DIGITAL TEXT BOOK DUAL LANGUAGE MATHS YEAR 4 MIKE POJAN 2020

Fill in the blanks. 5 09 4
×0

2 7 28 0

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

e 3 × 4 822 = f 4 × 9 051= g 6 × 9 730=
h 7 × 5 463 = i 8 × 7 006 = j 9 × 8 142=

2 Calculate mentally. a

5 318 × 10 = b 981 × 100 = c 69 × 1000 =

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

3 Fill in the blanks. b 8 260 c 9 730
a 9 601 ×6 ×7
×3
40 500 33 807
08 003

4 Multiply. b 8× = 73 160
a 5 × 7 362 =

× 7 000 300 60 × 100 5

5 35 000 300 10 8 72 000 320 40

TEACHER’S 43
NOTES

Let's multiply Congratulations to 34 pupils who
will receive a present of 12books
1 each in this Nilam Award.

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

34 × 12 =

Multiply the onesdigit Multiply the tensdigit Add up the products
34
34 34
× 12 × 12 × 12
6 8 34 × 2
68 16 8
+ 3 4 0 34 × 10 + 3 40

408

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

2 67 × 23 =

Multiply theonesdigit Multiply thetensdigit Addup the products

1 1
22 2

67 67 67
× 23
× 23 × 23
201
2 0 1 67 × 3 201 + 13 40
+ 13 4 0 67 × 20
15 4 1

67 × 23 = 1541

44 4.1(ii) TEACHER’S Drill pupils to reinforce the multiplication concept using Diene's block or
NOTES square grid.

3 182 × 45 = Method 2
Method 1
182 = 100 + 80 + 2 18 2
× 45
× 100 80 2
40 4 000 3 200 80 10 2 × 5
5 500 400 10 4 0 0 80 × 5
5 0 0 100 × 5
4 500 3 600 90 8 0 2 × 40
4 500 + 3 600 + 90 = 8 190 3 2 0 0 80 × 40
+ 4 0 0 0 100 × 40
182 × 45 = 8 190
8 19 0

4 603 × 52 = 603 600 1 603 × 2
52 50 603 × 50
Round off 603 and 603
52 to the nearest 600 × 52 Actual
ten to estimate the × 50 answer
answer. 1 206
30 000 + 30 150

31 356

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

603 × 52 = 31 356

5 548 × 73 =

548 × Next, solve
7 using standard
13 22 15 3 written method.
586
4 11 2

0 524

004
548 × 73 = 40 004

4.1 TEACHER’S Carry out quiz activity or mental calculation. 45
(ii), (iv) NOTES http://www.superteacherworksheets.com

6 852 × 99 = 99 is 100

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

= 85 200 – 852 852 × 1 = 852

11 9
4 12 1010

85 200

– 852

8 4 3 48 852 × 99 = 84 348

7 × 80 = 58 160 727

7 × 8 = 56 8 )5 816

7 = 56 ÷ 8 –5 6

Relate multiplication to division. 58 160 21
80 – 16

× 80 = 58 160 56
= 58 160÷ 80 – 56

0

727 × 80 = 58 160

1 Complete the calculations.

a 21 b 5 24 c 3 78
× 26
x 46 × 55
68
12 2 2 0 +5

+ + 6 20 8

6 28 20

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

3 Calculate. b 5 hundreds multiply by 18.
a The product of 95 and46. d 288 hundreds is multiply 10tens.
c Multiply 34 tens by 9 tens.

TEACHER’S http:www/.superteacherworksheets.com
NOTES
4.1
46 (ii), (iv)

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

5 pupils in a group.

Steps

1 Put 1set 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.

ja l h
e
cg
i
Complete the cross number puzzle.

Across Down k
d
a. 58 × 66 = g. 1360 × 9 = b
b. 232 × 15= h. 466 × 2 =
c. 111× 64=
d. 50 × 1000= i. 72 × = 72 000
e. × 100 = 43 300
j. × 20 = 13460

k. × 42 = 42000

f. 275 × = 27 500 l. 7 × = 59 150 f

TEACHER’S Do exercises or times table quiz to reinforce multiplication skill.
NOTES
4.1 47
(i), (ii)

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 8 280 8 280 8 280 8 280 8 280

Solve 6 × 8 280 =

14

8280
×6

4 9 6 80

Check Check your answer by
adding repeatedly.
8 2 80
+ 8 280 6 × 8 293 = 49 680
The total number of eggs ordered is 49 680.
16 5 60
+ 8 2 80

2 4 8 40
+ 8 2 80

33 120
+ 8 2 80

4 1 4 00
+ 8 2 80

4 9 680

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

48 4.2 (i) TEACHER’S Solve problems using various strategies such as repeated addition.
NOTES 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 30days.

