÷ 64 =

5 .1 (i)

b

20 ) 7 160

c

42 ) 90 807

d

murid menggunakan jadual sifir untuk membahagi. Guide pupils to use the times tables to divide. TEACHER’S Latih NOTES

80 ) 39 682

55

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

k

r

l

f

671

155

187 remainder 2

1 034

729 remainder 16

d

a

o

n

324

869

1 155 remainder 3

1 164

y 584 remainder 5

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

56

5 .1 (i)

25 ) 8 100

37 ) 6 921

46 ) 39 974

55 ) 36 905

64 ) 73 923

73 ) 84 972

82 ) 59 794

90 ) 93 060

97 ) 56 653

TEACHER’S NOTES

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

Solve the problems 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. 6th Floor 5th Floor 48 000

4th Floor 3rd Floor 2nd Floor 1st Floor



Operation

Division



Solve

48 000 ÷ 6 =



?

8 000

48 000 = 8 000 6 1



Check

8 000 × 6 = 48 000



48 000 ÷ 6 = 8 000 8 000 tiles are needed for each similar floor.

5.2 (i)

TEACHER’S NOTES

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

57

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? Total number of soya drink: 26 907 bottles 26 907 1 box: 24 bottles – 24 000 Remainder of soya drink bottles: ? 2 907 Number of boxes needed: ? – 2 400 26 907 ÷ 24 = 507 – 240 267 Why is the number of – 240 boxes needed 1 122? 27 – 24 remainder 3

24 bottles

24 × 1 000 24 × 100 24 × 10 24 × 10 24 × 1 1 121

26 907 ÷ 24 = 1 121 remainder 3



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?

58

5.2 (i)

TEACHER’S NOTES

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

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. 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?

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.

Stand at 0 round number card

Move to touch the remainder

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.

5.2 (i)

TEACHER’S NOTES

Prepare enough question sets for a few groups of players.

59

1

Complete the following. a 9 700 ÷ 100 = c ÷ 1 000 = 93

b 41 003 ÷ 1 000 = d 82 506 ÷ = 825 remainder 6

2 Solve. a 6 ) 24 690 b 9 ) 50 652 c 27 ) 63 669 d 42 ) 36 625 g 84 840 ÷ 60 = e 8 560 ÷ 20 = f 67 604 ÷ 38 = h 94 567 ÷ 11 = i 36 801 ÷ 100 = j 90 000 ÷ 1 000 = 3 Complete the table below. Number Divisor 23 385 24 72 050 64

Quotient 50 1 270

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



d

60

5.2 (i)

What is the number of boxes needed to pack 56 790 packets of biscuits?

100 P

ackets

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? 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

6

School

MIXED OPERATION Addition and subtraction 1

Bus sto

Bus sto

p1

p2

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

12 + 9 – 6 =



1

1 11



1 2 + 9 2 1

21 – 6 15



12 + 9 – 6 = 15



Solve the first operation, then the second operation.

The number of passengers that are still in the bus after the second bus stop is 15. Calculate 9 – 6 first. Then, add the answer to 12. Is the answer the same? Why?

6.1 (i)

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.

61

2 9 472 – 295 + 68 =

16 3 6 12

9 4 7 2 – 2 9 5 9 1 7 7

1 1

9 1 77 + 68 9 245

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

9 472 – 295 + 68 = 9 245

3 74 204 + 12 798 –

1



1 1

= 83 901 6 10

74 204 + 1 2 7 9 8 8 7 0 0 2

87 002 – 83 90 1 3 101

7 + 1 – = 8 8 – = 8 8 – 8= 0

74 204 + 12 798 – 3 101 = 83 901

Create number sentences from the cards to 62 394 48 726 give the largest and the smallest values. – + = 50 272

1 Calculate. a 708 + 5 360 – 24 = c 8 765 + 10 642 – 6 826 = e 10 718 + 29 372 – = 9 390 2 15 000 – 4 000

+ 5 000 = 10 000

6 000

62

6.1 (i)

b 374 + 21 213 – 8 635 = d 40 452 – 11 023 + 32 005 = f – 17 624 + 6 378 = 81 237

TEACHER’S NOTES

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

Use number cards to create mixed operation number sentences. http://www.funbrain.com/cgi-bin/alg.cgi?A1=s&A2=1

Multiplication and division 1 All these chocolate biscuits need to be packed equally in the 3 jars.



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

4 × 18 ÷ 3 =

Method 1

Method 2 6

3

24 3)72 –6 12 –12 0

18 × 4 72

4 × 18 = 4 × 18 3 3

1

= 4 × 6 1

= 24

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

1

22 × 6 132

2 200 ÷ 100 × 6 = 132 6.2 (i)

TEACHER’S NOTES

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

63

2 54 756 ÷ 18 × 11 = Build the 18 3 042 18 ) 5 4 7 5 6 times table. 1 8 18 – 54 Add the tens 1 08 18 digits and retain 0 7 the ones. – 0 2 16 36 75 3 24 54 – 72 4 32 72 36 5 40 90 – 36 0

3 042 × 1 1 3 042 + 30 420 33 462

54 756 ÷ 18 × 11 = 33 462 3 2 550 × 4 ÷ 2 2 2 5 5 0 × 4 1 0 200

= 1 020

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

10 200 ÷ = 1 020 10 200 = 1 020 × 10 Relate division to multiplication.

2 550 × 4 ÷ 10 = 1 020

1 Calculate. a 14 × 750 ÷ 12 = c 2 048 ÷ 8 × 3 = e 1 526 ÷ 14 × 11 = 2 Complete the following. a 7 × 5 000 ÷ = 3 500 c × 3 000 ÷ 60 = 1 000



b 18 × 1 010 ÷ 10 = d 26 232 ÷ 6 × 10 = f 100 × 480 ÷ 16 =

b 4 030 ÷ 10 × = 8 060 d ÷ 10 × 80 = 80 000

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

64

6.2 (i)

TEACHER’S NOTES

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

Materials 2 laminated number sentence cards, answer cards, whiteboard pens, duster and calculator. + 10 Players

– 20

–

= 30

40

50

60

+ 70

= 80

90

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. 1 740 + 15 – 1 725 = 30 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. 4 000

129

72

4 000 360 10 000 1 200

8

8

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 =

6.1 (i)

TEACHER’S NOTES

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

65

Solve the problems 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 =

1 1





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

1 1

Check

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

2

10 0 17

63 1 78 – 3 1 480 3 1 698 12 5 2

11

63 1 78 – 27 428 35 750

35 750 + 27 428 – 31 480 = 31 698 The number of hibiscus planted on the second day is 31 698.

66

6.3 (i)

TEACHER’S NOTES

Guide pupils to identify the key information and build 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

M ALAY S I A N F O O D F E S T IVA L

MALAYSIAN

FOOD FESTI

VAL

80 × 250 ÷ 5 =

4 4 0 0 0

250 20 000 = 4 000 × 80 5 1 20 000 Check 4 0 0 0 80)20 – 16 × 5 4 20 000 – 4 80 × 250 ÷ 5 = 4 000

250 000 0 00 00 00 – 0 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 24 by 11 schools. bean buns 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)

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.

67

1 Calculate. a 197 + 2 386 – 5 = c 71 892 + 18 543 – 6 799 = e 6 × 5 265 ÷ 9 = g 14 × 3 806 ÷ 28 =

b d f h

2 Complete the following. a 712 + 430 – = 1 000 c 64 ÷ 8 × = 56

b 1 245 – d 70 × 2 ÷

10 012 – 4 609 + 3 815 = 98 250 – 62 054 + 25 898 = 18 832 ÷ 22 × 5 = 26 780 ÷ 10 × 34 = + 312 = 749 = 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?

68

2.3 (i) 2.4 (i)

TEACHER’S NOTES

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

7

School

FRACTIONS Recognise mixed numbers and improper fractions 1

There are 1 kuih bakar and

1 cut cake. 2

Pizza

Cheese Cake

Banana Cake

Kuih bakar

What is the fraction of the kuih bakar ?

1 cake 1 1 cake 1 2 2 There is 1 1 kuih bakar. 2 Mixed numbers is written as 1 1 2 1 1 is read as 2 11 2 one, one over two. Whole number Proper fraction Mixed number shows the value of more than 1. INFORMATION 7.1 (i) a, b

TEACHER’S NOTES

Give other examples of mixed numbers.

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

69

2 What is the fraction for the cheese cake?

One whole cake is cut

1 cake 1 cake

into 4 equal parts.

1 cake 4

9 parts of a cake is 9 . 4 Nine over four is an improper fraction.

1 1 1 4

1 4



1 4 1 4

4 4

1 4

1 4

+

1 4 1 4

1 4

4 4

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

9 4

1 4

+

1 4

=

9 4 The numerator is larger than the denominator.

9 4

numerator denominator

INFORMATION

Give other examples of improper fractions.

70

7.1 (i) a, b

TEACHER’S NOTES

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

3 Mixed number and improper fraction. a

1 2

1

1 2

1 2

1 2

1 1 2

3 2

2 3 5

13 5

b



Mixed number

Improper fraction

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

0

1 4

2 4

3 4

1

A

B

C

2

1 4

2 4

3 4

4 4

5 4

6 4

7 4

8 4

Proper fractions

Improper fractions

7 a mixed number? 5 Discuss. Is 1

7.1 (i) a, b

TEACHER’S NOTES

Guide pupils to shade improper fractions and mixed numbers on diagrams. Build a fraction board. http://www.edhelper.com/math/fractionstg513.htm

71



Place the improper fractions and mixed numbers at the correct places on the number line. 11 4

13 8

11 8

11 2

17 8

1

1

7 4

11 8

21 2

19 8

21 4

17 8

2

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.

72

a

12 7



1 2 d 3

c

7.1 (i) a, b

TEACHER’S NOTES

b

11 4 24 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

Relationship between improper fractions and mixed numbers 1 Convert 2 1 to improper fraction. 2 21 = 2



1

+

1

+

1 2



2 2

+

2 2

+

1 = 2



21 2

=

5 2

mixed number

improper fraction

21 = 5 2 2

Convert 7 to mixed number. 2 3 7 = 3

0 7.2 (i)

1 3

2 3

3 3

4 3

5 3

6 3

7 3

8 3

1 3

2 3

1

11 3

12 3

2

21 3

22 3

7 = 3

21 3

TEACHER’S NOTES

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

73

3 Convert 9 to mixed number. 5 Use division 9 = 5 operation. 9 is 5 9 divided by 5.

1 5 ) 9 4 – 5 is written as 1 5 4

9 = 14 5 5

16 = 3 5 Talk about the 3 ) 16 mistake made. – 15 1 16 = 3 1 3 5

4 Convert 20 to mixed number. 6 20 = 6 3 32 = 32 ÷ 2 6 ) 20 6 6 ÷ 2 – 18 = 31 3 2 20 = 3 1 6 3 5 Convert 2 1 as improper fraction. 4 2 1 = 4 2 1 = 4 = = 2 1 = 4 74

7.2 (i)

TEACHER’S NOTES

1 + 1 + 1 4 4 + 4 + 1 4 4 4 9 4 9 4

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

6 Convert 3 1 to improper fraction. 10

31 = 10



31 = 3 + 1 10 10



= 30 + 1 10 10



= 31 10 10 10

20 10

1

2

0

31 = 10

30 10 3 31 10

40 10 4

31 10

Convert 4 2 7 to improper fraction. 7 42 7

=



=

4 2 7

4

× 7 7



= 28 + 2 7



= 30 7



7.2 (i)

42 7 TEACHER’S NOTES

=

+

2

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

30 7

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

75

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.

11 = 1 3 8 8

12 = 2 2 5 5

12 = 1 5 7 7

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 51 = b 95 = c 11 = d 23 = 4 6 9 10 3 A pizza has 8 parts. How many parts are there in 1 5 pizzas? 8 76

7.2 (i)

TEACHER’S NOTES

Addition of fractions 1

1 + 2 = 4 4

1 4



1 4

1 + 2 = 4 4

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

1 4

3 4

INFORMATION

3 + 2? 2 What is the total of 7 7 3 + 2 = 7 7 2 7 0

1 7

2 7

3

1 + 1 = 2 4



1 + 1 = 3 2 4 4



1 + 1 = 2 4

7.3 (i) a

TEACHER’S NOTES

3 7

4 7

5 7

3 + 2 = 7 7

3 4

1 2

6 7

7 7

8 7

5 7

1 4 1 4

1 4

Use paper strips or objects to reinforce pupils’ understanding.

77

4

1 + 5 = 2 7



1 + 5 = 1 × 7 + 5 × 2 2 7 2 × 7 7 × 2



= 7 + 10 14 14



= 17 14



= 13 14



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.

1 + 5 = 1 3 2 7 14

4 + 2 + 1 = 5 9 9 9 4 + 2 + 1 = 4 + 2 + 1 9 9 9 9 = 7 9

4 + 2 + 1 = 9 9 9

6

1 + 3 + 1 = 4 8 4



2 + 3 + 2 = 7 8 8 8 8

1 + 3 + 1 = 4 8 4

78

7.3 (i) a, b

TEACHER’S NOTES

7 9

Make the denominators the same. 1 4

7 8

1 4

1 4

1 4

1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8

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

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 16 ÷ 2 = 8 10 ÷ 2 5 = 13 5

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

1 + 2 + 7 = 2 5 10

13 5

Materials A4 paper, ruler, pencil, colour pencil, fraction cards 1 + 3 8 8 Steps 1 2 3 4 5

Fold paper into 8 equal parts. Draw lines along the folded parts. Colour 1 part blue and 3 parts red. Calculate the total of the coloured parts. Repeat steps 1 to 4 for other fractions.

Solve. a 1 3 c 1 5 e 2 3 g 7 8 7.3 (i) a, b

+ 1 = b 3 + 2 + 1 = d 5 5 + 5 = f 6 + 1 + 3 = h 2 8 TEACHER’S NOTES

2 7 1 4 1 2 2 3

+ 4 = 7 + 3 + 4 + 7 = 9 + 5 + 6

3 = 4

2 = 3

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

79

Subtraction of fractions 1

How many parts of the cake left?

5 – 1 = 6 6



5 – 1 = 4 6 6 6



5 – 1 = 6 6

4 ÷ 2 = 2 6 ÷ 2 3 2 3

What is the difference between 4 and 2 ? 2 5 5 4 – 2 = 5 5 4 – 2 = 5 5 3

80

7.4 (i) a

2 5

4 5

6 – 1 – 2 = 7 7 7 0



2 5

1 7

2 7

6 – 1 – 2 = 7 7 7 TEACHER’S NOTES

3 7

3 7

4 7 2 7

5 7

6 7

1

1 7

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

4 Subtract 1 from 4 7 – 1 8 4 7 – 1 8 4 7 – 1 8 4

7. 8 = = 7 – 8 = 7 – 8 = 5 8

5 – 1 – 1 = 5 6 3 6 5 – 1 – 1 = 6 3 6 = = 5 – 1 – 1 = 6 3 6 1 – 1 – 1 = 6 2 10 5 1 – 1 – 1 = 2 10 5 = = 1 – 1 – 1 = 2 10 5 7.4 (i) b

TEACHER’S NOTES

1 × 2 4 × 2 2 = 5 8 8

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

1 2 5 10 2 10

1 6 1 1 3

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

× 5 – 1 – 1 × 2 × 5 10 5 × 2 – 1 – 2 10 10 10 is in the ÷ 2 = 1 2, 5 and 10 ÷ 2 5 times tables. 1 5

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

81

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 Make sure the answer is given in

= 14 – 9 – 3 18 18 18

the simplest form.

= 14 – 9 – 3 18



= 2 18 2 ÷ 2 = 1 18 ÷ 2 9



7 – 1 – 1 = 9 2 6

1 9

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

Subtract. Give answer in fraction of the simplest form. a

3 – 1 = b 5 5

5 – 4 = 7 7

c

8 – 5 – 1 = 9 9 9

7 – 3 – 1 = 10 10 10

e

3 – 1 = f 4 2

5 – 1 = 9 5

g

6 – 2 = h 7 3

5 – 1 – 1 = 6 2 6

i

9 – 2 – 1 = j 10 5 5

2 – 2 – 1 = 3 9 9



4 – 1 – 3 = l 5 4 10

7 – 1 – 1 = 8 4 2

k

82

7.4 (i) b

TEACHER’S NOTES

d

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

Addition and subtraction of fractions 1

2 + 3 – 1 = 5 5 5



2 + 3 – 1 = 5 5 5

2

7 – 3 + 1 = 8 8 4



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

4 5

= 7 – 3 + 2 8 = 6 8 6 ÷ 2 = 3 8 ÷ 2 4

7 – 3 + 1 = 8 8 4

3 4

6 – 2 + 4 = 6 – 2 + 4 7 7 7 7 = 6 – 6 7 = 0 7 What is the mistake in the above calculation?

7.5 (i) (a)(b)

TEACHER’S NOTES

Carry out simulations using real objects or materials.

83

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

0

1 10

2 10

3 10

4 10

5 10

6 10

7 10

8 10

9 10

2 + 7 – 1 = 5 10 2

3 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



= 11 12

7.5 (i) b

5 – 2 + 3 = 6 3 4 TEACHER’S NOTES

10 10

5 10



= 10 – 8 + 9 12 12 12

84

7 10

Multiples of 3, 4, 6 3 4 6 3 4 6 6 8 12 9 12 12

11 12

Guide pupils to understand the concept of addition and subtraction using simulations and diagrams. http://www.education.com/activity/fractions/

11 10

Materials

Thinker board card Players and stationaries.

