Mathematics Year 3

2 The table shows the number
of passengers on a train from
Sungai Buloh to Kajang.

Passenger Number

Adult 1 283
Teenager 790

Calculate the difference between adult passengers
and teenage passengers.

1 283 – 790 =

Subtract ones. 1 18
Change 1 hundreds to 10 tens.
1 283
– 790

3

0 11
1 18
1
283
– 790

Subtract tens. 93
Change 1 thousands to 10 hundreds.

Subtract hundreds. 11 3
0 1 18 0
3
1 28
– 79 2.2.1

49

1 283 – 790 = 493

The difference between adult passengers and

Saiz sebentaerenage passengers is 493.

44 TEACHNOETRE’SS • Emphasise that subtraction needs to be done starting from ones place
value followed by tens, hundreds, and thousands.
• Surf www.mymrt.com.my>sbk>route-map. Create questions based on

the information for pupils to solve.

3 8 000 – 1 203 =
Method 1

7 10

8 000
–1 2 0 3

9
7 10 10

8 000
–1 2 0 3

99
7 10 10 10

8 000
–1 2 0 3

6 797

Method 2 8 000 – 1 203 = Subtract 1 from 8 000.
–1 –1 Subtract 1 from 1 203 as well.

7 999 – 1 202 =

7 999
– 1 202

6 797

8 000 – 1 203 = 6 797 Saiz sebenar

TEACHNOETRE’SS • Guide pupils to subtract using representatives such as coloured chips 2.2.1
and abacus.
• Provide exercises involving subtraction using number puzzles. 45

4 4 910 – 1 362 = Subtract 1 362.
Up 4 910. Down 1 thousands.
Down 3 hundreds.

10 Subtract 2 ones, no 10 Subtract 6 tens, lower
lower beads. beads are not enough.

2 8 The big friend of 2 is 8. 6 4 The big friend of 6 is 4.
So, remove 1 tens. So, remove 1 hundreds.
Up 8 ones. Up 4 tens.

Let’s check. 10
8 0 10
SCAN THIS
4 910
The answer is 3 548. – 1 362

3 548

4 910 – 1 362 = 3 548

Think!

Saiz sebenar 4 910 – 1 372 =

2A6B-28 TEACHNOETRE’SS • Surf the Internet to obtain an abacus module that shows examples of 2.2.2
subtraction in detail.
46 • Surf http://www.zapmeta.com.my/video?q=abacus+subtraction

5 2 400 – = 1 970 6 – 891 = 1 305

1 970 2 000 2 400 1 5 –2=3
5 =3+2
– 30 – 400 1 305
+ 891
400
+ 30 2 1 96

430 2 196 – 891 = 1 305

2 400 – 430 = 1 970

Form two numbers 7
using digits 1, 2, 4,

5 and 6. Find the – 3

MMIINNDD largest difference
CCHHAALLLLEENNGGEE between them.

LET’S TRY b 9 425 c 4 086
– 173 – 1 902
1 Calculate.
a 5 134
–5

2 Subtract. b 5 369 − 97 =
a 4 723 − 8 = d 7 000 − 3 028 =
c 5 456 − 670 =

3 Find the answers and fill in the blanks.

a 3 247 − = 1 152 b − 1 309 = 4 04S1aiz sebenar

AB28 TEACHNOETRE’SS • Provide more exercises involving unknowns to enhance pupils’ understanding. 2.2.1
• Guide pupils to use simpler strategies to find unknowns. For example,
2 400 – = 1 970 is simplified to 6 – 1 = 5. So, 6 – 5 = 1 . 47

SUBTRACT SUCCESSIVELY

Buy 12 young plants

There are 2 458 young plants. Buy 103 young plants
1 How many young plants are left?

2 458 – 103 – 12 =

Method 1 2 355 Method 2
2 458 – 12 2 458

– 103 2 343 – 12
2 355 2 446
2458
Method 3 – – 103
103 2 343

+ 12 Is there any other
method to find the
answer? Discuss.

2 458 – 103 – 12 = 2 343

2 343 young plants are left.

Saiz sebenar

TEACHNOETRE’SS • Guide pupils to subtract successively without regrouping first before 2.2.2
proceeding to subtraction by regrouping.
48
• Emphasise that the answer carried forward from step 1 to step 2 must

be the same.