950 × 30 = Check

950 × 21
3
210 0 9 500
750 9 500
+ 9 500
20 0 0 28 500
8 000
950 × 30 = 28 500
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 114chairs for a company.
28 companies place the same number of order. What is the total
number of chairs ordered?

TEACHER’S http://www.youtube.com/watch?v=jwMmCYRNpTs
NOTES
4.2 (i) 49

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

2 Calculate.

a 3 × 2 121= b 5 × 6 018= c 8 × 7 109 =
f 664 × 94 =
d 42 × 33 = e 82 × 60 = i 53 × = 53 000

g 174× 100= h 78 × 1000 = l × 30 = 8 940

j × 1000 = 92 000 k 4 × = 8812

3 Findthe product of the underlined digits on the cards below.
4 756 3 194

4 In the calculation on the right, the 543
answer 4 344 is incorrect. Correct × 62
the mistake in the calculation.
1 086
+ 3 2 88

4344

5 Solve.

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

reams of paper produced in 15days.

b. TheHeathrow Airport, London receives 7 926 passengers every
hour. Find the total numberof passengers in 5 hours.

Source: Airport Council International

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

d. A supermarket places an order of 1000 boxes of cerealbiscuits.
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
kefahaman murid.
2.3 (i) NOTES
2.4 (i)
50

5 School
DIVISION

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

How many bags are distributed to each school bookshop?

39 630 ÷ 3 = Division Guide
1.Divide ten thousands digit
13 210 2. Divide thousands digit
3. Divide hundreds digit
3 )3 9 6 3 0 4. Divide tens digit
5. Divide ones digit
–3
09 INFORMATION

–9
06

–6
03

–3
00

–0
0

39 630 ÷ 3 = 13 210

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

5.1 (i) TEACHER’S Emphasise the steps of division in detail. 51
NOTES http://fivejs.com/math-strategies-multiplication-division-video-tutorial

2 50 475 ÷ 6 = 3 78 600 ÷ 100 =
Method 1
8 4 12 Remainder must
be less than the 78 600 ÷ 100= 78600 = 786
6 )5 0 4 7 5 divisor. 100

–4 8 15 Method 2
24 – 12
Remainder 78 6 0 0 . ÷ 10 0 = 786
–2 4
07

–6

3

78 600 ÷ 100 = 786

50 475 ÷ 6 = 8 412 remainder 3

4 93 021 ÷ 1 000 = Check The inverse of division
is multiplication.
93
93 021 ÷ 1000 = 93 remainder21
1000 )9 3 0 2 1
Multiply: Add remainder:
–9 0 0 0
3 0 21 93 93 000
× 1 000 + 21
–3 0 00
21 93 000 93021

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 )15782

e 37 465 ÷ 4= f ÷ 1000 =91 g 87 006 ÷ 8=

2 Calculate mentally.

a 54 210 ÷ 10= b 73 200 ÷ 100= c 5 6013 ÷ 1000 =
÷ 1000= 91remainder 5
d 76 700 ÷ = 767 e ÷ 100= 543 f

TEACHER’S Revise division basic facts using flash cards and objects. Guide pupils to identify

52 5.1(i) NOTES the pattern of 1-digit tables.

Let's divide 752 durians
are packed
1 equally.
Farm orsA ssoc iati on

Build the 16 16baskets
times table
based on1and 1 6 16 752 ÷ 16 =
6 timestables. 1 06 16
2 12 32 47
3 18 48
4 24 6 4 16 )7 5 2
5 30 80
6 36 96 –6 4
7 42 11 2 1 12
8 48 128
9 54 144 – 112
0

752 ÷ 16 = 47

2 6 950 ÷ 30 =

Method 1 Partition 6 950 to Method 2
6 000 + 900 + 50.
200 + 30 + 1
Then, divide one
30 )6 000 + 900 + 50
2 3 1by one.
– 6 000 – 900 – 30
30 )6 9 5 0 0 0 20 remainder

–6 0 200 + 30 + 1= 231

95

– 90

50

– 30

20

6 950 ÷ 30 = 231 remainder 20

5.1 (i) TEACHER’S Guide pupils to build times tables. In the 16times table example, retain the ones 53
NOTES digit in the 6 times table and add the tens digit in the 1and 6 times tables.

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

3 Encik Wahab distributed 34 800 quail eggs equally to

25 customers. Each customer receives quail eggs.

34 800 ÷ 25=

5 6 960 1 392
25
5 )3 4 8 0 0 5 )6 9 6 0
5
25 = 5 × 5 –3 0 –5
48 19

–4 5 – 15
30 46

– 30 – 45

00 10
–0 – 10

0 0

34 800 ÷ 25 = 1 392

Each customer receives 1 392 quail eggs.