Think Board Card

Steps 1 2 3

Each group completes the think board card Diagram based on the topic given by the teacher. 1 1 + Demonstrate your work 2 in front of the class. Teacher acts as a fasilitator. Display your work in the Mathematics corner.

1

1 2

1 Solve. a 5 + 2 – 3 = b 7 7 7 c 4 – 1 + 2 = d 9 9 3 e 2 + 1 – 7 = f 5 3 10 2

1 ℓ 2 7.5 (i) a, b

4 pupils in a group.

A

7 ℓ 8

B

Concrete material/object 1 1 2

1

1 2

Number sentence Topic: Add Fraction 1 + 1 = 11 2 2 Story Ali has an apple. 1 His brother has an apple. 2 1 Altogether there are 1 apples. 2

5 – 1 + 3 = 6 6 6 2 + 4 – 3 = 5 5 4 9 – 2 + 3 = 10 5 4

Pour the water from container A into container B. Pour out 3 ℓ of water 4 from container B. Calculate the volume of water left in container B.

85

Solve the problems 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 Solve

Addition 4 7 4 + 7 = kg kg 5 10 5 10 4 + 7 = 8 + 7 5 10 10 10 15 ÷ 2 = 8 + 7 = 3 10 ÷ 2 10 2 = 15 = 11 10 2 8 4 10 5 7 7 10 10 Check 11 – 7 = 3 – 7 2 10 2 10 = 3 × 5 – 7 2 × 5 10 What is the difference in mass = 15 – 7 of the two types 10 of prawns? 8 ÷ 2 = 4 = 8 10 ÷ 2 5 10 4 + 7 = 1 1 kg 5 10 2 The total mass of prawns bought by Miss Kim is 1 1 kg. 2 86

7.6 (i)

TEACHER’S NOTES

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

2 Jasmin takes 5 hour to finish Mathematics exercise 6 1 and 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. Finishes exercises Mathematics: 5 hour 6 1 Science: hour 2 5 + 1 – 3 = 6 2 4 5 + 1 – 3 = 5 × 6 2 4 6 × = 10 + = 7 12 5 + 1 – 3 = 7 6 2 4 12

5 hour 6

Helps mother Difference in time 3 hour 4

1 hour 2

hour 2 + 1 × 6 – 3 × 3 2 2 × 6 4 × 3 6 – 9 12

3 hour 4

hour

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?

1m 2

7m 10 Zaidi’s house 1 km 1 km 2 The diagram shows the distance from 4 5 A B Zaidi’s house to the library. Calculate the 3 km Library difference between the distance of route A and route B. 5 7.6 (i)

TEACHER’S NOTES

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

87

1

Fill in the blanks with improper fractions and mixed numbers. 1 2 1 2

0

5 2

3 2 1

7 2

2

3

2 Write the improper fractions and mixed numbers for the diagrams below. a b 3 Find the value of Q. 3 10

0

4 Calculate. a 1 + 1 = 3 3 d 5 – 1 = 7 7 g 8 + 7 – 2 = 9 9 9 5

4 5

1

Q

1

1 2

1 + 2 = 5 3 e 3 – 1 = 8 4 h 5 – 1 + 1 = 6 2 3 b

c f i

1 + 3 + 1 = 2 4 6 9 – 1 – 1 = 10 5 2 1 + 5 – 2 = 4 8 3

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? TEACHER’S NOTES

88

8

School

DECIMALS Recognise decimals 1

1.25 metres.

Thirty-eight point five degrees Celcius.

T SPOR

ON EATI RECR

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

8.1 (i)

cm 130 129 128 127 126

TEACHER’S NOTES

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

Countries

Score

China

422.30

Australia

366.50

Malaysia

359.20

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

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

95 89

2

Zero point one four three

1

0.005 Three decimal places

0.143

1• 005

0.14

0.15

Three decimal places is three digits after the decimal point.

Decimal point

One point zero zero five

INFORMATION

3 This is the smallest fish in the world. Write decimal in Its length is 7.900 millimetres. words. Sourcer: http://www.nhm.ac.uk/about-us/ Paedocypris Progenetica



Seven point nine hundred

news/2006/jan/news_7501.html

Seven point nine zero zero

Who wrote correctly? Discuss.

• 3 0 9 0 90

8.1 (i),(ii)

TEACHER’S NOTES

Form a decimal number with three decimal places.

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

Materials Graph paper, scissors, glue, A4 coloured paper, pen.

Players 5 pupils in a group.

Steps 1 2 3 4 5

Cut out 1 000 squares from a graph paper. Colour the graph paper to form a pattern. Paste the graph paper onto an A4 coloured paper. Write the coloured parts in decimal. Cross-check each members’ work in the group. Keep in Mathematics file or display your work in the Mathematics corner.

1

State the coloured parts in decimal. a b

2 Write in words. a 0.7 e 90.054

b f

1.43 52.6

c

c 8.011 g 371.08

3 Complete the table. ones tenths hundredths thousandths Number 0 • 1 0.317 8 • 0 4 5

8.1 (i), (ii)

TEACHER’S NOTES

Words

six point two five

• •

d 64.78 h 109.125

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

97 91

Relationship between fractions and decimals 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 = 27 ÷ 1 000 1 000 0.027 1 000)27.000 – 0 27 – 20 7 – 7

00 00 000 000 0

27 out of 1 000 parts 27 is 3 zeroes 1 000 27 out of 1 000 parts 3 decimal places

is 0 . 0 2 7

27 = 0.027 1 000

2 Convert 2 9 to decimal. 1 000 9 = 2 1 000 9 9 =2+ 2 1 000 1 000 = 2 + 0.009 = 2.009

1 000 1 000 9 2 009 2 = 1 000 1 000 = 2.009

1 = 1 000 1 000

Use place value chart.

ones tenths 2 • 0

1 =

9 1 000

hundredths thousandths 0 9

9 = 2 2.009 1 000

92

8.2 (i)

TEACHER’S NOTES

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

3 Convert 1.076 to fraction of thousandths.

1.076 =



1.076 = 1 + 0.076 76 =1+ 1 000 76 =1 1 000















1 = 1 000 1 000

0.076 = 76 1 000

1.076 is 1 ones, ones tenths hundredths thousandths 0 tenths, 1 • 7 6 0 7 hundredths and 7 6 thousandths. to Change 1.076 = 1 + 0 + 7 + 6 100 10 100 1 000 equivalent fraction.







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

1 Match. 19 1 000

7.009

9 1 000

0.197

7

2 Write in decimals. a 72 b 13 46 1 000 1 000

1 1 000

197 1 000

9.017

0.019

9 17 1 000

9.001

9

c

48 81 1 000

3 Write in fraction of the thousandths. a 0.037 b 1.815 c 5.203 8.2 (i)

d

25 903 1 000

e

60 5 1 000

d

39.040

e

17.9

TEACHER’S Carry out activities like matching fraction cards to decimals number cards. NOTES http://www.onlinemathlearning.com/decimals-to-fraction.html

93 93

Compare decimals 1

Which is the larger value, 1.023 or 0.97?



1.023



1.023 is larger than 0.97

Compare

2

The more the coloured parts, the larger the value.

0.97

2.168 with 2.45 . ones • tenths 2 • 1 2 • 4

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

hundredths thousandths 6 8 5 0

same value 1 is less than 4 2.168 is less than 2.45 2.45

2.168

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



94

8

P Q

R 9

Which letters have the values of 8.3 and 8.35 on the number line above? Explain. 8.2 (ii)

TEACHER’S NOTES

Compare decimal numbers using number line. http://www.mathsisfun.com/numbers/ordering-game.php?m=Dec-Tricky

3

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

Can you drop the zero? Discuss.

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

3.09 0.8

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

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

0

0.05



a 0.08 c 0.31

0.1

0.2 0.11 0.13

0.3

b 0.27 d 0.4

0.4 0.3 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 c 2.08 2.080 d 4.953 8.2 (ii)

TEACHER’S NOTES

1.06 4.95

Do various exercises and activities using flash cards.

95 95

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

0.2 m

0.2 m + 0.5 m =

0.5 m



0.2

m

ones 0 • Arrange the numbers + 0 • so that the decimal points are lined up in 0 • 0.5

the same column.

tenths 2 5 7

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

Add the tenths: 2 tenths + 5 tenths = 7 tenths 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 .056 +2.980 4.036 1.056 ℓ + 2.980 ℓ = 4.036 ℓ The total volume of water is 4.036 ℓ. 1.056 ℓ 3.17 + 5.238 = 1 3.1 7 +5.238 5.555

96

8.3 (i)

2.98 ℓ

Is the answer correct? Discuss.

TEACHER’S Use addition of decimals involving measurements without conversion of units. NOTES http://interactive.onlinemathlearning.com/dec_addition.php?action=generate& numDigits0=2&numDigits1=2&numProblems=10

3 RM4.72 + = RM10.05 9 10 1 0 . 05 – 4 . 72 5 . 33

RM4.00 +

= RM10.00 = RM10.00 – RM4.00 Relate addition to subtraction.

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. 2.0

0.6 2.0

2.0

0.9 1.4 1.8 1.6

1.4

1.4

1.3

1

1.8 1.6

Complete the following. a 0.29 + 3.48 = c 2.4 + 6.36 = e + 3.08 = 9.154

1.8 1.6

b 8.07 + 6.493 = d 4.209 + 8.874 = 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 0.87

8.3 (i)

8.07

0.780

8.7 8.7

7.08

7.800

TEACHER’S Emphasise to pupils that adding decimal numbers is the same as adding whole numbers. NOTES http://www.math-play.com/soccer-math-adding-decimals-game/adding decimals-game.html

97 97

Subtraction of decimals 1 What is the distance from National Monument to Perdana Lake Gardens? 3.7 km 2.1 km

National Monument

Merdeka Square

3.7 km – 2.1 km = 3.7 – 2. 1 1 .6

Perdana Lake Gardens

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 = tens ones tenths 1 – 1

7 6 1

• • •

kg hundredths

8

10

9 8 0

0 5 5

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

17.9 kg – 6.85 kg = 11.05 kg

98

8.4 (i)

TEACHER’S NOTES

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

3



– 8.342 = 15.67 1 1



– 1 = 2 3 = 2 + 1 3 – 1 = 2

1

1 5 . 6 7 0 + 8 . 3 4 2 24.0 1 2

24.012 – 8.342 = 15.67



Fill in the blanks.

– 6

1

Complete the following. a 10.7 – 0.3 = c 2.15 – 1.6 = e 50.81 – = 7.293

. .

9

b 9.211 – 4.37 = d 34.46 – 5.182 = 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?



a c

8.4 (i)

0.625

1.13

3.3 – 2.17 = N 8.4 – 7.685 = I

0.715 b

0.625

1.13

7.125 – 6.5 = O

TEACHER’S Guide pupils to subtract using partitioning or counting down. NOTES http://interactive.onlinemathlearning.com/dec_subtraction.php?action=generate& numDigits0=2&numDigits1=2&numProblems=10

99 99

Multiplication of decimals 1 000 mℓ 900 800 700 600 500 400 300 200 100

1 What is the total volume of water in the two beakers? 2 × 0.9 ℓ =

1 000 mℓ 900 800 700 600 500 400 300 200 100

0.9 ℓ

0.9 ℓ 1

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

0.9 × 2 1 .8

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

2 × 0.9 ℓ = 1.8 ℓ 1.8 ℓ.

The total volume of water is

INFORMATION

2 6 × 3.28 = 3

100

7 × 19.403 =

1 4 3 . 2 8 × 6 1 9 . 6 8

1 9.403 × 7 135.821

6 × 3.28 = 19.68

7 × 19.403 = 135.821

8.5 (i)

TEACHER’S NOTES

6 2

2

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

4 10 × 0.5 = 0.5 ×10 5.0

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

10 × 0.5 = 5.0 10 × 0.5 = 5.0 5 100 × 7.214 =

INFORMATION

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

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



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 = c 5 × 0.219 = e 100 × 1.5 =

1.68

10.0 4.2

5.0

b 4 × 2.64 = d 9 × 15.036 = 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? 8.5 (ii)

TEACHER’S NOTES

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

101

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

1 Afif’s house



School

0.86 km

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

0.86 km ÷ 2 = 0.43 2)0.86 – 0 0 8 – 8 06 – 6 0

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

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 60 –60 0

1.6 ÷ 10 = 0.16

1.6 ℓ ÷ 10 = 0.16 ℓ

102

8.6 (i), (ii)

TEACHER’S NOTES

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

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

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

3 12.9 ÷ 100 =



4 57.0 ÷ 1 000 =

0. 1 2 9 1 0 0 ) 1 2.9 0 0 – 0 129 –100 290 –200 900 –900 0

0.0 5 7 1 0 0 0 ) 5 7.0 0 0 –0 570 – 0 5700 –5000 7000 –7000 0

12.9 ÷ 100 = 0.129

57 ÷ 1 000 = 0.057

5

÷ 6 = 72.415 1 2

3

7 2.4 1 5 × 6 434.490

64.0 ÷ 10 = 6.4 64.0 ÷ 100 = 0.64 64.0 ÷ 1 000 =

How do you divide? Explain.

434.490 ÷ 6 = 72.415

1 Complete the following. a 9.4 ÷ 2 = c 17.25 ÷ 5 = e ÷ 8 = 5.634 g = 60.9 ÷ 100

b 3.27 ÷ 3 = d 36.108 ÷ 9 = f ÷ 10 = 0.76 h 2.803 = ÷ 1 000

2 Find the quotient of 13.5 divided by 6. 8.6 (i), (ii)

TEACHER’S Carry out quiz or mental calculation. NOTES http://interactive.onlinemathlearning.com/dec_divbywhole.php?action=generate &numDigits0=1&numDigits1=3&numDigits2=1&numProblems=10

103

Solve the problems 1

Malaysia Sport

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

Names of Gymnast Final Score Placing Contingent Tai Qing Tong 1 Wilayah Persekutuan 24.225 Shok Yuki 2 Selangor 23.19 1 Izzah binti Azman 3 Selangor ? 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 =

Izzah’s score must

be less than Shok Yuki’s score.

2

11

Check

23. 1 9 1 – 0.34 1 22.850

23.191 – 0.341 = 22.850 Izzah's score is 22.850. Calculate the total score for the first and the third placing. Check by estimation.

104

8.7 (i)

TEACHER’S NOTES

Guide pupils to solve problems using mantic reasoning.

1

22.850 + 0.34 1 23. 1 91

RECYCLE CAMPAIGN

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 = Draw a diagram. 8.5 8.5 8.5 8.5 8.5 8.5 8.5

8.5

8.5

4

8.5 × 9 76.5

Check the answer using repeated addition.

9 × 8.5 kg = 76.5 kg The total mass of newspapers collected was 76.5 kg. If there are 100 piles of newspapers, what is the total mass? Calculate mentally.

Volumes of drinks bought Volumes of each container (ℓ)

C JUI

E

M ILK

ORANGE

Number of containers

3.5 ℓ 3

1.25 ℓ 8

0.325 ℓ 9

Calculate the total volume of each type of drinks bought. 8.7 (i)

TEACHER’S NOTES

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

105

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. 2.52 m

?

Operation

Division

Solve

2.52 m ÷ 6 = 0.42 6)2.52 – 0 2 5 – 2 4 12 – 12 0

Check with multiplication.



1

0.42 × 6 2.52

2.52 m ÷ 6 = 0.42 m 0. 42 m of lace is used for one pair of L-sized shirt. Calculate the length of lace for one pair of M-sized shirt.

106

8.7 (i)

TEACHER’S NOTES

Solve problems using paper strips or simulation activities.

Materials

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

Steps 1 2 3

Gather information on prices, lengths, masses, volumes of liquid involving decimal points from magazines or the Internet. Cut and paste pictures on A4 paper. 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.

STUD

ENT᾽

Y AR

N

S

R

RM4

DICTIO

8.50

M1 Solve. 2. 60 RM27.90 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 451.4 72835 his car? TEACHER’S NOTES

107

1

Calculate. a 3.6 + 25.49 = d 5.8 × 10 = g ÷ 8 = 23.44

b 48 – 5.07 = e 70.4 ÷ 100 = h 51.42 + = 80.065

c 6 × 7.082 = f 0.981 ÷ 9 = i 68.391 = – 21.609

2 How much more is 0.9 than 0.75? 17 and 0.54. State the total in decimal. 3 Add 1 1 000 4 13.95 × 99

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 27.04 ℓ in the pail? d The incomplete table below shows the result of 100 m running event. result i The difference time recorded between The of 100 m (M) Running Olympic 2012 the first winner and the second was 0.12 seconds. What was the time recorded Usain Bolt ? by Usain Bolt? Yohan Blake 9.75 s ii Usain Bolt was 0.16 seconds faster than Justin Gatlin ? Justin Gatlin. Calculate the time recorded Source: http://www.london2012. com/athletics/event/men by Justin Gatlin. 100m/indx.html TEACHER’S NOTES

108

9

Sekolah

PERCENTAGE Relationship between percentages and decimals

MARCH EXAMINAT ION

I got 95%.

CER EAL

BAHASA MALAYSIA Name: Chin We i Class: 4 Arif Marks: 95%

1

Write 95% in decimal.



2

CER

EAL

Se NU rvin TR gs IEN AM ize O : TV 30 UN AL g TP UE Pro ER IN t SER Tot ein FO Se a V r RM v l I Ch ing Fat NG AT o Pe IO Tot lest rC N ero al o 30 nta Die Carb l i g n T o t e pe ota r Su ary hyd : r 9 Nit ga Fib rat 2. 1 serv l Ene rat r er e rgy e 0.2 g ing : 4 11 0.0 g %0A % 1 kca l %KG 25 mg 4% * 0% 0. 9 .5 g 90%% 2. 1 g 20 0% 4% 0.0 g mg - 9% 4 9%% 9%

State 4% in decimal.