2 4 267 – 29 – 301 =

5 17

4 267
– 29

4 238

3 12

4 238
– 301

3 937

4 267 – 29 – 301 = 3 937

3 7 000 – 167 – 3 481 =

99 4 11
6 101010
3 519
7 000 – 167
– 3 48 1

3 519 3 352

7 000 – 167 – 3 481 = 3 352 Saiz sebenar

2A9B-30 TEACHNOETRE’SS • Guide pupils to subtract successively using data or information involving 2.2.2
business transactions.
49

FUN PROJECT

Tools/Materials whiteboard marker, 2 number sentence cards,
rubber, calculator

Examples of a number sentence card

– –=

––=

Participants pupils work in pairs (A and B)

Method

1 Pupil A chooses one number sentence card.

2 Pupil B writes three numbers using the digits from 0 to 9
on the card. Calculate the answer.

3 Pupil A checks the answer using a calculator. If the number
sentence and answer are correct, pupil B gets 5 marks.

4 Take turns. Repeat steps 1 to 3.

5 The pupil with the highest score wins.

LET’S TRY

Subtract.

a 8729 8729 b 7405 8729
– 61 – 254
– 1 4 – 603

c 5 276 − 38 – 105 = d 6 093 − 815 – 41 =

Saiz seebe8na5r06 − 6 492 – 177 = f 9 000 − 347 – 78 =

TEACHNOETRE’SS • Use laminated number sentence cards for the Fun Project. 2.2.2
• Carry out reinforcement activities such as mathematics quizzes that
50 include a variety of questions.

ADDITION AND SUBTRACTION

1

15 red hats 20 blue hats 3 hats are worn

How many hats are not worn?

15 + 20 – 3 =

Method 1 Add first. Method 2 The answer
Then, is the same.

subtract.

15 35 15 12
+20 –3 –3 +20

35 32 12 32

SCAN THIS

15 + 20 – 3 = 32
32 hats are not worn.

20 +15 Calculate.
–3 Explain how you
get the answer.

TEACHNOETRE’SS • Carry out addition and subtraction activities using objects and simulation. Saiz sebenar
• Emphasise that pupils should solve number sentence in the order of
operations. 2.5.1

51

2 8 728 – 524 + 39 =

Method 1 1 Method 2 – 524

8 728 8 204 8 728
– 524 + 39 + 39

8 204 8 243

8 728 – 524 + 39 = 8 243

3 Look at the following.
9 007 – 215 + 640 =

Method 1 9 Method 2
8 1010
215 9 007
9 007 +640 – 855

– 215 855

8 792
+ 640

Which method is
correct? Discuss.

LET’S TRY

1 Solve these.

a 56 b 6 052
– 300
+12 –27 + 81

c 6 240 + 517 – 389 = d 4 709 − 2 156 + 314 =

2 Complete the following using + and – symbols.

a 3 625 574 89 = 3 140

Saiz sebebnar 6 412 1 302 247 = 7 467

A3B1-32 TEACHNOETRE’SS • Provide more simulation methods involving mixed operations to enhance 2.5.1
pupils’ understanding.
52

CREATE STORIES

1 5 640 + 3 290 = 8 930

There are 5 640 males and 3 290 females
taking part in the National Day poster
drawing contest. The total number of
participants is 8 930.

HAPPY NATIONAL DAY

2 6 240 – 4 800 = 1 440

A factory produces 6 240 boxes of
biscuits. 4 800 boxes of biscuits are
donated to pupils. The number of
biscuits left is boxes.

3 1 050 – 148 + 59 = 961

people ride a train from Johor Bahru to Butterworth.
When the train reaches Kuala Lumpur people get off
and people get on the train. The number of passengers
left after leaving Kuala Lumpur is .

LET’S TRY

Create stories based on the number sentences.

a 6 321 + 869 = 7 190 b 4 000 − 2 115 = 1 885

c 625 + 53 – 120 = 558 d 1 805 − 246 + 72 = 1 631

Saiz sebenar

3A3B-34 TEACHNOETRE’SS • Guide pupils to create stories based on suitable picture cards 2.7.1 53
and number sentences. 2.7.2

• Carry out a story making competition using MS Word.

SOLVE THE PROBLEMS

1 Pandalela has 3 409 Malaysian
postcards and 965 foreign
postcards. Calculate the total
number of her postcards.

Given 3 409 Malaysian postcards
Find 965 foreign postcards

total number of postcards

Method Draw a diagram.

965 foreign
3 409 Malaysian postcards postcards

Total

3 409 + 965 = Check 3 13 6 14

11 4 374
– 965
3 409
+ 965 3 409

4 374

3 409 + 965 = 4 374

The total number of postcards is 4 374.

Saiz sebenar

TEACHNOETRE’SS • Guide pupils to identify important information by underlining it. 2.7.3
• Guide pupils to solve problems by simulation using base ten blocks.
54

2 Dev’s father rears 6 000 catfish.
He sells 846 of the catfish.
How many catfish are left?

Given 6 000 catfish
846 catfish sold

Find number of catfish left

6 000

Method

846 sold Number of catfish left

6 000 – 846 =

99 Check 1 11
5 101010
5 1 54
6 000 + 846
– 846
6 000
5 154

6 000 – 846 = 5 154
The number of catfish left is 5 154.