4 79 871 ÷ 79 = 1 Add up the
1 0 quotients
Estimate the answer. 1 000

79 871 80 000 79 )7 9 8 7 1
79 80
– 79 000
1 000 871

80 000 = 1000 – 7 90
80 81

1 – 79
2 remainder

1000 + 10+ 1= 1011

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

79 871 ÷ 79 = 1 011 remainder 2

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

54 5.1(i) NOTES

5 24 360 ÷ 12 = 45 155 ÷ 11=

2030 1
4 11 5
24 360 = 2030
12 45 155 = 415
11
1
1
24 360 ÷ 12 = 2 030
Where is the mistake?
6 ÷ 52 =431 Discuss.

÷ 52 = 431 The inverse of division 1
= 431 × 52 is multiplication.
431
22 412 ÷ 52 = 431
× 52

11

8 62

+ 2 1 550

2 2 4 12

6 400 ÷ = In this number sentence, the numbers in
are the same. What is the number?

Divide.

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

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

h 72 009 ÷ 36= i 81048 ÷ 49 = j 96 324 ÷ 64=

5 .1(i) TEACHER’S LaGthi umi deurpidupmilsentogguusenathkeantimjaedsuatalbsliefirsutontduikvimdee.mbahagi. 55
NNOOTTEESS

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

g kr l f

671 155 187 remainder 1034 729 remainder
2 16

y da o n

584 remainder 324 869 1155 1164
5
remainder 3

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

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

25 )8 100 37 )6 921 46 )39974

55 )36 905 64 )73 923 73 )84 972

82 )59 794 90 )93 060 97 )56 653

56 5 .1(i) TEACHER’S Encourage pupils to explore the website www.education.com/worksheets to try out
NOTES 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.

48 000 6th Floor
5th Floor
4th Floor ?
3rd Floor
2nd Floor
1st Floor

Operation Division
Solve
48 000 ÷ 6 =
Check
8 000

48 000 6= 8000

1

8 000 × 6 = 48000

48 000 ÷ 6 = 8 000

8 000 tiles are needed for each similarfloor.

5.2 (i) TEACHER’S Discuss other methods such as the standard written method and number patterns
NOTES to solve problems.

57

2 26 907 soya drink bottles are packed in 24
several boxes. Each box can be filled with bottles
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
1box: 24 bottles
Remainder of soya drink bottles: ? – 2 4 0 0 0 24 × 1000
Number of boxes needed: ? 2 907
26 907 ÷ 24 =
– 2 4 0 0 24 × 100
Why is the number of 507
boxes needed 1122?
– 2 4 0 24 × 10
267

– 2 4 0 24 × 10
27

– 2 4 24 × 1

remainder 3 1 121

26 907 ÷ 24 = 1 121remainder 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 45730 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?

TEACHER’S Encourage pupils to estimate before calculating the actual answers.

58 5.2 (i) NOTES 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,
Players sticky tape, pencils, paper and a few sets of questions.

3 pupils in 1group (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 ÷ 1000 = 70 remainder ?
d. 40 013 ÷ 5 = 8 002 remainder ?
e. 72 033 ÷ 8 = 9 004remainder?

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.

TEACHER’S Prepare enough question sets for a few groups of players.
NOTES
5.2 (i) 59

2 Solve.

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

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

h 94 567 ÷ 11= i 36 801 ÷ 100= j 90 000 ÷ 1000=

3 Complete the table below.

Number Divisor Quotient
23 385 24
72 050 50
64 1270

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 dayoff on Monday?

b. A flower wholesaler sells 12375 stalks of flowers to 75
florists. What is the number of flowers for each florist?

c What is the number of boxes needed to
pack 56 790 packets of biscuits?
100Packets

d 15680 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 Gunakan blok Diene’s, carta nilai tempat dan kad nombor untuk menjalankan aktiviti
menambah secara berpasangan.
60 5.2 (i) NOTES Banyakkan aktiviti yang melibatkan pengiraan secara mental.

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

6 School
MIXED OPERATION

Addition and subtraction

1

Bus stop 1 Bus stop 2

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

12 + 9 – 6 = Solve the first
operation, then the
1 111 second operation.

12 21
+9 –6

21 15

12 + 9 –6 = 15

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 Guide pupils to master the process involving addition and subtraction based on 61
NOTES real objects or simulation.
Carry out role-play to reinforce pupils᾽ understanding.