95% = 4% = 0.95 95% = 95 100 ) 9 5 . 0 0 4% = 4 100 100 –90 0 5 00 = 95 ÷ 100 = 4. ÷ 100 –5 00 = 0.04 0 95% = 0.95 4% = 0.04 3

Convert 0.73 to percentage.

Method 1 0.73 = 73 100 = 73%

0.73 =

Method 2 0.73 = 0.73 × 100% = 73%

0.73 = 73% 9.1 (i)

TEACHER’S NOTES

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

109

4

State 0.9 in percentage.





0.9 =



0.9 = 9 × 10 10 × 10 = 90 100 = 90%



0.9 = 90%

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

10 20 30 40 50 60 70 80 90 100 100 100 100 100 100 100 100 100 100 100

State 0.01 in percentage.



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 73% 0.29 0.5 8% 0.7 0.03

Percentage 35% 61%

3 State the values of P and Q in percentages. P 0

110

9.1 (i)

0.1

Q 0.2

TEACHER’S NOTES

0.3

0.4

0.5

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

0.7

Materials

0.11

5%

6%

Answer card, pen, coloured pencils/crayons.

29%

Steps

0.51

1

48%

Teacher prepares answer card.

82% 0.98 30%

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᾽.

Secre

ardtage C t G g r ee tin r percen bet. Find t he m lo ha

3 Decorate your greeting card. 4 Email the code breaker table to your friend.

9.1 (i)

CODE BREAKER TABLE S P 0.02 7% C Y 90% 1.0 L O 0.32 0.5 B E 0.2 48%

0.48

numb

atchin cima e alp d rep g de with th 100% lace hem 32% t % 32 0.48 32% 0.7 0.940% % 5 85% 0% 8 .7 10 0 5% 25% 2 % 1 0.7 0.1 1 .65 0 100% 20% 85% 25%

er an

H T 2% 0 .07 65% 10% 0.99 R F 50% 0 0.25 99% .1 0.7 0.0 7 0.0 7 U I 0.85 0.4 A D 70% 0.11

TEACHER’S Prepare answer cards according to the number of pupils. Recreate activity according to pupils’ abilities. NOTES http://www.mathgoodies.com/lessons/vol4/decimals_to_percents.html

111

1

Write the decimal number and percentage for the shaded parts.



a

b

c

d

8% 2 Complete the decimal number and percentage on the number line. 0

0.5



0.03



3%

1

3 Fill in the blanks. a 0.11 = b 0.2 = × 100% = % = %

c

38% = =

4 Convert to percentage or decimal.

a 0.7 f 0.84

b 42% g 9%

c 0.6 h 0.23

d 30% i 17%

e 0.05 j 100%

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

112

6

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



a

9.1 (i)

TEACHER’S NOTES

b

c

12. Subtract 49 hundreds from 7 ten thousands. A Answer the following questions. 13. Write the mixed numbers that represents the shaded parts of the whole diagram.

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 14. 7 . 02 13 . 467 digit value. Find the difference in value for the two underlined digits on the 4. Write the numerals for eightycards above. one thousand and four. 15. 21 780 ÷ 36 =

5. What is the value of P on the number line below? 23 189 23 339

P

23 789

6. Add 9 043, 62 319 and 127. Round off the answer to the nearest ten thousand. 7.





3 to improper 7

Q

R

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.

fraction.

9. Convert 15 19 to decimal 1 000 number.

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

10. What is the value of 0.02 less than 43.015? 11. 36 402 is 9 000 less than

P

2.7 km

52 009 – 628 + 4 745 =

8. Convert 1

5.28 km

16.

.

19. How many hundreds are there in 90 000?

113

20.

29. Subtract 5.9 from 60.12.

Thousands Hundreds Tens Ten thousands



Ones

What number is represented by the spike abacus above?

21. 12.36 ÷ 4 = 41 900 39 900

22.

43 900 42 900

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.

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 7 and 2 . 9 3 33. Given 1 058 × 9 = 9 522, therefore, 1 058 × 63 = 34. Solve. 54 768 –

= 9 317

35. Convert 1.101 to fraction.

26.

State the shaded parts in decimal. P

81 750

64 018

37. State 3% in decimal.

38. 1 + 1 + 5 = Form a number by adding the 4 2 8 digit values of the underlined Give answer in mixed numbers. digits on the number cards above.

28. 20 120 × 4 ÷ 8 = 114

0.7

State the value of P in percentage.

27. 32 804

0.5

36. Complete the following. a. × 1.58 = 1 580 b. 42.9 ÷ = 0.429



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

5 5. Faiz uses ℓ of blue paint and 8 1 ℓ of white paint to paint the living 8 room of his house. What is the

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



B Solve the following problems. 1.

Model Number

Myvi 28 407

Proton 25 964

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. 9.12 m

total volume of paint used?

7 6. Chew cycles a distance of km 8 3 on Saturday and km on 4 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 Champion Runner Up



9.

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.

2.1 minutes ?

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. 9.43

11.69 P 2.04

5

Q 28.6

The total of three numbers in each row is the same as shown in the diagram. Find the total of P and Q. 115

10. Encik Rosli delivers 985 newspapers each day. How many newspapers does he deliver in two weeks? 11. Vehicle Car Bus Lorry Total



Number 28 109 15 486 ? 61 027

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. 1 280 buttons



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.

14.

C

A

5.8

6 km

km

0 12.7 B



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. Long Bean Cabbage Cucumber



2 kg 5

7 kg 10

1 kg 4

Calculate the total mass of vegetables bought by Puan Intan.

1 16. A container holds ℓ of water. 2 1 Ai Lin drinks ℓ of the water. 5 What fraction, of the water is 17.

left in ℓ? 140 pieces

140 pieces

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



Nathan 1.4 m

116

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?

10

School

MONEY Combination of money Sir, this is my money and form.

1

Counter 2

What is the total amount of money deposited?





50 pieces

100 pieces

100 pieces

56 pieces

RM5 000

RM5 000

RM2 000

RM560

Twelve thousand five hundred and sixty ringgit

RM12 560

Notes

Number of pieces 50 100 100 56

Value (RM) 5 000 5 000 2 000 560

Total (RM)

RM100 RM50 12 560 RM20 RM10 The total amount of money deposited is RM12 560 .



10.1 (i)

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

117

2

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

es

6

3

pi

pi

pi 4

en

im

ec

Sp

ec

ec

es

es

15

30

0

0



pi

pi

ec

ec

es

es



ec

RM ?

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?

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

0

10

ec pi

0

10

ec es

c pie

pi

ec pi 0 20

ec e pi 0 50

2

50

s

b

p

e iec

es

50

es

es

s

s

e iec

50

1

Complete the combinations of money for RM70 362. Value of money RM100 RM50 RM20 RM10 RM5 Combination 1 700 Combination 2 600600

118

10.1 (i)

Carry out simulation activities using play money. TEACHER’S " NOTES

RM1

Round off values of money 1

How much is our food?

a

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



RM30.20



RM30

RM30.50



RM31



RM30.20 is close to RM30. RM30.20 rounded off to the nearest ringgit is RM30 . b Round off RM30.95 to the nearest ringgit. RM30.95 RM30



RM30.50



RM31

RM30.95 is close to RM31. RM30.95 rounded off to the nearest ringgit is RM31 . What is the value of RM30.50 when rounded off to the nearest ringgit?

10.2 (i)

Encourage pupils to relate the usage of rounding off in daily situations. TEACHER’S " NOTES

119

2 State five values of money when rounded off to the nearest ringgit become RM600. RM600.49

-----

-------

RM 600 RM599.50

RM600.05 RM599.80 RM599.95

RM600.50

RM600.45

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

1

Complete the table.

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

2 State three values of money when rounded off to the nearest ringgit become: a RM1 692 b RM72 100 c RM93 995

120

10.2 (i)

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

Addition of money 1

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

RM7 430

RM410.90

RM7 430 + RM6 135 = RM 7 4 3 0 + RM 6 1 3 5 RM 13 5 6 5



RM6 135

Adding money is the same as adding whole numbers.

RM7 430 + RM6 135 = RM13 565 The total cost of a computer set and a broadcasting set is RM13 565.

b What is the total cost of all the items above? RM7 430 + RM6 135 + RM410.90 = RM 7 4 3 0 + RM 6 1 3 5 RM 1 3 5 6 5



R

10.3 (i)

RM 1 3 5 6 5 . 0 0 4 1 0.90 + RM RM 1 3 9 7 5 . 9 0

Align the dots that separate the ringgit and the sen.

INFORMATION

RM7 430 + RM6 135 + RM410.90 = RM13 975.90 The total cost of all the items is RM13 975.90.

TEACHER’S " Carry out addition operations using sales brochures, price tags and picture cards. NOTES

121

2

RM517.85 + RM6 809.50 + RM21 043.20 = 1

RM RM 6 + RM 2 1 RM 2 8

2 1

51 7 .8 5 8 0 9. 5 0 043.2 0 370.5 5

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

3 RM32 451 +

+ RM23 041. 30 = RM89 793 .95 Simplify the case 3+ +2=8 5+ =8 =8–5

RM 3 2 4 5 1 . 0 0 + RM 2 3 0 4 1 . 3 0 RM 5 5 4 9 2. 3 0 RM55 492.30 +

= RM89 793.95 = RM89 793.95 – RM55 492.30 RM 8 9 7 9 3 . 9 5 – RM 5 5 4 9 2 . 3 0 RM 3 4 3 0 1 . 6 5

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 000 122

10.3 (i)

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

Subtraction of money 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

RM38 715 – RM11 400 = RM 3 8 7 1 5 – RM 1 1 4 0 0 RM 2 7 3 1 5

RM11 400

RM38 715 – RM11 400 = RM27 315 The difference of the cost for the two sets is RM27 315. 2

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

Yama

RM88 400

Wasaki

RM87 350

RM100 000 – RM88 400 = 9 9 10 10

RM 1 0 0 0 0 0 – RM 8 8 4 0 0 RM 1 1 6 0 0 RM100 000 – RM88 400 = RM11 600

RM100 000 – RM87 350 = 9 9 9 10 10 10

RM 1 0 0 0 0 0 – RM 8 7 3 5 0 RM 1 2 6 5 0 RM100 000 – RM87 350 = RM12 650

I will choose Wasaki motorcycle so that the balance in my saving is more than RM12 000. 10.4 (i)

Use business or sale catalogues to compare prices. TEACHER’S " NOTES

123

3



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

Withdrawal (RM)

Balance (RM)

16/02/2014

600

18 754.17

27/03/2014

1 500

02/05/2014

2 400

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 = RM 1 8 7 5 4 . 1 7 – RM 1 5 0 0 . 0 0 RM 1 7 2 5 4 . 1 7

6 12

RM 1 7 2 5 4 . 1 7 – RM 2 4 0 0 . 0 0 RM 1 4 8 5 4 . 1 7

RM18 754.17 – RM1 500 – RM2 400 = RM14 854.17 The balance in Miss Sim’s account on 2nd May 2014 is RM14 854.17. 4 RM39 257 – 8 12

= RM16 304.12 6

100

RM 3 9 2 5 7 . 0 0 – RM 1 6 3 0 4 . 1 2 RM 2 2 9 5 2 . 8 8 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? 124

10.4 (i)

TEACHER’S " Emphasise on identifying the key words which mean subtraction in questions such as balance, difference and compare. NOTES

Addition and subtraction of money



Hasnah made a record of income and expenditure of her layered 1 cake business in June. Income

(RM)

Money in bank

Expenditure

68 047.35 Cake ingredients bought 3 470.00

Layered cakes sold

9 500.00



Calculate the balance.



RM68 047.35 + RM9 500 – RM3 470 = 1

RM 6 8 0 4 7 . 3 5 + RM 9 5 0 0 . 0 0 RM 7 7 5 4 7 . 3 5

(RM)

Find other ways to get the answer.

4 14

RM 7 7 5 4 7 . 3 5 – RM 3 4 7 0 . 0 0 RM 7 4 0 7 7 . 3 5

RM68 047.35 + RM9 500 – RM3 470 = RM74 077.35 The balance is RM74 077.35.

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



Savings

Donation to Lahad Datu victims

Business profit

Balance of saving account

RM80 000

RM12 500

RM23 864

?

RM80 000 – RM12 500 + RM23 864 = 9 7 10 10

RM 8 0 0 0 0 – RM 1 2 5 0 0 RM 6 7 5 0 0

1 1

RM 6 7 5 0 0 + RM 2 3 86 4 RM 9 1 3 6 4

RM80 000 – RM12 500 + RM23 864 = RM91 364 The balance in Encik Akid’s savings account is RM91 364. 10.5 (i)

TEACHER’S " Encourage pupils to plan and record their expenditure. NOTES

125

3

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 8 13

RM 5 0 8 9 3 . 5 5 + RM 1 6 0 0 0 . 0 0 RM 6 6 8 9 3 . 5 5

RM 6 6 8 9 3 . 5 5 – RM 4 5 7 1 4 . 1 0 RM 2 1 1 7 9 . 4 5

RM50 893.55 – RM21 179.45 + RM16 000 = RM45 714.10 The cost of repairing Encik Kamal’s house is RM21 179.45.

1

Calculate.



a

RM63 750 + RM2 840 – RM30 128 =



b

RM76 835.40 – RM21 096.55 + RM38 415.75 =



c

RM63 502.70 +



d

– RM52 321.15 = RM22 066.55

– 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?

126

10.5 (i)

TEACHER’S NOTES



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

Multiplication of money Harmony Company Sdn. Bhd ( MA109877)



No. Description 1 2 3

Encyclopedia Sports shoes Jersey



No. 3343 Date : 11.5.2014

Quantity Price per unit (RM) 62 100 1 000

Total (RM)

174.50 218.90 12.60 Total

a Calculate the total payment for encyclopedias.

62 × RM174.50 = RM ×

1 74.50 62 349 00 + 10 470 00 RM1 0 8 1 9 . 0 0

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. Calculate the total cost of jerseys.

10.6 (i)

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

127

Given

x 3 = RM2 520



x

= RM25 200

Find the value of

and

1 Multiply. b 12 × RM880 = a 3 × RM9 143 = 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 8 bicycles.

RM14 210 3

b What is the cost for 27 cupboards?

RM658 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. Item Quantity Price per unit (RM) Skate board 95 117 Skating shoes 34 143.90 128

10.6 (i)

Total cost (RM)

.

Division of money 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 – 40 50 – 48 20 – 16 40 – 40 0

Innovation Champion 2014 RINGGIT MALAYSIA FORTY-FIVE THOUSAND RM45 000

How much will each pupil get if there are 10 pupils in a group?

RM45 000 ÷ 8 = RM5 625 Each pupil received RM5 625.

2

Based on the situation shown, calculate the donation received by each orphan on Hari Raya celebration gathering.



RM30 000 ÷ 50 =



The donation of RM30 000 is for 50 orphans.

6 00

RM 30 000 = RM600 50 1



RM30 000 ÷ 50 = RM600 Each orphan receives RM600.

10.7 (i)

TEACHER’S " Remind pupils to put the dot separating the ringgit and sen correctly when dividing money involving ringgit and sen. NOTES

129

3 RM74 580 ÷ 100 = RM74 5 8 0. ÷ 100 = RM745.80 RM74 580 ÷ 100 = RM745. 80

4

÷ 1 000 = RM96 RM 9 6 × 1 000 RM 9 6 0 0 0



RM96 000 ÷ 1 000 = RM96

1

Divide. a RM10 347 ÷ 6 = c RM52 710 ÷ 42 = e RM81 700 ÷ = RM817

The inverse of division is multiplication.

b RM74 129.60 ÷ 8 = d RM30 708 ÷ 60 = f ÷ 1 000 = RM92

2 6 siblings share an amount of money equally to buy a car for their mother. How much money must each person pay? RM 42 900 3

130

Calculate the price of each unit. Quantity Price per unit (RM) Total Cost (RM) Item 30 37 227 Air conditioner 1 000 54 900 Iron

10.7 (i)

TEACHER’S " Show pupils the easy way to divide an amount of money by 100 and 1 000 . NOTES

Solve the problems 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 Profit in September RM16 381.60 Operation Addition

Total profit in August and September

August

RM14 270.35

September

RM16 381.60

Total

? Check

Solve

2 10

RM14 270.35 + RM16 381.60 = 1

1

RM1

4 2 7 0. 3 5 + RM16 38 1. 60 R M 30 6 5 1 . 9 5

5 15

RM 3 0 6 5 1 . 9 5 – RM 1 6 3 8 1 . 6 0 RM 1 4 2 7 0. 3 5

RM14 270.35 + RM16 381.60 = RM30 651.95 The total profit in August and September is RM30 651.95.

The profit made in October is RM12 843.10. What is the difference of profit between September and October?

10.8 (i)

῾drawing a diagram᾽ method or modelling to solve problems. " TEACHER’S Use NOTES

131

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. Asset Normal price Promotion price Given Terrace house Car



Find

RM98 750 RM64 300

RM88 640 RM59 020

The differences in prices for the house and the car.

Operation Subtraction Solve Difference in price: RM98 750 – RM88 640 = for the house RM 9 8 7 5 0 – RM 8 8 6 4 0 RM 1 0 1 1 0



DAMAI INDAH TERRACE HOUSE

RM98 750 – RM88 640 = RM10 110

Promotion Price RM88 640

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 5 14 2 10



RM 6 4 3 0 0 – RM 5 9 0 2 0 RM 5 2 8 0



RM64 300 – RM59 020 = RM5 280



Promotion Price RM55 020

The difference between the normal price and the promotion price for the car is RM5 280. How do you check the answer? Discuss.

132

10.8 (i)

TEACHER’S " Introduce various strategies to solve problems such as drawing pictures, finding patterns, trial and error and mantic reasoning. 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 Find Operation

Rental for 1 day is RM4 320 . Rental for 3 days . Multiply

Solve



Mark the key words.

RM4 320

RM4 320

RM4 320

First Day

Second Day

Third Day

3 × RM4 320 = RM 4 3 2 0 3 × RM 1 2 9 6 0

How to check the answer?





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 Find

Cost to open workshop is RM18 000, Monthly saving is RM600. Number of months to save money.

Operation Division

Solve

RM18 000 ÷ RM600 ×

Check

= RM600 = RM18 000

RM

600 30 × RM18 0 00

3 0

RM18 000 = 30 RM600 1

RM18 000 ÷ 30 = RM600

Kumar must save his money for 30 months.

10.8 (i)

TEACHER’S " Carry out group activities using story cards, for example tourism activity or picnic. NOTES

133

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 RM28 500

1 participant RM?

Solve

Check 4

1 900 × 1 5 19 500 + 19 000 28 5 0 0



RM 1 900 15 R M 2 8 5 0 0 – 1 5 1 35 – 1 35 00 – 0 00 – 0 0 RM28 500 ÷ 15 = RM1 900



The cost of each participant is RM1 900.



134

RM28 500 ÷ 15 =

10.8 (i)

TEACHER’S NOTES

http://www.flickr.com/photos/dylwalters/509076089/

Solve. a The picture shows the price of an electric oven and a water purifier. Find the total cost of both items.

RM896

RM1 734.90

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. Food and drinks

Hotel accomodation

Transport

RM200

RM587

RM100



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. TEACHER’S NOTES

135 135

Materials

Brochures from supermarkets, bookshops and shopping malls, expenditure record form. Name: .............................. Class: .............. Record of Expenditure

No.

Item

Quantity Price Per Unit

Total

Total Cost (RM)

RM1 000

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.

136 136

TEACHER’S NOTES



Recognise foreign currency ASEAN Countries

Brunei Cambodia Indonesia

Malaysia Myanmar Philippines Singapore Thailand Vietnam

Kip

en

im

ec

Sp

CHINA

MYANMAR

Kyat

en

cim

e Sp

LAOS

en

im

ec

Sp

Dong en

im

c pe

en

cim

e Sp

CAMBODIA en

Peso

S

THAILAND

Baht

Laos

VIETNAM

PHILIPPINES

Riel

cim

e Sp

en

cim

Dollar

e Sp en

cim

Ringgit

MALAYSIA

e Sp

BRUNEI

SINGAPORE

en

Rupiah

en

im

ec

Sp

Dollar

im ec

Sp

INDONESIA

TEACHER’S Peta menunjukkan negara-negara ASEAN. random andAnggota describe their characteristics using flash cards.

" Carry out an activity on guessing the names of ASEAN countries currencies at

10.9 (i)

NOTES



ASEAN: The Association of Southeast Asian Nations.

137

United States of America

Great Britain

en

cim

en

e

en

im

ec

e Sp

cim

Sp

Canada Sp

Dollar

Dollar

Pound

Australia These are some of the currencies we should know.

en

im

ec

Sp

Dollar

Switzerland

en

im

ec

Sp



Yen



Hong Kong

en

im

ec

Sp

en

im

ec

Sp

Swiss Franc

China



Dollar



Korea

en

im

ec

Sp



Which country uses Euro?



India

Won

Bangladesh

en

Nigeria en

en

cim

cim

cim

e Sp

e Sp

e Sp

Rupee 10.9 (i)

en

im

ec

Sp

Renminbi

138

Japan

Taka



Naira

TEACHER’S " Carry out an activity to make scrapbooks of the currencies ASEAN countries and world leading nations. NOTES http://www.jepbanknotes.com/index.

Copy the word maze. Answer the questions and colour the answers. 1 The currency used in buying and 5 The Phillipines is famous for selling in Singapore is . her . 2 Indonesia’s currency is

.

3 Kyat is the currency used in 4 Chinese Athletes uses their country.

6 What is Cambodia’s currency? .

7 Malaysian northern neighbour uses .

in

8 This ASEAN country uses the same currency as Singapore.

N

R

E

N

M

I

N

B

I

Z

M

X

K

C

E

T

D

W

H

P

T

Y

N

I

U

H

P

Q

O

E

A

P

A

G

E

B

Y

G

D

S

L

G

I

N

O

N

D

E

B

O

C

R

L

H

M

R

U

P

I

A

H

J

K

J

A

A

W

R

R

X

M

K

H

L

E

I

R

N

B

A

H

T

O

Z

W

R

Y

M

Complete the table below. Countries

Laos

Currency

10.9 (i)

TEACHER’S NOTES

Dong

Brunei Swiss Franc

India Yen

Taka

139

The value of foreign currency Country

The value of foreign currency compared to RM1

Singapore Thailand Brunei Philipines Indonesia Vietnam Laos Cambodia Myanmar United States Great Britain China Japan Korea Saudi Arabia Bangladesh Nigeria

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

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?

140

10.9 (ii)

TEACHER’S NOTES



http://www.coinmill.com/MYR_calculator.

Payment instruments Methods of payment I pay RM20 for 2 tickets. The total payment is RM107.45.

Cash Money

Pay bills

Charge the cost of shoes from my debit card.

en

im

ec

Sp

Buy tickets

Father pays with debit card. They pay with cash.

SHOES

Buy shoes

Debit Card

Pay for petrol

Is payment by cash suitable for a big expenditure? Discuss.

10.10 (i)

TEACHER’S " Discuss the usage and safety of card as an instrument of payment. NOTES Pupils use their creativity to create payment card with safety features.

141

RM60

Ride a monorail

Prepaid Card

Pay tolls

Sir, please sign here to endorse the payment.

Credit Card

Talk about each activity in the picture.

Bank Kita

Please accept our donation for the land slide victims. 2 4 1 0 1 4 Yayasan Budiman

Bank Kita

RM40 000

ONLY E YE PA

Cheque Donation

BANK KITA BERHAD

Forty thousand only

AC BAYAR/ PAY

STAMP DUTY PAID

Tarikh Date

D

JANGAN TANDA TANGAN DI BAWAH GARISAN/NO SIGNATURE BELOW THIS LINE

AC NO.

Write a suitable situation for the usage of these payment instruments. Payment instrument Cash money Debit card Prepaid card Credit card Cheque 142

10.10 (i)

Situation 1

Situation 2

Buy fish at the market

Pay taxi fare

M

ATAU PEMBAWA/OR BEARER

RINGGIT MALAYSIA

CHEQUE NO.

D

TEACHER’S " Carry out activities to create a suitable payment instrument based on NOTES pupils’ creativity.

M

Y

Y

1 Total up the value of money.

en

ecim

Sp

en

ecim

Sp

RM10 000

RM10 000

RM10 000 en

en

ecim

Sp

en

ecim

ecim

Sp

Sp

RM150

RM6

RM1 000

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. TEACHER’S NOTES

Bil Total Electric RM75.20 Water RM21.80 Telephone RM84.70

RM715.90

RM1 243.75

143

7 State the currency and country for the following notes. a

d

b

en

im

ec

Sp

e

en

im

ec

Sp

en

im

ec

Sp

c

en

cim

e Sp

en

im

ec

Sp

f

en

im

ec

Sp

8 Name the country that uses the following currencies. a Pound Sterling

b Won

c Renminbi

d Naira

e Rupiah

f

Riel

g Baht

h Kyat

i

Peso

9 Which payment instrument is suitable to use for each situation?

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.

144 144

TEACHER’S NOTES

Payment instrument

11

School

TIME Recognise time Day and hour

The earth rotates on its axis in 1 day.

1

Sundial

Water Clock

Analogue Clock

Hourglass

Yes, the complete rotation takes 24 hours.

Ancient people used various instruments to determine the time.

1 day = 24 hours

----

----

Day and night

----------

----

----

Day

----

  

----

Sun rays

----

----

----



Night

Direction of rotation

2 days is equal to how many hours?

2 days =

hours

2 days = 24 hours + 24 hours = 48 hours 2 days = 48 hours

----

Axis

11.1 (i) a

TEACHER’S " Infuse the elements of EMK in exploring the history of time. NOTES http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/time/ index.htm.

145

2

In a year, the Rafflesia blooms for 3 to 5 days only. State 3 days in hours.



3 days =

hours

24 hours 24 hours 24 hours 0



1

2

3

1

24 hours × 3 72 hours How many hours in 5 days?

3 days = 72 hours

3 96 hours = 96 ÷ 24 =

days days x 24



4 24 96 – 9 6 0

day

hour ÷ 24



INFORMATION

96 hours = 4 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

146

11.1 (i) a

• Convert 6 days to hours. 6 × 24 hours = 144 hours

How many days and hours in 100 hours? Explain.

Relate days and hours based on the situation given. TEACHER’S " NOTES

Week and day 1 The Patriotic Month is celebrated for 4 weeks. How many days are there in 4 weeks? 31

4 weeks =

days

4 × 7 days =

days

Remember the 7 times table.

4 × 7 = 28

National Day

4 weeks = 28 days There are 28 days in 4 weeks. 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 =

×7



5 7 41 – 35 6



week



day ÷7

INFORMATION

5

weeks

6

days

They were in the village for 5 weeks 6 days.

In the life cycle process of a butterfly,

10 days to transform into



takes about

. State the time in

weeks and days. Source: http://www.butterfly-insect.com/diy.book.php

11.1 (i) b

Relate weeks and days based on the life cycle of insects such as the cockroach, the TEACHER’S " fly and others. NOTES http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/time/ index.htm

147

Year and month Father 45 years 6 months

1 Study Kak Ngah’s family chart. How old is Usu in months? 5 years =

months

12 × 5 60



Kak Long 15 years 7 months

5 years =

60 months

2 187 months = 15 12 1 8 7

Kak Ngah 10 years 5 months

Abang Chik 8 years 3 months

years

months

– 12 67 – 60 7

× 12



year

185 months =

15

years

Usu 5 years

Whose age is the same as 504 months? Explain.

Usu’s age in months is 60 months.



Mother 42 years

7

months

month ÷ 12

INFORMATION

Time taken by planets to make one

complete rotation around the sun. Jupiter 12 years Uranus 7 times the time taken by Jupiter State the time, in months, taken by Uranus.



Source: http://www.thestar.com.my./20130401/world/ploto-is-a- planet-again.asp



148

11.1 (i) c

TEACHER’S " Emphasise that leap year and normal year have the same number of months, but different number of days. NOTES " Guide pupils to identify the leap years.

http://www.sheppardsoftware.com/mathgames/time/TimeConversions.htm

Players 4 persons Steps 1 2 3 4 5 6

Materials

21 pieces of time cards (10 pairs of cards, 1 piece of stork card)

Distribute 21 pieces of cards to all players. Determine the players turn. The player with the most cards gets the first turn. Pull out a card from each player according to turns. If there are matching cards, the 2 cards are taken out. Repeat steps 3 to 4 until all matching cards are taken out. The player who gets the stork card wins the game.

1 Convert. a 9 days = hours c 37 hours = days hours e 2 weeks 4 days = days g 10 years 3 months = months i How many hours in 7 days?

2 3

b d f h j

3

4

8 days 5 hours = hours 6 weeks = days 84 days = weeks 9 years = months State 14 months in years and months.

How many weeks and days are there in May 2014?

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.

11.1 (i) a,b,c

TEACHER’S " Prepare a few sets of time cards for enrichment activity. Game like “Happy Family” is encouraged. NOTES

149

Addition of time 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 = day 1 + 1 2

1 day 8 hours

1 day 9 hours

days

hours 2 days 16 hours

hour 9 8 1 7



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 =

day hour 2 1 9

1 + 2 4

150

8 16 33

hours

4 days = 4 x 24 hours = 96 hours

4 days 33 hours = 96 hours + 33 hours = 129 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.

11.2 (i) a

TEACHER’S " Use time line for addition operation. NOTES " Emphasise the conversion of units from hour to day.

2

Pulau Redang 4 weeks 2 days

Belum Rainforest 6 weeks 1 day

FRIM 1 week 5 days

The photography association shot films at the locations above. a Calculate the time taken for shooting films at Pulau Redang and Belum Rainforest. 4 weeks 2 days + 6 weeks 1 day = weeks days week day 4 + 6 1 0



2 1 3

4 weeks 2 days + 6 weeks 1 day = 10 weeks 3 The time taken for shooting films at Pulau Redang and Belum Rainforest is 10 weeks 3 days.

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



week

day

4 6 + 1 11

2 1 5 8

11 weeks 8 days – 7 + 1 12 weeks 1 day

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. State 2 locations which take 42 days for filming.

11.2 (i) b

" Emphasise the conversion of units from day to week. TEACHER’S " Encourage pupils to talk about their school activities in weeks and days like NOTES Reading Campaign and sports practice.

151

Service Record 3 Calculate the duration of service for Cikgu Sarah at the three schools based Name Duration on the service record. of school 4 years 9 months + 3 years SK Baiduri 4 years 9 months 8 months + 10 years 4 months SK Angkasa 3 years 8 months SK Aman 10 years 4 months = years months year 4 3 + 10 17

month 2

9 21 months ÷ 12 = 1 year 9 months 8 4 17 years 21 months = 17 years + 1 year + 9 months = 18 years 9 months 21

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. 152

11.2 (i) a, b, c

TEACHER’S " Diversify questions using a calendar. NOTES

Subtraction of time 4 days 17 hours

1

urs

s1



o 2h

3

y da

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 = day hour 4 – 3 1

days

hours

17 12 5



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.

days hours 2 5 days 5 hours – 2 days 9 hours – 14 hours = day hour day hour • 9 hours can be subtracted 4

29

1 10 from 5 hours. 2 2 0 5 5 • Convert 1 day to 24 hours. – 2 – 14 9 24 hours + 5 hours = 29 hours 2 6 2 20



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.

11.3 (i) a

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

153

3 What is the difference, in weeks and days to complete mural A and mural B?

Mural A 2 weeks 6 days

2 weeks 6 days – 1 week 5 days = weeks days week day 2 – 1 1

Mural B 1 week 5 days

6 5 1

2 weeks 6 days – 1 week 5 days = 1 week 1 day The difference in time to complete mural A and mural B is 1 week 1 day. Solve by changing the unit from week to day first. Is the answer the same?

4

19 weeks – 4 weeks 3 days – 6 days = week

day

18

1 9 – 4 14

7

0/ 3 4

week

day

13

11

1 4 – 1 3

19 weeks – 4 weeks 3 days – 6 days =



weeks

days

4/ 6 5 13

weeks

5

days



Assume 1 month = 4 weeks. Calculate the time difference in days for the growth of this chick. 3 weeks

154

11.3 (i) b

TEACHER’S " Do subtraction by counting down. NOTES

3 months

5

Find the difference of life span between the orang-utan and the panda. Give answer in months.

30 years 2 months

45 years 3 months



45 years 3 months – 30 years 2 months = months year month 4 5 3 15 years 1 month = 180 months + 1 month – 3 0 2 = 181 months 1 5 1



45 years 3 months – 30 years 2 months = 181 months The difference of life span is 181 months.

6 14 years 7 months – 8 months – 2 years 3 months = years months 11 16 1 2 years 4 months 1 4 years 7 months – 8 months – 2 years 3 months 1 1 years 8 months 1 2 years 4 months 14 years 7 months – 8 months – 2 years 3 months = 11 years 8 months

11

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 d 31 years – 12 years 8 months – 5 months = years 2

days months

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?

11.3 (i) c

TEACHER’S " Carry out activities to find difference in age amongst friends and relatives. NOTES

155

Multiplication of time This wood carving is done in 1 day 3 hours.

1 How much time, in days and hours, is taken by Raden to do 5 similar wood carvings? 5 × 1 day 3 hours = day

days

hours

hour

1 × 5

3 5 1 5

5 × 1 day 3 hours =

5

days 15

hours

Time taken to do 5 similar wood carvings is 5 days 15 hours.

Estimate the number of wood carvings that can be done in 11 days. Discuss.

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



1

1 8 days × 2 3 6 days 2 × 2 weeks 4 days =

36 days

The total time of the two courses is 36 days.

156

11.4 (i) a, b

2 weeks 4 days

TEACHER’S " Do multiplication using different suitable methods, like repeated addition. " Use schedules for school holidays and co-curriculum activities involving NOTES multiplication of time.

b

I attended the third course for the same duration.

Calculate the duration of

the three courses. State the

answer in weeks and days.

3 × 2 weeks 4 days =

weeks

2 weeks 4 days 3 × 6 12 + 1 – 7 7 weeks 5 days 3 × 2 weeks 4 days=

days

12 days = 7 days + 5 days = 1 week + 5 days 7

weeks

5

days

The duration of the three courses is 7 weeks 5 days.

3

4 × 10 years 7 months =

years

months

year month 10 7 4 × 4 0 28

40 years 28 months = 40 years + 24 months + 4 months = 40 years + 2 years + 4 months = 42 years + 4 months

4 × 10 years 7 months = 42 years

11.4 (i) b, c

TEACHER’S NOTES

4

months

" Guide pupils to build conversion of units chart.

157

Players

4 to 6 persons.

Materials

Pupil’s register book, question cards.