2 9 472 – 295 + 68 = 11 Add 9 472 and 68. Subtract295
from the total. Is the answer the
16 9 17 7 same? Explain.
3 6 12

9 472

– 295 + 68

9 17 7 9 2 45

9 472 – 295 + 68 = 9 245

3 74 204 + 12 798 – = 83 901

1 11 6 10 7 + 1– = 8
8– = 8
74 204 87 002
+ 12 7 9 8 –83 901 8 – 8= 0

87 002 3 10 1

74 204 + 12 798 – 3 101 = 83 901

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

1 Calculate.

a 708 + 5 360 – 24 = b 374 + 21213 – 8 635 =

c 8 765 + 10642 – 6 826= d 40 452 – 11023 + 32 005 =

e 10 718+ 29 372 – = 9 390 f – 17624 + 6 378 = 81237

2 15000– + 5 000 =

4 000 10 000 In the number sentence above,
represents the same number. Which of the
6 000
number cards on the left is the value of ?

62 6.1(i) TEACHER’S Use number cards to create mixed operation number sentences.
NOTES 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

3 24 4 × 18 = 6
3
18 3 )72 4 × 18
×4 3

72 –6 = 1
12
4× 6
– 12
1

0 = 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 = 1
2 200 =22
100 22
×6

132

2 200 ÷ 100 × 6 = 132

6.2 (i) TEACHER’S Guide pupils to understand the process involving multiplication and division 63
NOTES based on stimulus.
Drill and practise using number of small values.

2 54 756 ÷ 18 × 11 =

1 8 Build the 18 3 0 42 3 0 42
× 11
1 8 times table. 18)5 4 7 5 6
3 0 42
Add the tens –5 4 +30 420
1 08 18 digits and retain
07 3 3 4 62

2 16 36 the ones. –0

3 24 54 75
4 32 72 – 72

5 40 90 36
– 36

0

54 756 ÷ 18 × 11 = 33 462

3 2 550 × 4÷ = 1020 1000 ÷ = 100
1000 = 100 ×
22 10 200 ÷ = 1020 = 100 × 10

2 5 50 10200 = 1020 × 10 Relate division to
×4 multiplication.

10 2 0 0

2 550 × 4 ÷ 10 = 1 020

1 Calculate. b 18× 1010 ÷ 10=
a 14× 750 ÷ 12= d 26 232 ÷ 6 × 10=
c 2 048 ÷ 8 ×3 = f 100 × 480 ÷ 16=
e 1526 ÷ 14× 11=

2 Complete the following.

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

c × 3 000 ÷ 60 = 1000 d ÷ 10× 80 = 80 000

3 Multiply 62 by 1004. Then, divide the product by 8. What is the answer?

64 6.2 (i) TEACHER’S Drill and practise to complete number sentences.
NOTES Guide pupils to build multiplication times tables.

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

+– = –+ =

10 20 30 40 50 60 70 80 90
In pairs (Player A and Player B)
Players

Steps

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

2 Player Bcompletes the number sentence card based on the answer

card chosen by Player A. 1740 + 15 – 1725 = 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 1to 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 1200 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 21007 – 12007 + 1000= L 68 + 72 – 11=

O 8 000 ÷ 20 × 3= T 12× 300 ÷ 10=

A 3 072 + 1682 – 754 =

TEACHER’S http://www.funbrain.com/cgi-bin/alg.cgi?A1=s&A2=1
NOTES
6.1 (i) 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 theremainders 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.
31480 hibiscus planted on the firstday.

Find The number of hibiscus planted on the second day.

Operation Add, then subtract.

Solve 35 750 + 27 428 – 31 480 =
Check
11 10
2 0 17
35 750
+ 27 428 6 3 17 8
–3 1 480
63 178
3 1 698

11 12
5 2 11
3 1698
+ 31480 6 3 17 8
–27 428
6 3 17 8
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 Guide pupils to identify the key information and build number sentences based on
NOTES the problems given.

2 During Malaysian Food Festival, 80 containers of MALA YSI AN FO OD FES TIVA
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?

MALAYSIANFOOD FESTIVAL

Solve 80 × 250 ÷ 5 =

4 400 0

2 50 2 0 0 0 0 = 4 0 0 0
× 80 5
1
2 0 0 00

2 50

Check 4 0 00 8 0 )2 0 0 0 0

× 5 – 16 0

2 0 0 00 4 00
– 4 00

00

–0

80 × 250 ÷ 5 = 4 000 0

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

Solve.

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

b. A total of 18300 tickets to the Military Tattoo show are divided equally

to 25 schools. Calculate the number of tickets received 24
by 11schools. bean buns

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

6.3 (ii) TEACHER’S Guide pupils to identify the key information based on the problems given.
NOTES Drill on creating number sentences based on the problems given.

67

1 Calculate. b 10012 – 4 609 + 3 815=
a 197+ 2 386 – 5= d 98 250 – 62 054 + 25 898 =
c 71892 + 18543 – 6 799 = f 18832 ÷ 22 × 5 =
e 6 × 5 265 ÷ 9= h 26 780 ÷ 10× 34 =
g 14× 3 806 ÷ 28 =

2 Complete the following. b 1245 – + 312 = 749
a 712+ 430 – = 1000 d 70 × 2 ÷ = 14
c 64 ÷ 8 × = 56

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?

3 Solve.

a. Berjaya Company buys 1125boxes of 2B pencils. Each box
contains 24 pencils. The pencils are repacked with 5 pencils each.
What is the number of packetsmade?

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 KLSentral 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 11920 grade A chicken eggs and 10750 grade Beggs.
The grade Cchicken eggs are 12300 less than the total of grade A
and grade Beggs. What is the number of grade Cchickeneggs?

TEACHER’S Banyakkan latihan yang merangkumi pelbagai bentuk soalan
untuk mengukuhkan kefahaman murid.
2.3 (i) NOTES
2.4 (i)
68

7 School
FRACTIONS

Recognise mixed numbers and improper fractions

1 There are 1kuih bakar and 1c2utcake.

Pizza Banana Cake

Cheese Cake Kuih bakar

What is the fraction of the kuih bakar ?

1cake 21cake 1 1
2

There is 11kuih bakar. Mixed numbers is written as 112
2 11
2
112is read as
Whole number Proper fraction
one, one over two.

Mixed number
shows the value
of more than 1.

INFORMATION Give other examples
of mixed numbers.

TEACHER’S Carry out the activity of writing improper fractions and mixed numbers.
NOTES
7.1(i) 69
a, b

2 What is the fraction for the cheese cake?

One whole cake is cut

1cake 1cake 41cake into 4 equal parts.

9 parts of a cake is 9 .
4

11 Nine over four is an
improper fraction.

1
4

1 1 1 9
4 4
1 41 14 1
4 14 41 4

4 4

4 + 4 + 1 = 9
4 4 4 4

Improper fraction is a The numerator is
fraction which numerator larger than the
is equal or larger than its denominator.
denominator.
9 numerator
INFORMATION 4 denominator

Give other examples of improper fractions.

7.1(i) TEACHER’S Guide pupils to master the concept of improper fractions by simulation activities
a, b NOTES and diagrams.

70

3 Mixed number and improper fraction.

a 12 11 12
1 22

11 3
2 2

b

23 13
5 5

Mixed number Improper fraction

4 What fractions are represented by A, Band C?

12 3 1ABC 2

44 4 8
4
0 12 3 4 56 7
44 4 4 44 4

Proper fractions Improper fractions

Is 157 a mixednumber?
Discuss.

7.1(i) TEACHER’S Guide pupils to shade improper fractions and mixed numbers on diagrams. 71
a, b NOTES Build a fraction board.

http://www.edhelper.com/math/fractionstg513.htm

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

11 13 11 11 17 11 7 2 1 19 2 1 17
4 8 8 2 8 84 28 48

12

1 List out five mixed numbers and five improper fractions.
2 Write the mixed numbers and improper fractions of the shaded parts.

ab

3 Redraw the diagrams and colour the fractions given.

a 12 b 11
7 4

c 12 d 24
3 5

7.1(i) TEACHER’S Use paper folding technique and matching cards to recognise, say and write
a, b NOTES improper fractions and mixed numbers.

72 http://www.edhelper.com/math/fractions_tg516.htm

Relationship between improper fractions and mixed
numbers

1 Convert 2 1to improper fraction.
2
21 =
2

1+ 1+ 1 = 21 mixed
2 2 number

2 + 2 + 1 = 5 improper
2 2 2 2 fraction

2 21= 5
2

2 Convert 7to mixed number.
3

7=
3

1 23 4 5 6 7 8
3 33 3 3 3 3 3

0 1 2 1 11 12 2 2 1 22
3 3 33 33

7 = 21
33

7.2 (i) TEACHER’S Carry out paper folding activities to help pupils convert improper fractions to
NOTES mixed numbers.