Steps 1 2 3 4

Teacher retrieves information about pupil’s age from the register book and give the data to pupils. Distribute question cards to each group. Pupils answer the questions in the allocated time. 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 2

Solve. a Multiply 6 by 4 days 8 hours. Give answer in days.



b 9 × 8 weeks 4 days =



158

s pupil air of ge of p a d a 1. Fin the total with rs. age a 21 ye ference in ths. if o d m n e 2. Th pupils is 3 onths m 2 4 f o ars 10 ye 3. 3 × __ years. = __

Multiply. a 7 × 8 days 2 hours = b 6 × 6 years 4 months = c 3 × 9 weeks 5 days = d 8 × 3 days 4 hours = e 4 × 5 weeks 3 days = f 5 × 4 years 7 months =

11.3 (i) c 11.4 (i) a,b, c

c

days years weeks hours days years

ard

tion C

Ques

hours days

months

days

Show the simplest method. Calculate the product for 8 and 10 years 9 months. TEACHER’S " Relate multiplication of time in everyday life. " Inculcate moral values such as valueing time during group activity. NOTES

Division of time 1 a

Duration of completion

Based on the table, how long does it take to complete a 3 units Single-storey 6 days 15 hours model of a single-storey 4 units Double-storey 9 days 4 hours house? 6 days 15 hours ÷ 3 = days hours



2 days

5 hours



3 6 days

1 5 hours



Quantity Type of house

–6

– 15

0

0

6 days 15 hours ÷ 3 =

Welcome

2

days

5

hours

The time taken to complete the model of a single-storey house is 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 + 24 2 days 7 hours = 24 hours + 24 hours + 7 hours 1 2 8 = 48 hours + 7 hours – 28 = 55 hours 0 9 days 4 hours ÷ 4 = 55 hours The time taken to complete a model of a double-storey house is 55 hours.



5 workers can paint a house in 10 hours. Can a worker paint the house in 2 hours? Discuss.

11.5 (i) a

TEACHER’S " Guide pupils to divide units of time by subtracting consecutively. NOTES

159

2 14 weeks 4 days ÷ 6 =



weeks

days

2 weeks 3 days 6 1 4 weeks 4 days – 12 + 14 2 18 – 18 0

14 weeks 4 days ÷ 6 =

3 12 years ÷ 9 =

2

Convert the remainder 2 weeks to 14 days.

weeks

3

days

months

1 year 4 months 9 1 2 years 0 months + 36 – 9 3 36 1 year 4 months = 12 months + 4 months – 36 = 16 months 0

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

e 20 weeks 4 days ÷ 6 = f 45 days 12 hours ÷ 7 =

weeks days

22 days 7 hours days hours

2 Divide 30 years 9 months by 9. Give answer in months.

160

11.5 (i) b, c

TEACHER’S " Expose various calculation and conversion of units strategies to pupils. NOTES

Solve the problems 1

The table below shows the duration of operation times for two multipurpose shops. Find the difference in time the two shops operate.



Multipurpose shop Era Kota

Duration of operation Whole day 8 hours

Given

Duration of operation of Era is whole day or 1 day. Duration of operation of Kota is 8 hours.



Difference in time

Find

Operation Subtraction Solve

1 day – 8 hours = hours 1 day = 24 hours 24 hours – 8 hours =

hours

1 14



2 4 hours – 8 hours 1 6 hours

Check

16 hours + 8 hours = 24 hours

kedua-dua

1 day – 8 hours = 16 hours



Beza masa

The difference in time the two shops operate is 16 hours. If another multipurpose shop operates 2 hours more than Kota, calculate the duration the shop operates.

11.6 (i)

TEACHER’S " Solve daily problems by drawing diagrams or making tables. NOTES

161

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. 1 week 4 days

1 week 4 days

1 week 4 days

Total

3 × 1 week 4 days =

weeks

days Check.



1 week

4 days 1 week 4 days = 11 days × 3 4 1 1 days 3 12 7 33 × 3 + 1 – 7 – 28 3 3 days 4 weeks 5 days 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

2 years 3 months 4 9 years 0 months –8 +12 1 12 –12 0

162

months 9 years Phase 1 Phase 2 Phase 3 Phase 4 ? How do you check the answer? Explain.

9 years ÷ 4 = 2 years 3 months The time taken to complete one phase is 2 years 3 months.

11.6 (i)

TEACHER’S " Underline the key information before solving the problem. NOTES

A

Solve. a How much time boat A sails more than boat B as given in the information?

B 2 days 9 hours 1 day 3 hours

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.

Project History Science English

Duration 10 hours 9 hours 7 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 The poster shows the sale of children᾽s GRAND PROMOTION CHILDREN’S CLOTHINGS clothings. The sale is held for 1 week 2 days. 18 July – 26 July 2014 The promotion is extended for 9 more days Bukit Jalil Stadium because of good response. Calculate the time, in weeks and days, the promotion is held.

TEACHER’S NOTES

163 163

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 16 weeks = days

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.

164 164

TEACHER’S NOTES



12

School

LENGTH Recognise units of length 1

The length of the pencil lead is 75 millimetres. pencil lead 24

0.5 mm 5 mm

75 mm Long

Millimetre is used to state the length of small and short objects. The symbol is mm.

2

The distance from Merdeka Square to Petronas Twin Towers KLCC is 3.5 kilometres. Kilometre is used to state the distance between two places. The symbol is km. What unit will you use to state: (i) the thickness of a textbook? (ii) the distance between Kota Bharu, Kelantan and Kangar, Perlis? Explain.

12.1 (i) a, b

TEACHER’S NOTES

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.

165

Relationship between centimetres and millimetres 1 cm

The length of the blue line is 1 cm or 10 mm.

0

cm

1

2

3

4

5

× 10 cm

0

mm

10

10 mm

20

30

40

50

1 cm = 10 mm

mm ÷ 10

INFORMATION

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 mm 4 83 mm = cm mm 3 3 cm 7 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

Is 120 mm longer than 19 cm? Discuss.

Complete the following. a 152 mm = cm 2 mm c 4 cm mm = 49 mm e cm 9 mm = 909 mm

166

12.1 (ii) a

TEACHER’S NOTES



b 631 mm = 63 cm d 71 mm = cm f 34 mm = 3 cm

mm mm mm

http://www.ixl.com.math/grade-3/compare-and-convert-metric-units-of-length

Relationship between kilometres and metres Saiful will run 100 m back and forth 5 times for training today.

0 metre

× 1 000 So, Saiful will run a distance of 1 000 m. This distance is equal to 1 km.

km

m

÷ 1 000

100 metres

INFORMATION

1 km = 1 000 m 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 m 4 25 300 m = km m 3 71 km 900 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 5 km 25 m equals to 5 250 m. Explain.

Complete the following. a 12 km = c 3 km = e 8 km 12.1 (ii) b

m m m = 8 407 m

TEACHER’S NOTES

b 78 000 m = km d 90 km = m f 50 km m = 50 021 m

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

167

good luck

Measure length of objects 30 mm Start measuring from 0 mm. Read the measurement at the other end.

ERASER

The length of the eraser is 30 mm.

DICTIONARY

The thickness of the dictionary is

. The width of the bookmark is

.

Y

X

Z

mm

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

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

(ii) (i)

mm

168

12.2 (i)

TEACHER’S NOTES

i

mm

ii

mm

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/

Estimate distance The estimated distance from jetty to chalet is about 1 km.

Chalet

Jetty

1 km

Health Centre

Jetty

X

Robotic Museum

Amusements Centre

1 What is the estimated distance from the chalet to the health centre? 1 km Chalet Jetty Chalet

The estimated distance is 2 times more than 1 km.

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 X . The health centre is located almost 4 km from X.

3 What is the estimated distance from the jetty to the amusement centre? Jetty

Estimated distance = 5 km

Chalet 1 km

Amusement centre 5 km

The estimated distance from the jetty to the amusement centre is about 5 km . A digital library will be built within 3 km from the jetty. Where is the suitable location? Explain.

12.2 (ii)

TEACHER’S NOTES

Create more questions on estimation of distances based on the above map. Discuss the importance of estimation in daily life.

169

X A

A

Route

B

C

Estimated distance (km)

B m

C 1k

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.

Use thread to measure the curved route. Compare with the given estimated distance of 1 km.

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. Library

Library Nelly’s House

1k Bus Station

School

m Bus Station Internet Centre

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. 170

12.2 (ii)

TEACHER’S NOTES

Guide pupils to determine the estimated distances between two places based on a given reference.

Addition of length

After 3 days

1 Based on the picture, what is the height of the seedling after 3 days? 5 mm + 2 cm 3 mm =

cm + 2 2

5 mm

cm

mm

Increased by 2 cm 3 mm

mm 5 3 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





32 + 40

cm

mm

mm 5 9 14

Convert 14 mm to 1 cm 4 mm.



cm

mm

1



32 + 40 73

5 9 4

32 cm 5 mm + 40 cm 9 mm = 73 cm 4 mm 12.3 (i) a

TEACHER’S NOTES

http://www.k5learning.com/free-math-worksheets/fourth-grade-4/measurement

171

3 Calculate, in mm the total length of the ropes P, Q and R below. P 18 cm 2 mm Q 16 cm 5 mm R 17 cm 8 mm

18 cm 2 mm + 16 cm 5 mm + 17 cm 8 mm =

cm

mm



18 16 + 17



cm

mm

mm

2 1

2 5 8 1 5

18 16 + 17 52

2 5 8 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

Day First Second

Distance of cycle 76 km 433 m 10 km 662 m

Calculate the total distance in the cycling competition for the two days. 76 km 433 m + 10 km 662 m =

km

m

km

km

m

m

1



76 + 10

433 662 1 095

76 433 + 1 0 662 87 095

76 km 433 m + 10 km 662 m = 87 km 95 m 172

The total distance in the cycling competition is 87 km 95 m. 12.3 (i) a, b

TEACHER’S NOTES

Drill pupils on conversion of units using flash cards.

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 = km

m

km

m



8 20 + 5



34 km 155 m = 34 000 m + 155 m = 34 155 m

1

2 4 0 790 125 1 155

1 1

8 20 + 5 34

m

1

240 790 1 25 1 5 5



8 km 240 m + 20 km 790 m + 5 km 125 m = 34 155 m

1 Calculate. a cm mm b km m 34 7 1 4 261 + 22 9 + 82 972

c

cm 51 10 + 41

mm 8 3 7

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

d

km m 3 128 1 1 492 + 7 1 01

m

R

m

3 Solve. a What is the total length, in cm and mm, when 125 mm is added to 40 cm 8 mm? 72 P 00 b The distance from Q to R is 642 m more than the distance from P to Q. Q What is the distance, in km and m, from P to R? 12.3 (i) b

TEACHER’S NOTES

Drill conversion of units using flash cards.

173

Subtraction of length 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 3 cm 2 mm 5 cm 6 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 = Method 1 cm mm cm mm 2 7 16 28 6 27 8 – 8 – 13 5 2 7 8 14 3 14 cm 3 mm = 140 mm + 3 mm = 143 mm

mm

Method 2 7 16

2 8 6 mm – 8 mm 2 7 8 mm

2 7 8 mm – 1 3 5 mm 1 4 3 mm

28 cm 6 mm – 8 mm – 13 cm 5 mm = 143 mm Which method would you choose? Why?

3 78 km 607 m – 23 km 179 m = km m



km

m

9 5 10 17

78 607 – 23 1 79 5 5 4 2 8

78 km 607 m – 23 km 179 m = 55 km 428 m 174

12.4 (i) a, b

TEACHER’S NOTES

Encourage pupils to check the answers using addition.

4 12 km 742 m – 145 m – 3 km 415 m = km m km m



13 6 3 12

12

7 4 2 – 1 4 5 1 2 5 9 7



m

9 km 182 m = 9 000 m + 182 m = 9 182 m

12 597 – 3 415 9 182

12 km 742 m – 145 m – 3 km 415 m = 9 182 m

5

32 km 720 m 15 km 785 m

8 km 950 m A

C

B

D

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 2 11 3 1

m 1612 17 2 0

km

m

2 2

16 16 10 17 7 0

m

Convert 1 km to 1 000 m.

3 2 7 2 0 23 770 – 8 9 5 0 – 1 5 785 23 770 7 985 32 km 720 m – 8 km 950 m – 15 km 785 m =

km

7 km 985 m

The distance from C to D is 7 km 985 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?

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 12.4 (i) b

TEACHER’S NOTES

http://www.bbc. uk/bitesize/ks2/maths/shape_space/measures/read/2/

175

Multiplication of length Ribbon Pink White

1

Length 32 cm 2 mm 61 cm 5 mm

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 32 2 × 3 9 6 6



cm

mm

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 61 5 61 5 × 8 × 8 4 8 8 4 0 488 40 + 4 – 4 0 4 × 10 mm 488 cm 40 mm = 488 cm + 4 cm 492 0 = 492 cm 8 × 61 cm 5 mm = 492 cm The total length of ribbon, in cm, for 8 white bows is 492 cm.

176

12.5 (i) a

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.

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

km

m

km



m m

2

5 6 0 2 × 4 2 4 0 8

5 602 × 4 22 408

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 278m = 8 278 m × 6 4 9 6 6 8 m 6 × 8 km 278 m = 49 668 m Multiply first. Then, convert km to m. Is this method easier?

Solve. a

2 × 9 cm 3 mm =

cm

c

5 × 18 cm 2 mm =

e g

3 × 4 km 118 m =

cm m

mm

b

mm d f

6 × 36 cm 4 mm = 8 × 61 km 24 m = 7 × 35 km 302 m =

mm km km

m m

Multiply 8 by 2 108 m. Give answer in km and m.

12.5 (i) b

TEACHER’S NOTES

Drill multiplication using flash cards and check the answers using calculator.

177

Division of length 1 What is the length of one part of the wood? 72 cm 9 mm ÷ 3 = cm mm 2 4 cm 3 mm A wood which is 72 cm 9 mm 3 ) 7 2 cm 9 mm long is cut into 3 equal parts. – 6 – 9 1 2 0 – 12 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 – 54 + 5 0 = 66 mm 5 54 – 54 First, convert 59 cm 4 mm to mm. Then, divide by 9. 0 Is this method easier? 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 – 49 – 7 0 02 – 0 21 – 21 0 49 km 721 m ÷ 7 = 7 km 103 m The distance taken by Jane in a day is 7 km 103 m. 178

12.6 (i) a, b

TEACHER’S NOTES

Remind pupils to give answers in the required units.



MURNI

PETROL STATION

4

SEJAHTERA SUPERMARKET MeGA SUPERMRKET

79 km 464 m

km Murni Petrol Station is located 79 km 464 m ÷ 2 = between Sejahtera Supermarket 3 9 km 732m and Mega Supermarket. 2 ) 7 9 km 464m What is the distance from Murni – 6 + 1 000 Petrol Station to Mega Supermarket? 19 1464 – 18 – 14 1 06 79 km 464 m ÷ 2 – 6 = km m 04 – 4 How do you solve this problem 0 to give the answer in m?



m

79 km 464 m ÷ 2 = 39 km 732 m

The distance from Murni Petrol Station to Mega Supermarket is 39 km 732 m.

60 km 600 m

The distance from P to R is 60 km 600 m. The P Q 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 = c 62 cm 5 mm ÷ 5 = e 79 km 200 m ÷ 6 = 12.6 (i) b

TEACHER’S NOTES

cm mm km

mm m

b 9 cm 2 mm ÷ 4 = d 21 km 819 m ÷ 7 = f 5 km 715 m ÷ 3 =

R

cm km m

mm m

Prepare question cards for division and carry out a quiz activity in groups.

179

Solve the problems 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

Draw a diagram.

Addition



15 cm 2 mm

23 cm 5 mm

13 cm 8 mm

Total length

Solve

15 cm 2 mm + 23 cm 5 mm + 13 cm 8 mm =

cm mm 1 1 15 2 23 5 + 1 3 8 52 5 Check

cm

mm

5 1

15



5 8 7



52 –13 3 8

52 cm 5 mm = 520 mm + 5 mm = 525 mm

cm 38 – 23 15

mm 7 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.

180

12.7 (i)

TEACHER’S NOTES

Guide pupils to solve problems using tables.

mm

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.



The remaining journey in km and m.

Find

Operation Subtraction Total distance : 47 km 850 m

998 m

Remaining distance

35 km 810 m

Meeting venue

Solve

47 km 850 m – 998 m – 35 km 810 m =



km

m



4 6

17 14 10 18 5 0





47 –



4 6

8 5 0 9 9 8 8 5 2

km 46 – 35 1 1

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

km

m

m 852 810 42 Estimate the answer to the nearest 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. 12.7 (i)

TEACHER’S NOTES

Guide pupils to underline information or keywords based on the given problem and solve it with various strategies.

181

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 60 cm 3 mm 60 cm 3 mm 60 cm 3 mm 60 cm 3 mm 60 cm 3 mm 60 cm 3 mm

Solve

cm 60 × 360

6 × 60 cm 3 mm = mm 3 6 18

cm

mm

360 cm 18 mm = 360 cm + 10 mm + 8 mm = 360 cm + 1 cm + 8 mm = 361 cm 8 mm

Check

6 0 cm 3 mm 6 ) 3 6 1 cm 8 mm – 3 6 + 10 0 1 18 – 0 – 18 1 0

Check your answer by dividing it.

6 × 60 cm 3 mm = 361 cm

8 mm

The length of string needed to tie all the parcels is 361 cm 8 mm.

182

12.7 (i)

TEACHER’S NOTES

Guide pupils to solve problems by simulation using real objects.

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 Find

The distance is 10 km 500 m. There are 4 runners. The distance, in m, by each runner.

Operation Division

Runner 1

Runner 2

Runner 3

Runner 4

10 km 500 m

Solve

10 km 500 m ÷ 4 =

m

2 km 625m 4 ) 1 0 km 500m – 8 +2000 2 km 625 m = 2 000 m + 625 m 2 2500 = 2 625 m – 2 4 10 – 8 20 – 2 0 0 Check km m Check by multiplying 2 1 2 2 km 625 m by 4. 2 625 × 4 10 500 10 km 500 m ÷ 4 = 2 625 m The distance of each runner is 2 625 m. 12.7 (i)

TEACHER’S NOTES

Ensure that pupils check the answers and explain the importance of checking them.