73

3 Convert 95to mixed number.

9 = Use division 16 =
5 operation. 95is 3

1 9 divided by 5. 5 Talk about the
5 )9 mistake made.
3 )16
– 5 is written as 145
4 – 15

1

9 14 16 = 31
5 5 3 5
=

4 Convert 20 to mixed number.
6

20 =
6

3 32 = 32÷ 2
6 6÷ 2
6 )20

– 18 = 31
2 3

20 = 31
63

5 Convert 2 1a4s improper fraction.
2
1 =

4

21 = 1+ 1 + 1
4 4

= 4 + 4 + 1
4 4 4

= 9
4

21 = 9
4 4

TEACHER’S Explain to pupils how to use division to convert improper fraction to mixed number.
NOTES
74 7.2 (i)

6 Convert 3 1to improperfraction.
10

31 =
10

31 = 3 + 1
10 10

= 30 + 1
10 10

= 31
1
0

10 20 30 40
10 10 10
10
4
01 2 3 1
3
10

31 = 31
10 10

7 Convert 4 27to improper fraction.

4 2 =
7
• Multiply 4 by 7.
42 4 × 7 + 2
7 = 7 • Add 2 to the product of
4 and 7.
• Maintain the denominator 7.
28 + 2
= 7

= 30
7

42 = 30
7 7

7.2 (i) TEACHER’S Remind pupils to multiply the numerator and denominator by the same value to get
NOTES equivalent fractions.

75

Materials MSWord.

Steps

1 Execute MSWord 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 = 13 12 = 22 12 = 15
88 55 77

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 9 5 = c 11= d 23 =
4 6 9 10

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

158 pizzas?

76 7.2 (i) TEACHER’S
NOTES

Addition of fractions

1 1 + 2 =
4 4

1 Forfractions with thesame
14 denominators:
1 4 (a) Maintain the denominator.
(b) Add or subtractthe
4
numerators only.
(c) Simplify the answer.

1 + 2 = 3 INFORMATION
4 4 4

2 What is the total of 3 + 2 ?
77

+37 2 =
7

2
7

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

3 + 2 = 5
7 7 7

3 1 + 1 =
2 4

1 + 1 = 3 1 11
2 4 4 2 44

1 + 1 = 3 1
2 4 4 4

TEACHER’S Use paper strips or objects to reinforce pupils’ understanding.
NOTES
7.3 (i) a 77

4 1 + 5 = Multiples of 2, 7
2 7

1 + 5 = 1 × 7 + 5 × 2 2 2 4 6 8 10 12 14
2 7 2 × 7 7 × 2 7 7 14

= 7 + 10 Find the common denominator
14 14 for 7 and 2.

= 17
14

= 13 Is thiscorrect?
14
1 1 1
1 + 5 = 13 3 + 5 = 8 .
2 7 14
Discuss.

5 4 + 2 + 1 =
9 9 9

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

= 7
9

4 + 2 + 1 = 7
9 9 9 9

6 1 + 3 + 1 = Make the denominators the same.
4 8 4

2 + 3 + 2 = 7 1111
8 8 8 8 4444

1 + 3 + 1 = 7 11111111
4 8 4 8 88888888

7.3 (i) TEACHER’S Explain to pupils how to find the Least Common Multiple (LCM)for fractions with
a, b NOTES different denominators.

78

7 1 + 2 + 7 =
2 5 10

1 + 2 + 7 = 1 × 5 + 2 × 2 + 7 Multiples of 2, 5, 10
2 5 10 2 × 5 5 × 2 10 2 5 10

= 5 + 4 + 7 10 2 5 10
10 10 4 10

= 16 6
10 8

16 ÷ 2 = 8 10
10 ÷ 2 5

= 13 1 + 2 + 7 = 13
5 2 5 10 5

Materials A4 paper, ruler, pencil, colour pencil, fraction cards 1+ 3
88

Steps

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

Solve.

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

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

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

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

7.3 (i) TEACHER’S Study the questions before solving them. Solve fractions with the same
a, b NOTES denominators first.

79

Subtraction of fractions

1

How many parts of the cake left?

5 – 1 =
6 6

5 – 1 = 4 4 ÷ 2 = 2
6 6 6 6 ÷ 2 3

5 – 1 = 2
6 6 3

2 What is the difference between 4 and 2 ?
55

4 –2 =
5 5

4 –2 = 2 4 2
5 5 5 5 5

3 6 – 1 – 2 =
7 7 7

0 12 3 4 5 6 1
77 7 7 7 7

6 1 2 3 2 1
7 7 7 7 7 7

– – =

7.4 (i) TEACHER’S Carry out simulation of subtracting fractions using fraction strips to reinforce
a NOTES pupils’ understanding.

80

4 Subtract 14from 78.
7 –1
8 4=
7 – 1 7 1× 2
8 4 = 8 – 4×2
78

= 5– 2 = 5
8 8 8

7 – 1 =
8 4

5 5 – 1 – 1 =
6 3 6

5 – 1 – 1 = 5 –2 – 1
6 3 6 6 6 6

= 5 –2 – 1
6

= 2 ÷2 = 1
6 ÷2 3

5 – 1 – 1 = 13
6 3 6

6 1 –1 – 1 = Multiples of 2, 5, 10
2 10 5 2 2 , 4 , 6 , 8 , 10
7.4 (i)
b 1 – 1 – 1 = 1× 5 – 1 – 1× 2 5 5 , 10
2 10 5 2× 5 10 5 ×2 10 10

= 5 – 1 –10 10 2
1100 is in the
= 2 ÷2 125, 5 and 10
10÷ 2 = times tables.