183

Solve.

c

12 km 18 m

Office

Music Class

41

30

m

m

m

m

m

7m

b

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? 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. 7c m

a

Mr Singam’s House



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. Distance from Taman Kenanga Place 10 km 217 m Taman Setia ? Taman Anggerik

f

184 184

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? 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? TEACHER’S NOTES

Materials

Ruler, pencil, pen and Players location map.

5 pupils in a group.



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. KESUMA JAYA TOWN PLAN Multipurpose Shop

X 1 km

X

X

Police Station

Community Hall

X Lake

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.

7.6 (i)

TEACHER’S NOTES

Make enough copies of the location map for each group.

185

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 c cm 5 mm = 85 mm

b d

2 576 m = km m 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 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 = d 3 × 12 cm 8 mm = cm mm e 7 × 6 km 404 m = m f 53 km 124 m ÷ 4 = km m

Z

mm

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

186 186

P Q The lengths of the lines X and Y 25 cm are less than the line PQ as X shown in the diagram. Calculate 80 mm the difference in length, in mm, Y 120 mm the lines X and Y. TEACHER’S NOTES

13

School

MASS Addition and subtraction of mass 1

Oh, uncle you have over weighed the beans! Can you make it 150 g lesser?

Azim, how many grams do you want to buy?

10 k

g



0 500 100 gram 400

1 kg

900 g

300

200

Crackers 2 kg



What is the total mass of the items bought?



2 kg + 400 g – 150 g =



kg

k g

g

k g

g

2

000 400 400

2

400 1 50 250

+ 2

– 2

g

3 10



2 kg + 400 g – 150 g =

2

kg 250 g



The total mass of the items bought is 2 kg 250 g. Add the two masses of dodol. What is the difference in mass between the dodol and the crackers bought?

13.1 (i)

1 kg

900 g

TEACHER’S " Add and subtract masses based on situations and simulation activities. " Explain that adding and subtracting units of masses is the same as adding NOTES and subtracting whole numbers.

187

2 10 kg 80 g – 3 kg 450 g + 2 kg 370 g = kg

9

g

450 g connot be subtracted from 80 g.

1 080

10 8 0 – 3 450 6 630

10 kg 80 g = 9 kg + 1 000 g + 80 g = 9 kg 1 080 g kg g 1

6 +2 9





kg

1

630 370 000

630 g + 370 g = 1 000 g = 1 kg

10 kg 80 g – 3 kg 450 g + 2 kg 370 g =

3 26 kg + 8 760 g – Convert 26 kg to 26 000 g.



kg 1

26 000 g + 8 760 g 34 760 g

9

kg

g = 4 815 g 13 2 3

17 5 10

34 760 g – 4 815 g 29 9 45 g

× 1 000 kg

g ÷ 1 000

INFORMATION

29 945 g = 29 kg 945 g 26 kg + 8 760 g – 29 kg 945 g = 4 815 g

1 kg 500 g

1 kg 50 g

1 kg 550 g

P Q R Determine the 2 packets of biscuits that should be mixed first. Then, reduce 100 g so that the mass becomes 2 500 g. 188

13.1 (i)

Pay attention on regrouping from g to kg. TEACHER’S " Emphasise on conversion for values more than 1 000 g. " NOTES

Materials Weighing scale, pebbles, exercise book. Players

4 pupils in each group.

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 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

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. 13.1 (i)

Diversify activities such as cross number puzzles, simulations and games to TEACHER’S " reinforce the concept of mixed operations. NOTES

189

Multiplication and division of mass 1

Hadi, please repack these 3 packs of crisps into 8 smaller packs. crisps



Based on the picture, what is the mass of crisps in 1 small pack? 3 × 1 200 g ÷ 8 = g 4 5 0 g 1 200g 8 3 600 g × 3 – 3 2 3 600g 4 0 – 40 00 – 0 0

4

50 kilogram 1 3

2

3 × 1 200 g ÷ 8 = 450 g The mass of crisps in 1 small pack is 450 g.

2

8 x 2 kg 500 g ÷ 4 =

kg kg g 2 500 × 2 4 1 000 + 1 – 1 000 5 0

2

8 × 2 kg 500 g

4 1



190

8 × 2 kg 500 g ÷ 4 =

13.1 (ii)

5

Why subtract 1 000 g and add 1 kg? Explain.

kg

TEACHER’S " Guide pupils to multiply and divide units of mass through simulation or based on given situation. NOTES

3

18 kg 945 g ÷ 9 × 2 =

g

2 kg 1 0 5 g 9 1 8 kg 9 4 5 g –18 –9 0 04 – 0 45 – 45 0

kg g 2 × 4

1

105 2 210

4 kg 210 g = 4 000 g + 210 g = 4 210 g

18 kg 945 g ÷ 9 × 2 = 4 210 g First, multiply 9 by 2. Then, divide 18 kg 945 g by the product. Is the answer the same?

4 31 kg ÷ 5 × 10 =

kg

Method 1

6 kg 200 g 5 3 1 kg 0 g –30 + 1 000 1 1000 – 10 00 – 0 00 – 0 0 2

Method 2 13.1 (ii)

31 kg × 10 = 31 kg × 2 5 = 62 kg 1

kg g 6 2 0 0 10 × 60 2000 60 kg 2 000 g = 60 kg + 2 kg = 62 kg

Which method do you choose? Why?

31 kg ÷ 5 × 10 = 62 kg TEACHER’S NOTES

" Expose various strategies involving multiplication and division to enhance pupils’ understanding.

191

200 g

4 kg

Each

has the same mass. What is the mass of

Players 4 to 6 pupils. Steps

, in g?

Materials Mass cards, symbol cards, number cards, envelopes.

1 Teacher prepares a few number cards, mass cards and symbol cards. Examples: 2 770 g – = 6 kg 550 g 10 kg 480 g + 6 kg 700 g (set 1) 2 3 4 5 6 7

8 350 g = 10 kg 20 g 6 ÷ × 5 (set 2) Keep 1 set of cards in an envelope. Teacher gives an envelope filled with the same set of cards to each group. Pupils arrange the cards to form a complete and correct number sentence. The fastest group with the correct number sentence is given 5 marks. Other groups are given 3 marks each. Repeat steps 2 to 5 for different sets of cards. The group that scores the highest mark is the winner.

Calculate. a 5 × 8 kg 60 g ÷ 10 = kg c 10 × 9 kg ÷ 12 = kg g e 21 kg ÷ 5 × 3 = kg g 192

13.1 (ii)

g

b 4 × 6 kg 300 g ÷ 6 = d 40 kg 500 g ÷ 9 × 10 = f 19 kg 110 g ÷ 7 × 8 =

g kg g

Diversify activities involving mass for mixed operations in co-curriculum such as TEACHER’S " cooking competition. NOTES

Solve the problems 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

I draw a diagram. Then, I calculate.

Total

3 kg 1 kg 750 g Solve

2 kg 500 g ?

2 kg 500 g + 3 kg – 1 kg 750 g = 4

2 kg 5 0 0 g + 3 kg 0 0 0 g 5 kg 5 0 0 g Check

2 500 g + 3 000 g 5 500 g

kg

g

14 10 15 0 0

5 kg 5 0 0 g – 1 kg 7 5 0 g 3 kg 7 5 0 g 4

14 4 10

5 500 g – 1 750 g 3 750 g 3 750 g = 3 kg 750 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. 13.2 (i)

Guide pupils to solve problems by making tables or mantic reasoning. TEACHER’S " NOTES

193

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?

600 g

I draw a picture.

600 g 600 g

Solve

2 × 600 g ÷ 12 =

100 g 12 1 200 g 600g – 1 2 × 2 00 1 20 0 g – 0 00 – 0 0

g



Check 12 × 1 00 g 1 200 g

600

1 200 g 2 1

2 × 600 g ÷ 12 = 100 g

194

The mass of raisins for each person is 100 g. If Nani shares 1 200 g of raisins with 5 friends, what is the mass of raisins will each of her friends get?



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

13.2 (i)

b 8 kg 400 g ÷ 7 × 4 = 4 800 g

TEACHER’S " Guide pupils to solve problems by trying a simpler case and working backwards. Simulation can be done in groups. NOTES " Expose various types of Higher Order Thinking Skills (HOTS) questions involving mass.

Solve.

2 kg 50 g

5 kg 280 g

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? P R Q c 1 kg 200 g



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? TEACHER’S NOTES

50 g 2 kg

Beans 3 kg 620 g

Murukku 640 g

195

1

Solve in standard written form. a 2 kg 400 g + 3 kg 690 g – 1 kg 286 g = kg 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

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 30 kg 500 g

29 kg 700 g

Mother

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? 9 kg

c 2 kg 80 g TEACHER’S NOTES

196

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.

14

School

VOLUME OF LIQUID Addition and subtraction of volume of liquid Let me fill up this bottle with watermelon juice.

I add 200 mℓ of watermelon juice into the jug.

1 ℓ 500 mℓ

Thank you, father. 3ℓ 3ℓ

1 ℓ 500 mℓ 2 ℓ 600 mℓ

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 =



2 ℓ 600 mℓ + 200 mℓ 2 ℓ 800 mℓ

ℓ

mℓ

2 ℓ 800 mℓ – 1 ℓ 500 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.

Find the difference in volume between the watermelon juice and the grape juice.

14.1 (i)

TEACHER’S NOTES

Grape Juice

Watermelon juice 1 ℓ 500 mℓ

Watermelon juice 365 mℓ

1 ℓ 200 mℓ

Carry out simulation activities using liquid and measuring cylinders.

197

2 49 ℓ – 13 ℓ 472 mℓ + 8 472 mℓ =

4 8

9 9 10 10 0 0

49ℓ 0 mℓ – 1 3 ℓ 4 7 2 mℓ 3 5 ℓ 5 2 8 mℓ

1

ℓ 1 1

3 5 ℓ 5 2 8 mℓ + 8 ℓ 4 7 2 mℓ 4 3 ℓ 1 0 0 0 mℓ

× 1 000 litre millilitre ÷ 1 000

43 ℓ 1 000 mℓ = 43 ℓ + 1 ℓ INFORMATION = 44 ℓ 49 ℓ – 13 ℓ 472 mℓ + 8 472 mℓ = 44 ℓ Add 49 ℓ and 8 472 mℓ. Then, subtract 13 ℓ 472 mℓ from the answer. Explain.

3 750 mℓ + 3 ℓ 900 mℓ – 260 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

mℓ Convert 4 ℓ 390 mℓ to mℓ.

750 mℓ + 3 ℓ 900 mℓ – 260 mℓ = 4 390 mℓ In the number sentence above, convert 3 ℓ 900 mℓ to mℓ. Then, solve it. Is the answer the same?

12 ℓ 15 000 mℓ 198

14.1 (i)

How do you fill up 9 ℓ of water into the green container using both the red and blue pails? Explain.

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

Players

Materials 4 sets of volume cards, task cards, A4 paper. Steps

A

2 ℓ 720 mℓ

B

4 pupils in a group. 4 ℓ 300 mℓ

C

650 mℓ

1 Determine each player’s turns. 2 Carry out the tasks based on the task cards. Show your calculation on an A4 paper. Example: 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 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.

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.

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 b 6 ℓ 78 mℓ – 988 mℓ + 3 ℓ 885 mℓ = mℓ c 368 mℓ + 17 ℓ 120 mℓ – 2 ℓ 388 mℓ = ℓ ℓ d 12 ℓ 198 mℓ – 10 ℓ 662 mℓ + 22 ℓ 464 mℓ =

mℓ

mℓ

2 Reduce 36 712 mℓ from 86 ℓ. Then, add the answer to 712 mℓ. State the answer in ℓ. 14.1 (i)

TEACHER’S NOTES

Prepare enough sets of cards for each member of the group and add questions on mixed operations.

199

Multiplication and division of volume of liquid Each bottle holds 1 500 mℓ of honey.

I transfer equally into 6 small bottles.

1 500 mℓ 1 500 mℓ 1 500 mℓ

1 What is the volume of honey in each small bottle based on the situation above? 3 × 1 500 mℓ ÷ 6 =

mℓ

1



1 500 mℓ × 3 4 500 mℓ

750 mℓ 6 ) 4 500 mℓ – 42 30 – 30 00 – 0 3 × 1 500 mℓ ÷ 6 = 750 mℓ 0 The volume of honey in each small bottle is 750 mℓ. 2 5 × 12 ℓ 800 mℓ ÷ 4 =

ℓ 3 200

5 × 12 ℓ 800 mℓ = 5 × 12 800 mℓ 4 4

Convert 12 ℓ 800 mℓ to mℓ.

1





= 16 000 mℓ

16 000 mℓ = 16 ℓ 1 000 5 × 12 ℓ 800 mℓ ÷ 4 = 16 ℓ 200

14.1 (ii)

TEACHER’S NOTES

Emphasise that answers must be given in units required. Drill pupils with questions involving cancellation method.

3 Divide 87 ℓ 836 mℓ by 14, then multiply by 9. 87 ℓ 836 mℓ ÷ 14 × 9 =

mℓ

6 ℓ 274 mℓ 63 14 ) 87 ℓ 836 mℓ 6 ℓ 274 mℓ – 84 + 3 000 × 9 3 3 836 54 ℓ 2 466 mℓ – 28 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 Convert 87 ℓ 836 mℓ to mℓ and solve. Is it easier?

4 827 ℓ ÷ 25 × 2 = 33 ℓ 25 ) 827 ℓ – 75 77 – 75 2

ℓ

mℓ

80 mℓ 0 mℓ + 2 000 2 000 – 2 00 00 – 0 0

33 ℓ

1

80 mℓ × 2 66 ℓ 160 mℓ

827 ℓ ÷ 25 × 2 = 66 ℓ 160 mℓ Does 33 ℓ 80 mℓ + 33 ℓ 80 mℓ give the same answer? Discuss.

14.1 (ii)

TEACHER’S NOTES

Get pupils to create stories based on division number sentences.

201

C B A 4 565 mℓ

Half the volume of C

Find the volume of water in ℓ and mℓ in container B.

4 times the volume of A

Answer the puzzle. Complete the answer with the matching letter in the blanks below. 3 × 2 ℓ 115 mℓ ÷ 5

T

35 ℓ 280 mℓ ÷ 7 × 9

70 ℓ 600 mℓ ÷ 10 × 12

L

O

6 × 12 ℓ 300 mℓ ÷ 2 E

8 × 5 ℓ 45 mℓ ÷ 4

B

What object has a neck but no head?

10 090 mℓ

45 360 mℓ

1 ℓ 269 mℓ

1 Calculate. a 2 × 7 ℓ 930 mℓ ÷ 5 = c 5 × 2 ℓ 884 mℓ ÷ 14 = e 3 × 7 ℓ 602 mℓ ÷ 9 = 2 a b

202

14.1 (ii)

1 269 mℓ

84 ℓ 720 mℓ

36 900 mℓ

ℓ mℓ b 8 ℓ 56 mℓ ÷ 8 × 9 = mℓ mℓ d 12 ℓ 640 mℓ ÷ 8 × 7 = ℓ mℓ f 9 ℓ 100 mℓ ÷ 13 × 50 = ℓ

mℓ

Find the product of 10 322 mℓ and 7 divided by 2. State the answer in ℓ and mℓ. What is the volume when divided by 5 and multiplied by 9 gives the answer 27 ℓ ? TEACHER’S NOTES

Carry out simulation to help pupils answer challenging questions. Drill the conversion of units orally.

Solve the problems 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

The volume of tea drank

520 mℓ

remainder

Solve 27 ℓ 850 mℓ + 14 ℓ 600 mℓ – 520 mℓ = ℓ 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 Check

1

4 1 ℓ 9 3 0 mℓ + 5 2 0 mℓ 4 2 ℓ 4 5 0 mℓ

4 1

mℓ

1 450

4 2 ℓ 4 5 0 mℓ – 1 4 ℓ 6 0 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)

TEACHER’S NOTES

Guide pupils to draw tables to solve problems. Guide pupils to estimate the reasonable final answers.

203

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. Milk

Milk

Milk

2 ℓ 750 mℓ

2 ℓ 750 mℓ

2 ℓ 750 mℓ

3 × 2 ℓ 750 mℓ ÷ 5 =

Solve

2

1

2 ℓ 750 mℓ × 3 8 ℓ 250 mℓ 8 ℓ 250 mℓ = 8 250 mℓ

Check

3 2

1 650 mℓ × 5 8 250 mℓ

mℓ

1 650 mℓ 5 ) 8 250 mℓ – 5 32 – 30 25 – 25 00 – 0 0 2 7 5 0 22 15

8 2 5 0 mℓ = 2 750 mℓ 3 1

3 × 2 ℓ 750 mℓ ÷ 5 = 1 650 mℓ The volume of milk in each container is 1 650 mℓ.

204

14.2 (i)

TEACHER’S NOTES

Give other daily situation for problem solving involving division and multiplication.

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 3 ℓ 752 mℓ 3 ℓ 752 mℓ

Mak Jah gave 3 containers of equal amount of porridge to 8 neighbours. Find the volume of porridge, in mℓ, received by each neighbour.

3 ℓ 752 mℓ

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.

TEACHER’S NOTES

Give more standard UPSR questions involving volume of liquid.