1 –1 – 1 = 1
2 10 5 5

TEACHER’S Use the Least Common Multiple (LCM)to get the common denominator.
NOTES
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 = 14 – 9 – 3 Multiples of 2, 6, 9
answer is given in 18 18 18 269
the simplest form. 269
= 14 – 9– 3 4 12 18
18 6 18
8
=2 10
18 12
14
2÷ 2 = 1 16
18 ÷ 2 9 18

7 – 1 – 1 = 1
9 2 6 9

Subtract. Give answer in fraction of the simplest form.

a 3 – 1 = b 5 – 4 =
5 5 7 7

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

e 3 – 1 = f 5 –1 =
4 2 9 5

g 6 – 2 = h 5 – 1– 1= 6
7 3 26

i 9 – 2 – 1 = j 2 – 2 – 13 =
10 5 5 99

k 4 – 1 –3 = l 7 8– 1– 1= 4 2
5 4 10

TEACHER’S http://www.edhelper.com/math/fractionsft213.htm
NOTES
82 7.4 (i) b

Addition and subtraction of fractions

1 2 + 3 – 1 =
5 5 5

2 + 3 – 1 = 4
5 5 5 5

2 7 – 3 + 1 =
8 8 4
7.5 (i)
(a)(b) 7 – 3 + 1 = 7 – 3 + 1× 2
8 8 4 8 8 4× 2

= 7 – 3+ 2
8

= 6 6 –2 + 4 = 6 –2 + 4 7
8 77 7

6÷ 2 = 3 = 6– 6
8÷ 2 4 7

7 3 1 3 =0
8 8 4 4 7

– + =

What is the mistake in
the above calculation?

TEACHER’S Carry out simulations using real objects or materials.
NOTES
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 7
10 ÷ 2 5 10

0 1 2 3 4 5 6 7 8 9 10 11
10 10 10 10 10 10 10 10 10 10 10

2 + 7 – 1 = 3 5
5 10 2 5 10

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 12 + 9 Multiples of 3, 4, 6
12 12
346

= 10 – 8 + 9 34 6
12
6 8 12

11 9 12
12
= 12

5 – 2 + 3 = 11
6 3 4 12

7.5 (i) TEACHER’S Guide pupils to understand the concept of addition and subtraction using
b NOTES simulations and diagrams.

84 http://www.education.com/activity/fractions/

Materials Thinker board card Players 4 pupils in a

and stationaries. group.

Steps Think Board Card

1 Each group completes the Concrete material/object

think board card based on Diagram

the topic given by the 11 1 1 Number
teacher. 2 2

2 Demonstrate your work 1 + 1 Topic: sentence
in front of the class. Teacher 2 Add 1+ 1= 11
Fraction
acts as a fasilitator. 22
Story
3 Display your work in the 11
Ali has an apple.

Mathematics corner. 2 His brother has 1a2n apple.

Altogether there are 11a2pples.

1 Solve.

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

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

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

2 Pour the water from container A into
container B.Pour out 3 ℓ4of water
1ℓ A 7 ℓ B from container B. Calculate the
28
volume of water left in container B.
7.5 (i)
a, b 85

Solve the problems

1 Miss Kim bought 45kg of tiger prawns and 7k1g0 of white prawns
at the market. What is the total mass of prawns bought byMiss Kim?

Given Tiger prawns 4 kg.
Find 5

White prawns 170kg.
Total mass of prawns.

Operation Addition
Solve
4 + 7 = 4 kg 7 kg
5 10 5 10

4 + 7 = 8 +7
5 10 10 10

= 8+7 15 ÷ 2 = 3
10 10 ÷ 2 2

= 15 = 11
10 2

45 8
7 10
10

7

10

Check 11 – 7 = 3 –7
2 10 2 10

What is the = 3 × 5 –7
2 × 5 10

difference in mass = 15 – 7
of the two types 10

of prawns? =8 8÷ 2 = 4
10 10 ÷ 2 5

4 + 7 = 11 kg
5 10 2

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

TEACHER’S Get pupils to use picture cards to create stories involving addition and
subtraction of fractions.
86 7.6 (i) NOTES

2 Jainanstdhme21inkihttacohkueersnfo5f6orhrSoc34uiernhtcooeufiern.xiCsehraclMcisuaelt.ahJteeamsthmaetiincdshifefeexlpreesrnchciseeerbmeotwtheeern 5 hour
the time she finishes her exercises and helps her mother. 6

Finishes exercises Helps mother Difference in time

Mathematics: 5 hour 3 hour 4
Science: 1hour6

2

5 + 1 – 3 = hour 21hour
6 2 4

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

= 10 + 6 – 9
12

= 12 7

5 + 1 – 3 = 7 hour 3 hour
6 2 4 12 4

The difference is 7 hour.
12

Solve.