205

1 Calculate. mℓ a 3 ℓ 201 mℓ + 54 ℓ – 18 ℓ 127 mℓ = ℓ 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

e f

12 ℓ 105 mℓ ÷ 15 × 3 = 8 ℓ 75 mℓ ÷ 5 × 7 =

mℓ

mℓ 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?

5 ℓ 130 mℓ

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?

TEACHER’S NOTES

206



15

Sekolah

SPACE Recognise angles 1

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.

What types of angles are there in the shapes above?

Right angle

A triangle has 3 sides and 3 angles.

An obtuse angle is bigger than a right angle. Acute angle

Obtuse angle

A right angle is An acute angle is smaller formed at the corner than a right angle. of a rectangle. 2 Look at my arm. What type of angle is formed?

Right angle

15.1 (i)

TEACHER’S " Encourage pupils to recognise angles for basic shapes found at a preschool playground or the reading corner. NOTES

207

Materials A4 paper, pencil, ruler and scissors. Steps Fold a sheet of A4 paper 2 Mark the right into two equal parts. angle.

1

3 Draw a line as in the picture and cut it.

Right

Right angle

angle

4 Mark the acute angle and the obtuse angle on both paper cuttings. Right angle Label them.

Can a right angle be formed from this paper? Explain.

Obtuse angle Acute angle

5

Paste the paper cuttings in your exercise book.

1

How many angles are there in each diagram? a b

2

Name the angles found in the following shapes.

c

a b c

208

15.1 (i)

Use the Geoboard to form various basic shapes and relate them to angles. TEACHER’S " NOTES

Recognise lines Parallel 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. 30 cm

30 cm

30 cm

30 cm

30 cm

a 1.4 m

The same distance

1.4 m

b

Both of these racks show examples of parallel lines.

0.6 m

0.6

30 cm

m

Observe the railway tracks. Why must they be parallel? Discuss.

Diagrams A and B show parallel lines. Does diagram C show parallel lines? Discuss.

15.2 (i) a

A

C B

TEACHER’S " Encourage pupils to tell stories about objects or places which have a lot of parallel lines. NOTES

209

Perpendicular lines

b

• Look at line a and line b at the picture. The two straight lines which intersects at a right angle are perpendicular lines.

a



Can you point to the perpendicular lines in the three pictures above?

Which parts of this door are 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. a b c

Draw a flag

210

15.2 (i) b

Draw a draughtboard

Draw hopscotch

State 10 objects in the classroom that have perpendicular lines. TEACHER’S " NOTES

g Name the pairs of straight lines that form parallel and perpendicular a lines in the diagram.

b

c

d

e

f

h

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.

15.2 (i)

b blue lines for perpendicular lines.

Prepare exercises as in questions 2(a) and (b) in the worksheets. TEACHER’S " NOTES http://www/superteacherworksheets.com

211

Perimeter

3

Mummy, what is the length of the lace that you used?

1

I use the lace according to the length around the pillow case.

3

3

3 The length of the lace is 12 units. The 12 units is the perimeter of the pillow case.



Perimeter:



3 + 3 + 3 + 3 = 12 units

4 cm 2

3

A is a rectangle and B is a right A angled triangle. 6 cm

3 cm

4 cm B 5 cm



Perimeter A:

Perimeter B:

4 cm + 6 cm + 4 cm + 6 cm = 20 cm

+

+

=

Draw the shapes of a square, a rectangle and triangles with the perimeters of 12 cm.

212

15.3 (i)

TEACHER’S NOTES



http://www/superteacherworksheets.com/geometry/perimeter-3_TZFFD.pdf



4

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.

5

6

Find the perimeter of the square.

10 cm

6 cm

12 cm 12 cm

8 cm

Perimeter = 6 cm + 8 cm + 10 cm = 24 cm

Multiplication is repeated addition. 12 cm

12 cm

INFORMATION

Perimeter = 12 cm + 12 cm + 12 cm + 12 cm = 4 × 12 cm = 48 cm

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 12 cm

c 13 cm

The length of each side is 5cm 5 cm 15.3 (i)

d 15 cm 8 cm

The length of each side is 4 cm

Carry out hands-on activities to measure perimeters of triangular and four-sided TEACHER’S " objects in the school compound. NOTES

213

Area 1 1 unit 1 unit 1 unit 2

The area of 1 unit square is 1 square unit. It is written as 1 unit2.

INFORMATION

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 Length

Width

3 cm

5 cm

Area = 15 units2

Area = Length × Width = 5 cm × 3 cm = 15 cm2



2 Find the area of the checkerboard. The area of each square of the checkerboard is 1 cm2.

The area of the checkerboard =

214

15.3 (ii)

TEACHER’S NOTES



cm2

" Carry out hands-on activities using grid book to measure areas of basic shapes. http://www.superteacherworksheets.com/geometry/area-1_TWBDW.pd

1 square forms two triangles of the same size.

Draw a line from vertex to vertex.

3

The area of a triangle is half the area of a square. 4 cm 4 cm

4 cm

Width 4 cm

Length Area

Area

= Length × Width = 4 cm × 4 cm = 16 cm2

4

Height

Base

8 cm

6 cm

Area

= Area 2 2 = 16 cm 2 = 8 cm2

= Base × Height 2 = 6 cm × 8 cm 2 2 = 48 cm 2 It is written as 2 = 24 cm 1 2

5 4 cm 3 cm 15.3 (ii)

Area

× Base × Height.

= 1 × Base × Height 2 = 1 × 3 cm × 4 cm 2 = 12 cm2 = 6 cm2 2

TEACHER’S " Emphasise that the height of a triangle must be measured from the base to the vertex of the triangle that has the right angle. NOTES

215



1

The perimeter of a rectangle is 48 cm. This rectangle consists of two squares. What is the area of the rectangle?

Look at the diagrams in the squared grid. Answer the questions. 1 unit 1 unit D

B

A

C

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 4 cm

c 12 cm

5 cm 10 cm



7 cm e

d 6 cm

9 cm f

7 cm





13 cm P

216 216

15.3 (ii)

5 cm

16 cm

8 cm 3

--------

8 cm

TEACHER’S NOTES

5 cm

P is a square. Find the area, in cm2, of the shaded part.

http://www.charliefrench.com/PDF/Gr4measure2PDF

Volume These small boxes are cubes.

1

How many cubes are needed to fill up the space of the big box?



12 cubes are needed to fill up the big box. This big box is a cuboid.



1 unit

Volume = 12 units3

1 unit Volume of cube = 1 unit × 1 unit × 1 unit = 1 unit3 1 unit

The volume of a cube is 1 unit cube. It is written as 1 unit3. This cube is known as cubic unit.

The volume of a cuboid can be determined by counting the number of cubes filled in it.

INFORMATION

2

1 cm 1 cm 1 cm

How do you count the number of the hidden cubes?

Volume of cube = 1 cm × 1 cm × 1 cm = 1 cm cube = 1 cm3



There are 8 unit cubes There are 18 unit cubes Volume = 8 units3 Volume = 18 units3

15.4 (i)

TEACHER’S " Carry out the activity to find the volume of cube and cuboid using unit cubes. NOTES

217

3 a



b

Volume = 27 cubic units = 27 units3

Volume = 32 cubic units = 32 units3

Length Width Height Volume (units3) 3 3 3 27

Length Width Height Volume (units3) 4 2 4 32 The formula for volume of cube or cuboid is Length × Width × Height.

Try to use the formula of volume of cube and cuboid to check the anwers for 3 a and 3 b .

4

1 cm

1 cm

1 cm

height

length

5

INFORMATION

Volume = Length × Width × Height = 5 cm × 2 cm × 3 cm = 30 cm3

width

Calculate the volume of the box. 20 cm

Volume = 50 cm × 30 cm × 20 cm = 30 000 cm3 Can volume be calculated by multiplying the area of base by height? Discuss.

218

15.4 (i)

30 cm 50 cm

TEACHER’S " Encourage pupils to draw nets to differentiate areas and volumes. NOTES

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

unit cubes.

unit cubes.

units3

Volume =

c

unit cubes.

units3

Volume =

units3

Volume =

2 Calculate the volume of the diagrams.

a

b

c

d

10 cm 4 cm

10 cm

4 cm 4 cm

10 cm

8 cm

2 cm

8 cm

12 cm 15 cm 3 cm

3 Calculate the volume of the cube and cuboid. 4 cm 8 cm 5 cm 15.4 (i)

TEACHER’S NOTES

10 cm http://www/superteacherworksheets.com/geometry/volume-cubes-1_TZWBB.pd.

219

1

Draw and mark the angle on the diagram. Fill in the blanks. Right angle A

2

3

Acute angle

A

Obtuse angle

Copy and draw: a parallel lines.

b perpendicular lines.

The perimeter of rectangle X is the same as the perimeter of square Y.

a b c

Find the perimeter of diagram X. Find the length of the sides of diagram Y. 3 cm 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 cm Y

X

A 3 cm

5

B

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? 2 cm A TEACHER’S NOTES

220

The perimeter of the surface B is 16 cm. Find the volume of this cube.

B

16

School

COORDINATES Recognise position 1 The picture shows the positions of pupils of 4 Bijak.

Farah The pupil in the fifth column, row two, are you a new pupil?

Siva

May

Ros

Izam

Ika

Amit

Shah

Joseph

Muaz

Wong

Ain

Yee

Adam

Nina

Yes, teacher.

What is Siva’s position? Siva is at 2 tables to the right and 3 tables to the back. So, Siva sits in the second column, third row. What is Yee’s position? State the position of other pupils.

16.1 (i)

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

221

2 The grid below shows the positions of the objects in the decor rack in Amin’s room.

State the position of the storybook.

The storybook is 4 squares to the right and 5 squares to the top.

Explain the positions of the toy car and the ball.

The toy car is located 6 squares horizontally and 3 squares vertically. The ball is located at . Explain the positions of the others object.

222

16.1 (i)

Use paper foldings, tiles or grids to create square grids to show the positions TEACHER’S " of the objects. NOTES Diversify the usage of vocabulary like north, south, east and west. "

3

The picture shows the positions of the chessmen. The numbers 1 to 8 are located at the vertical axis. This axis shows the locations at the row.

8 7 6

King

Queen

Bishop

Knight

5

4 3 2

Pawn

Castle

1 A

B

C

D

E

F

G

H

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.



is located at A4 and

What can you see at E2, F4 and B7? Discuss.

is located at H3. The position of an object is stated by the column first followed by the row. INFORMATION

16.1 (ii)

Guide pupils to say locations at the horizontal axis first then at the vertical axis. TEACHER’S " Relate the locations of objects in daily life such as seatings in a cinema. NOTES

223

6 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?

5 4 3 2 1 0

Materials MS Word

1

2

3

4

5

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.

224

5

Create another table under the animal grid. Complete the table.

6

Print and check your work. Display at the Mathematics corner.

16.1 (ii)

5 4 3 2 1 A

B Position

C

Diversify exercises, activities or games to recognise the positions of TEACHER’S " objects in or outside the classroom. NOTES

D

Animal

6

Tourist attraction places in Malacca 4

3

2

1 A



B



C

D

E

Key: Butterfly Garden

Crocodile Farm

Mini Malaysia

A Famosa

Malacca Zoo

Stadthuys Building

Samudera Museum

Independence Memorial

Complete. a The Independence Memorial is located at the same row as 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. TEACHER’S NOTES

and .

.

225 225

Determine the position Cameron Highlands



Strawberry Farm

5

4

Tea Museum and Plantation Gallery

Vegetable Farm

3 Bee Apiary Cactus Valley

2

Flower Garden

1 A



B



C

D

What is the location of the Bee Apiary based on the horizontal and vertical axes?

E The Bee Apiary is at A3.

Where are the Strawberry Farm and Cactus Valley located?



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

.

.

The location of the Flower Garden is 2E. The Museum and Gallery is at 5D. Is it true? Discuss.

226

16.2 (i)

TEACHER’S " 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. NOTES

The squirrel is searching for food at Pak Ali’s orchard. 5 1 State the positions of the following

4

fruits: a Ciku

b Papaya

3

c Durian

d Guava

2 1

2 The squirrel does not like chillies and bitter gourds. State the positions of the chillies and bitter gourds. A

B

C

D

E

5

Letter Grid Card j c f n t

4

s

k

q

b

z

3

d

o

g

v

l

2

r

a

i

e w

1

p m h

y

u

A B C Distribute the letter grid card to each pair. Teacher flashes the questions on the position of letters. Example: B3 A4 C1 A2 D2 Write the letters on an A4 paper based on their positions. Rearrange the letters to form a word. Example: h o r s e C1 B3 A2 A4 D2 The fastest group with accurate answers is given 5 marks. Repeat steps 2 to 5. The group with the highest score wins.

D

E

Players

2 pupils in each group.

Materials Letter Grid card (except x), questions on the position of letters using MS Word, A4 paper. Steps 1 2 3 4 5 6 7

16.2 (i)

TEACHER’S " Diversify game methods based on creativity. NOTES

227

1 Look at the positions of the shapes. Answer the questions. a is located 5 squares to and 4 2 squares to . 3 b A to F is located at axis. 2 c 1 to 4 is located at axis. d State the shapes seen at the 1 locations: A B C D E F i B1 ii D4 iii A3 2 Answer these questions based on the grid. a Choose a method how you would 5 explain the location of . 4 i First the digit 5 followed by the letter D. 3 ii First the letter D, second the 2 digit 5. 1 A B C D E F b State the location of . 3 6 a e 5 o l 4 y t 3 b x 2 n p 1 A B C D E F G

Look at the locations of the letters in the grid. Answer this riddle: Which box cannot be lifted? E1 C3

D6 F5

B2

A6

D5

B4



G4

G2

4 4 State the coordinates of these objects: 3 a b c 2 1 0

228 228

1 TEACHER’S NOTES

2

3

4

17

School

RATE Rates

RE

CIL BOOk STO KAN SPECIAL OFFER

1

SPECIAL OFFER PINTAR BOOKST ORE

I want to buy 6 pens. Which is cheaper?

Kancil Bookstore RM0.75 2 ) RM 1.50 – 0 15 – 14 10 – 10 0

Price at The price of a pen Kancil Bookstore:

Pintar Bookstore RM0.60 3 ) RM 1 .80 – 0 18 – 18 00 – 0 0

Price at Pintar Bookstore: The price of a pen

is RM0.75.

RM0.75 × 6 = RM4.50

The price of 17.1 (i)

6 × RM0.75 = 4 3 RM0.75 × 6 RM4.50

is RM0.60.

6 × RM0.60 = 3 RM0.60 × 6 RM3.60 RM0.60 × 6 = RM3.60

at Pintar Bookstore is cheaper, RM3.60.

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

229

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

44 6 × 44 = 30 ) 1 320 22 – 1 20 44 1 20 × 6 – 1 20 264 0 The number of passengers carried by 6 buses is 264 persons.



b

How many buses are needed to carry 220 passengers?



44 passengers 220 passengers 5 44 ) 220 – 220 0 220 passengers



1 bus 220 ÷ 44

220 ÷ 44 = 5 buses

5 buses are needed to carry 220 passengers. How many buses are needed to carry 110 passengers? Discuss.

2 books RM15.00

230

17.1 (i)

Fazlin wants to buy 12 storybooks for her friends. Help her to spend wisely.

3 books RM21.60 TEACHER’S NOTES

Diversify questions involving money, time and units of measurement. http://www.wiziq.com/tutorial/49646-grade6-unitary-method

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 1 marble 5 20 ) 100 – 100 0



1 marble 7 marbles



The mass of 7 marbles is 35 g.

100 g 100 g ÷ 20

5g 7 × 5 g = 35 g

What is the mass, in g of 25 marbles of the same size? Discuss.

4

? km

180 km A

B

C

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 ÷

3 hours

×

=

km

km =

km

The distance from Town B to Town C is

17.1 (i)

TEACHER’S NOTES

km.

Guide pupils to find a value involving unitary. Pose various types of questions to reinforce the unitary concept.

231

Materials Players Question card, A4 paper, pen.

2 pupils in a group.

Steps 1

Prepare 3 question cards for each group. Example: 24 cm What is the mass of 7 similar balls?

Find the length of 5 similar squares.

6 boxes 4 boxes

600 paper clips ?

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?

20 pieces

240 g

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?

232

17.1 (i)

TEACHER’S NOTES

Prepare enough sets of cards for pupils. Customise activities according to pupils’ creativity and ability.

Hasrul lost in a garden. Find the way out by colouring the answer for each question in order.

RM1.20 RM31.50

RM32.40

10 pieces

9 pieces

RM1.50

196 words

205 words

8 pieces

START

182 words

250 mℓ



5 envelopes

P

Hasrul’s way out is at

a 10 units 8 units d 15 minutes 7 minutes f 4 glasses 10 glasses

420 words words

5 kg 9 kg

R

Q

.

b RM1.50

2 050 mℓ

2 500 mℓ

4 envelopes

c RM17.50

e 120 stamps 100 stamps

12 m 40 m

3 pieces pieces

6 envelopes envelopes

1ℓ mℓ

TEACHER’S NOTES

233

1 Solve. a



b

c 45 cm

4 books cost RM30

How much does 3 books cost?

3 packets of sweets weigh 900 g

Find the mass of 7 packets.

Calculate the 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



Printing Machine B 1 1 hours produces 900 greeting cards 2

Printing Machine A 1 hour produces 600 greeting cards

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

12 m



234

9.1 (i)

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 TEACHER’S NOTES



18

School

DATA HANDLING Recognise and compare information These are three methods of presenting data.