1 12m and 7m10ribbons are used to tie 21m 170m
two boxes. What is the: Zaidi’s
a. total length of ribbons used?

b. difference between the length of ribbons used? 41km house

2 The diagram shows the distance from Zaidi’s A 51km
B
house to the library. Calculate the 3 km
5 Library
difference between the distance of route A and route B.

7.6 (i) TEACHER’S Encourage pupils to use various problem solving strategies such as working
NOTES backwards and making models or tables.

87

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

13 57
22 22

0 1 1 2 3
2
2 Write the improper fractions and mixed numbers for the diagrams

below.

ab

3 Find the value of Q.

0 3 4 1 Q 11
10 5 2

4 Calculate.

a 1 + 1 = b 1 + 23= c 1+ 3 + 1 6 =
3 3 5 24

d 5 – 1 = e 3 – 1 = f 9 – 1– 1= 10
7 7 8 4 52

g 8 + 7–2 = h 5 –1+ 1 3 = i 1 + 5 – 2 3=
9 99 62 4 8

5 Based on the diagrams, calculate the fraction
of the shaded parts.

6 a Asmah uses 3 kg of sugar to make biscuitsand
8

12kg of sugar to make cakes. Calculate the total mass of sugar used.

b Rahmat bought 130kg of red chillies, 1k4g of green chillies and 4 kg5
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
1.25 metres. cm
Recognise decimals 130
129
1 Thirty-eight point five 128
127
degrees Celcius. 126

SPO RT Countries Score

R E C R E A T IO N China 422.30

Wow! Malaysia Her score is three Australia 366.50
won the third hundred and fifty-nine
place! Pandelela point two zero. Malaysia 359.20
won bronze
medal. Source:
http://www.london
2012.com/diving/
event/women-10m/
index.html.

8.1 (i) TEACHER’S Tell stories to pupils based on pictures and activities about decimals. For example,
NOTES long jump scores and mass of objects or volumes of liquid.

8959

2

Zero point one four 1 0.005
three
Three decimal places
0.143
1• 0 05
0.14 0.15
Decimal point
Three decimal places is three digits
after the decimal point. One point zero zero five

INFORMATION

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

Paedocypris Progenetica news/2006/jan/news_7501.html

Seven point nine Seven point nine
hundred zero zero

Who wrote correctly?
Discuss.

• 3 0 90 Form a decimal number with
three decimal places.

90 8.1 TEACHER’S Carry out activity in pairs to guess decimal numbers written in numerals in the air
(i),(ii) NOTES or on pupils’ backs.

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

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

Steps

1 Cut out 1000 squares from a graph paper. Colour the graph paper to
form a pattern.

2 Paste the graph paper onto an A4 coloured paper.
3 Write the coloured parts in decimal.
4 Cross-check each members’ work in the group.
5 Keep in Mathematics file or display your work in the Mathematics corner.

1 State the coloured parts in decimal. c
ab

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

3 Complete the table.

ones tenths hundredths thousandths Number Words

0• 1 0.317 six point two
five
8• 0 4 5

•

• 9.408

8.1 TEACHER’S Form letters or patterns using square papers. Write the decimal values of the
(i), (ii) NOTES shaded and unshaded squares in numerals and in words.

9971

Relationship between fractions and decimals

1 There are 1000 tiles arranged on the wall.27 of them are
red. Convert 2170t0o0decimal.

27 = 27 out of 1000 parts
1000
is 27 3 zeroes
102070= 27 ÷ 1000 1000

0 . 0 27 27 out of 1000 parts

1 0 0 0 )2 7 . 0 00 is 0 . 0 2 7 3 decimal
places
–0
27 00 27 = 0.027
1000
–20 00
7 000

– 7 000
0

2 Convert 2 9 to decimal.
1000

2 9 =
1000

2 9 =2+ 9
1000 1000 1= 1000 1= 1000 9
1000 1000 1000
= 2 + 0.009

= 2.009 2 9 = 2 009
1000 1000
Use place
value chart. = 2.009

ones tenths hundredths thousandths

2• 0 0 9

2 9 = 2.009
1000

92 8.2 (i) TEACHER’S Relate decimals to fractions using MSPowerPoint.
NOTES Explain in detail about the movement of the decimal point when changing fractionsto
decimals.

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