MATHEMATICS CORNER BAR CHART My Friends’ Storybooks Number of books

PICTOGRAPH My Friends’ Storybooks Akif Hui Li Sarjit Ajol Key: represents 2 books

10 8 6 4 2 0

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

PIE CHART My Friends’ Storybooks Ajol 10%

Sarjit 30%

Akif 40% Hui Li 20%

Akif Hui Li Sarjit Ajol Friends’ names

Pictograph 1

My Friends’ Storybooks Akif Hui Li Sarjit

Picture

Ajol Key: represents 2 books Key

Title In a pictograph, pictures are used to represent data.

Akif has 8 storybooks. 2 + 2 + 2 +2 = 8 4×2=8 Hui Li has ×

storybooks. =

Who has the most number of storybooks?

18.1 (i) a 18.2 (i) a

TEACHER’S NOTES

" Emphasise that pictures must be appropriate with the title of the pictograph.

http://urbrainy.com/get/1507/interpreting-pictograms-6273

235

2

The Sales of Mangosteens for 4 Days Complete the table.



Day Monday

3 × 10 = 30

Tuesday

5 × 10 = 50 3 × 10 = 2 × 10 =

Wednesday

Monday Tuesday Wednesday Thursday Key:

Number of Mangosteen

Thursday

represents 10 mangosteens

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

What are the other ways can you calculate the total sales of mangosteens for four days?



On Friday, the number of mangosteens sold is 15 more than the sales on Thursday. Does this picture represent the number? Discuss.

236

18.1 (i) a 18.2 (i) a

Use various types of pictographs to retrieve information and create questions. TEACHER’S " NOTES http://urbrainy.com/get/2304/more-pictogrms-7825

Bar chart

Vertical axis

Number of pupils

Markings

20 18 16 14 12 10 8 6 4 2 0

Musical Instruments Played by a Group of Pupils

Title

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

Flute

Drum Angklung Piano

Musical Instrument

Horizontal axis

In a bar chart, bars are used to show data.

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, the angklung and like to play the piano.

like to play

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 =

.

What is the most favourite musical instrument? Why?

18.1 (i) b 18.2 (i) b

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

237

-------

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

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

Club Attendance of Year 4

30

35

40

Taekwondo

Club

Silat Robotic Cultural 0



5

10 15 20 25 Number of pupils

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. 1 Gather data on the hobbies of each friend in the class. Choose 4 types of hobbies. 2 Key in data in MS Excel.

1 Hobbie

s of P

5 Discuss the outcomes.

238 238

TEACHER’S NOTES

upils o

f 4 Ce rdas Numb er of Pup ils

Hobby Readin

g

2

12

Swimm

3 Highlight data, choose the menu Insert and click Column. Choose Chart Layout and click 2-D Column. 4 Type the title and label the horizontal axis and the vertical axis.

Players In pairs.

ing

5 Hobbies

of Pupils

s

of 4 Cerda

3

Hobbies

of Pupils

4

das

of 4 Cer

Hobbies

of Pupils

of 4 Cerd

as

chart Pie 1

Shida’s Pocket Money

Savings 30%

Food 50%

Transport 20%

A pie chart represents data in circles.

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

Favourite Breakfast of 10 Pupils Biscuits 10%

Nasi lemak 30%

Fried noodles 20% Bread 40%

The total percentage of a pie chart is 100%.

INFORMATION

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 . 18.1 (i) c 18.2 (i) c

TEACHER’S " Relate the percentages of pie chart to fractions. Emphasise the total percentage of a pie chart must be 100%. NOTES " Tell the history of the first pie chart created by William Player in 1801. 239 http://www.superteacherworksheets.com/graphing/pie-graph-simple 2_TWNWR.pdf

1 Study the pictograph and complete the answers. a saves RM2. Savings of 4 Pupils b saving is the most, which is . c The difference between Faizal’s and Faizal Sivam’s saving is . Ai Lin d The total saving of the four pupils is . Sivam Esha Key:

2

represents 50 sen

Answer the questions based on the bar chart.

Time in minute

Time to Answer a Mathematics Test 60 ---------------------------------- 50 --------------------------------- 40 ----------------30 b 20 10 c 0

Ina

Ho Ajay Dayang

Name

State the time taken to answer the Mathematics test. i Ina ii Ho iii Ajay iv Dayang Arrange the names in order of speed in answering. The difference in time taken between and

is 15 minutes.

3 Look at the pie chart and answer the questions. a The percentage of jasmine is . Types of Flowers in Painting b The and the have the same Chrysanthemum percentage. 20% c The total percentage is . Rose Jasmine d The percentage of the flowers, excluding 10% 50% chrysanthemum is . Ylang 20%

240 240

TEACHER’S NOTES

Gas in the Atmosphere

Other Gases 1%

State the percentage of oxygen in the atmosphere.

Oxygen

Nitrogen 78%

Materials Pictograph, bar chart, Players 4 groups of equal pie chart, number of pupils. numbered question cards. Steps 1 Display pictograph, bar chart and pie chart using MS PowerPoint. Example: Pupils’ Hobbies

Number of Books Borrowed Number of Pupils

Adam

Lily Mira

2 3 4 5

Ways of Going to School

-------------------------20 -------------

Bus 10%

16

Car 20%

12 8 4

Maria Key:

24

0

represents 10 books

TEACHER’S NOTES

Walking 40%

Reading Internet Swimming Singing surting Hobby

Put the question cards on the magnetic board. The group representative takes the numbered question card in turn and answer the question orally. Pupil who answers correctly is given 5 marks. The group with the highest score wins.

Bicycle 30%

hart ntage perce g is the lkin What upils wa p e th of hool? to sc

Pie C

Ba rC ha Fin rt pe d th r c pu en e dif p t a In ils g fere like tern who e be nce to et an like twe in en rea d t d b tho o su the oo se rf th ks wh e . o

Pictograph Who borrows the most number of books from the library?

241 241

1 Study the pictograph and answer the following questions. Sales of Ice Cream for 4 Days a How many ice creams are sold on Sunday? Sunday b Calculate the total number of Monday ice creams sold in 4 days. c What is the difference in sales of the Tuesday ice creams on Tuesday compared to Sunday? Wednesday d costs RM2. Calculate the sales Key:

of the first two days. represents 20 ice creams

2 Answer the questions based on the bar chart.

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

Sport Team

a Scores of 4 Sport Teams b Blue Red c Green Yellow 0

5

10



15 20 25 30 Mark

Green Team collects marks. The total score of and Teams is the same as the score of Red Team. 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 Items Recycled aluminium tins that are recycled is . Paper b The percentage of paper that is Aluminium Tins recycled is . 45% Glass c The difference in percentage 25% between the items most Plastic 10% recycled and the least is . 242 242

TEACHER’S NOTES

9. A Answer the following questions.

B

10. RM19 620 – RM8 765 – RM437 =

weeks

11. 10 years 6 months ÷ 9 = years months

3. RM70 406.15 + RM16 319 + RM782.90 =

12.

4. Convert 11 days 4 hours to hours.



5. a. b.

Convert 9 050 m to km and m. Calculate 8 km 40 m ÷ 8. Give answer in m.

6.

0 cm 1

7.

2

3

4

5

6

Number (pieces)

RM100 RM50 RM20 5 sen 100

80

7

Calculate the total value of money.

8. Solve: 6 cm 9 mm × 5

A

B

D

C

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.

State the length of the needle, in mm. Money

C

State the pair of perpendicular lines.

1. Round off RM53 247.65 to the nearest ringgit. 2. 63 days =

A

14 cm 7 cm



Find the perimeter, in cm.

9

4 cm

15. 9 cm



5 cm

Calculate the volume of the cuboid, in cm3.

16. 5 ℓ 80 mℓ ÷ 4 × 3 =

ℓ



mℓ

243

17. 17 years 11 months + 9 years 10 months 18. 20 kg 840 g + 9 kg 176 g – 6 kg 24 g = kg

25. The diagram below shows the height of 4 boxes of the same size. g 60 cm

19. 7 ℓ 680 mℓ – 4 ℓ 250 mℓ mℓ + 5 ℓ 90 mℓ = ℓ 20. – RM10 312.25 + RM948.75 = RM30 120. What is the value in ? 21. 6 × 1 600 g ÷ 8 =

g



Calculate the height, in cm, of 3 boxes.

26. 4 km 230 m = – 2 km 865 m State the answer in m.

22. 6 cm



What is the perimeter, in cm, of the pentagon?

27. 6 28 . A

23. 30 days 8 hours – 29 hours – 4 days 14 hours = days hours 24. Name the following angles. a.

b.

c.

244

)

years 35 years 8 cm

months

B 4 cm

D



C

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?

30. The grid below shows the positions of the shapes.

35. X

5 4 3 2 1



A

a. b.

B

C

D

Y

Z

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

E

State the positions of i. ii. iii. 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

1 km 700 m

37. RM4 138.50 – 725 sen = 38.

My Friends’ Stamps



32. State the 3 instruments of payments other than cash in our daily life.

Lin

Aiza

Zul

Nitish



Key:

33. Which is less than 4 020 m? a. 40 km 2 m b. 4 km 20 m c. 4 km 2 m



Look at the pictograph above and complete the answers.



a. Lin has

34.



b.



9 cm 9 cm

The diagram above is a square. Calculate the: a. Perimeter b. Area

represents 8 pieces

stamps.

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.

245

39.

42. Favourite Sports of 10 Pupils

P 5 cm Q



R

12 cm

The perimeter of the right angled triangle is 30 cm. Find the length of PR, in cm.

Volleyball 30% nis ten e l Tab 10%

40. The bar chart shows the Mathematics marks of 4 pupils.

Badminton 40%

Football 20%

Name

Mathematics Marks



a. % of the pupils like to play football. b. The most liked sport is . c. The difference in percentage 0 10 20 30 40 50 60 70 80 90 between and Mark is 20%. Complete. The diagram shows a. Gurmit scored marks in 43. a cuboid. The base the Mathematics test. area is 9 cm2. Find b. and got the the volume, in 7 cm same marks. cm3, of the cuboid. c. Shireen gots marks less than Gurmit.

Amy Gurmit Shireen Zamir



1 cm

41.

500 g

B

44.

1 cm

1 kg 1 kg

A



246

C

Calculate the area, in cm2, of the triangle ABC.

What is the mass, in kg and g, of 9 similar ?

B Solve the following problems.

6. A tailor takes 13 hours 20 minutes to sew 8 similar dresses. How long does she take to sew a dress?

1. MASS:

1.2 kg



MC MR M+ ALARM ZERO

MODE

TERA

ON OFF

Each vase has the same mass. Calculate the mass of 7 vases, in kg and g.

7. Liza jogs 2 km 500 m. Marina jogs 950 m more than Liza. How far has Marina jogged?

30 cm 6 mm



4.

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. Item Television Furniture Camera

Price RM3 499 RM10 520 RM2 880

The table shows the prices of three items. What is the total cost?

9 cm

2. The total age of a pair of twins, Aishah and Aizah, is 19 years 8 months. How old is Aizah? 3.

20 cm

8.



The diagram is a painting. a. Find the area, in cm2. b. Find the perimeter, in cm.

9.

Soya

1 ℓ 250 mℓ

Mother bought 3 bottles of soya milk. She poured equally into 25 glasses. What was the volume, in mℓ, for each glass?

5. Encik Ramu’s annual income is RM51 840. Calculate his monthly income.

247

10. The diagram shows 2 packets 12. P of milk powder of different sizes.

3k

m8

50



Chocolate Flavour

Original Flavour

1 kg

RM30.90



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.

2 kg

RM56.20

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.

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. 50 km 180 m

15.

11.

40 km 920 m

D P

15 ℓ 20 mℓ



248

R

Q

Free 250 g

Free 200 g

m

Q

F

40 m

17 km

8 4 km

E

3

940 mℓ

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.

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.

ANSWERS

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 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 13 136 13 156 13 176 13 116 64 109

64 129

Multiply by 3 125 375 1 041 7. 40, 1 970, 50

3 123

64 149

64 169

1 125

3 375

9 369

28 107

f. 10 098 4. 84 540

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 g. 17 400 h. 78 000 i. 1 000 j. 92 3. 63 000 4.

21

543 62 1 086 + 32 580 33 666 ×

e. 4 920 k. 2 203

5. a. 3 000 reams b. 39 630 passengers c. 25 000 pupils d. 20 supermarkets



TOPIC 7: FRACTIONS Mind Stretcher (page 88) 1. 2 4 2 2

f. 62 416 l. 298

d. 62 094 h. 91 052 d. 10 c. 96 passengers

6 2

1 1 1 3 2 2 2 2 17 5 13 1 3 3. 1 b. , 3 2. a. , 2 6 6 4 4 10 2 13 5 4. a. b. c. 1 3 15 12 1 4 2 f. g. 1 h. 5 9 3 5 7 1 5. 6. a. kg b. kg 8 8 10 1

TOPIC 8: DECIMALS Mind Stretcher (page 108) 1. a. 29.09 b. 42.93 c. 42.492 f. 0.109 g. 187.52 h. 28.645 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 d. i. 9.63 seconds ii. 9.79 seconds

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 2. 96 678 3. a. 2 070 b. 22 425 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 6: MIXED OPERATION Mind Stretcher (page 68) 1. a. 2 578 b. 9 218 c. 83 636 e. 3 510 f . 4 280 g. 1 903 2. a. 142 b. 808 c. 7 3. a. 1 119 b. 300 c. 85 100 4. a. 5 400 packets b. 5 504 km d. 10 370 eggs

TOPIC 9: PECRCENTAGE Mind Stretcher (page 112) 1. a. 0.08 b. 0.2, 20% 2. 0.03, 3%. 0.82, 82% 11 3. a. 11% 100 , 4. a. 70% f. 84% 5. 92%

0.2, 20%. b. 0.2, 20% b. 0.42 g. 0.09 6. a. 32%

29. 54.22 30. 15.0

d. 58 i. 90

e.

1 8

e. 0.704

c. 11.24 ℓ

c. 0.36, 36%

d. 0.24 , 24%

0.35, 35%.

0.68, 68%.

38 , 0.38 100 c. 60% h. 23% b. 19%

d. 0.3 i. 0.17 c. 49%

c.

SELF-TEST A (page 113) 1. Sixty-four thousand and thirteen. 2. Ten thousands 3. 90 000 + 5 000 + 100 + 7 5. 23 639 6. 70 000 9. 15. 019 10. 42.995 1 13. 3 14. 6.993 4 2 17. 1 18. 81 706 5 21. 3.09 22. 40 900 25. 0.38 26. 30%

4 7 5 i. 24

d.

11. 45 402

4. 81 004 10 7 12. 65 100

15. 605

16. 2.58 km

7. 56 126

e. 5% j. 1.0

8.

19. 900

20. 28 015

23. 52 928 27. 80 808 1 31. 5

24. 44 231 28. 10 060 1 32. 9

249

33. 66 654

34. 45 451

36. a. 1 000 b. 100 39. 1 40. 3 621 B (page 115) 1. 54 371 cars 3 5. 4 ℓ 9. 38.82

TOPIC 15: SPACE Mind Stretcher (page 220)

101 35. 1 1 000 37. 0.03

3 38. 1 8

10. 13 790 copies

12. 1 600 buttons 13. 1.21 m 14. 18.506 km 3 16. 10 ℓ 17. 70 packets

4. 27.36 m 8. 2.9 minutes 11. 17 432 lorries 7 15. 1 20 kg

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 e. 144 f. 7, 8 2. a. 3 days 23 hours c. 29 weeks 1 day 3. a. 202 hours b. 16 x 7 days 4. a. 10 months b. 11 days

b. 4 years 4 months d. 2 days 6 hours c. 29 weeks 1 day d. 42 months 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 3. a. more than 4 km 4. a. 18 cm b. 2 cm 1 mm d. 38 cm 4 mm e. 44 828 m 5. a. 22 km 452 m b. 14 cm 9 mm

c. 8 cm b. less than 2 km c. 208 mm f. 13 km 281 m c. 40 mm

d. 16 km

c. 15 520 g

d. 5 650 g

Topic 14: VOLUME OF LIQUID Mind Stretcher (page 206) 1. a. 39 ℓ 74 mℓ b. 60 ℓ 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

250

A A

2. 40 594 voters 3. 300 baskets 1 6. 8 km 7. 0.25 kg

TOPIC 13: MASS Mind Stretcher (page 196) 1. a. 4 kg 804 g b. 12 kg e. 4 kg 864 g f. 12 360 g 2. a. 8 505 g b. 12 kg 460 g 4. a. 55 kg 280 g b. 2 250 g

1.

c. 59

d. 119

3. 290 g c. 2 kg 680 g

c. 30 ℓ 744 mℓ

c. 1 200 mℓ

d. 2 ℓ 105 mℓ

B B B C B

B C

A 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. 2. a. ii b. D5 3. penalty box 4. a. (2, 1) b. (3, 3) c. (1, 2)

iii.

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 2. a. 25 b. yellow and blue 3. a. 70% b. 20% c. 35%

d. RM360 c. 5

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. 3. 214 cm 2 mm 4. 6. 1 hour 40 minutes 9. 150 mℓ 10. 11. 8 ℓ 540 mℓ 12. 14. 100 cm 8 mm 15.

9 years 10 months RM16 899 5. RM4 320 7. 3 km 450 m 8. a. 180 cm² a. RM12.90 b. 1 150 g 8 km 650 m 13. RM520 92 km 760 m

b. 58 cm

Dengan ini, SAYA BERJANJI akan menjaga buku ini dengan baiknya dan bertanggungjawab atas kehilangannya, serta mengembalikannya kepada pihak sekolah pada tarikh yang ditetapkan.

Skim Pinjaman Buku Teks Sekolah _______________________________________ Tahun

Darjah

Nama Penerima

Tarikh Terima

Nombor Perolehan: ______________________________ Tarikh Penerimaan: ______________________________ BUKU INI TIDAK BOLEH DIJUAL