Saiz sebenar

3A5B-36 TEACHNOETRE’SS • Train pupils to determine operations by identifying the keywords 2.7.3
that mean add or subtract.
• Guide pupils to check their answers by addition or using a calculator. 55

3 A school provides 1 340 bottles of mineral water.
The Parent-Teacher Association (PTA) contributes another
960 bottles. 1 550 bottles of mineral water are given to guests.
How many bottles of mineral water are left?

Method

1 340 bottles of PTA gives 1 340 + 960 – 1 550 =
mineral water another
960 bottles 11 12
Total 1 2 10
Total 1 340
+ 960 2 300
– 1 550

2 300 750

1 550 bottles given Balance 1 340 + 960 – 1 550 = 750
to guests

750 bottles of mineral water are left.

LET’S TRY

Solve the problems.

a In conjunction with Sports Day, a
school ordered 1 420 blue T-shirts
and 968 red T-shirts. What is the
total number of T-shirts?

b 1 580 participants took part in a patriotic song singing
competition. 27 participants made it to the finals. Calculate
the number of participants who did not make it to the finals.

c Table of durian collection Read the table. Airil’s father
sent 1 846 durians to the
at Airil's father's orchard fruit market. Calculate the
durians left.
Durian Number

D24 4 095

Saiz sebenaMrusang King 720

AB37 TEACHNOETRE’SS • Discuss methods such as using analogy to solve problems. 2.7.3
• Provide exercises using question cards to enhance pupils’
56 understanding.

RECOGNISE UNKNOWN The total
number
1 There are 7 fish Father is going to of fish
becomes 10.
in the aquarium. add in some fish.

An unknown is some fish. An unknown is a quantity
7 plus the unknown is 10. that is not specified.

Number sentence 7 + = 10
unknown

2 There are several chicks 5 eggs have just hatched.
under the chicken coop. There are 16 chicks altogether.

An unknown is several chicks.
The unknown plus 5 becomes 16.

+ 5 = 16 Saiz sebenar
unknown
TEACHNOETRE’SS 2.6.1
• Carry out simulation activities to identify the unknown. 2.6.2

57

3 I ate several

cupcakes.

12 cupcakes 9 cupcakes left

Several cupcakes from An unknown is several

12 cupcakes were eaten. cupcakes that were eaten.

12 minus the unknown equals 9.

12 – = 9

12 – r = 9 I can write the
number sentence
12 – ¶­= 9
like this.

4 Read the information

CAR PARK AT and identify the
unknown. Write the
GLOBAL SUPERMARKET
number sentence.

TOTAL NUMBER OF PARKING SPACES ?
NUMBER OF PARKING SPACES OCCUPIED 40
NUMBER OF PARKING SPACES UNOCCUPIED 596

The unknown is .

Saiz sebeNnaurmber sentence

AB38 TEACHNOETRE’SS • Guide pupils to identify the unknown based on stories told or picture cards. 2.6.1
2.6.2
58

LET’S TRY

Identify the unknowns. Write the number sentences.

a

I caught 6 silver
catfish. The rest

are catfish.

There are 11 fishes
altogether.

b Shanti sells a few quail eggs. Then, she
sells another 90 quail eggs. The number
of quail eggs sold is 105 eggs altogether.

c There are several mangoes
in the basket. 4 were eaten
and 14 were left.

d 15 storks are hunting
for fish in the lake.
A few fly away
and 12 are left.

Saiz sebenar

TEACHNOETRE’SS • Guide pupils to identify any unknown through various situations 2.6.1 59
in daily life involving addition and subtraction, such as using objects 2.6.2

in the classroom.

MULTIPLICATION Each box has
12 oranges.
1

What is the total number of oranges in 3 boxes?
3 × 12 =

Method 1 + 12 + 12 + 12 12
12
0 12 24 36 + 12

36

Method 2

tens ones tens ones tens ones

1 2
× 3

3 6

Multiply ones 3 × 2 = 2 × 3.
3 × 2 ones = 6 ones Is

Multiply tens 3 × 12 = 12 × 3?
3 × 1 tens = 3 tens

3 × 12 = 36

Saiz sebenar The total number of oranges in 3 boxes is 36.

60 TEACHNOETRE’SS • Guide pupils to multiply using counters and squared paper to reinforce 2.3.1
their understanding of the multiplication concept.

2 4 × 121 =

hundreds tens ones hundreds tens ones hundreds tens ones

121 121 121
×4 ×4 ×4

4 84 484

Multiply ones Multiply tens Multiply hundreds
4 × 1 ones = 4 ones 4 × 2 tens = 8 tens 4 × 1 hundreds
= 4 hundreds
4 × 121 = 484

3 2 013 × 2 = Estimate to check.

2 000 × 2 = 4 000

2 013 4 026 is nearer
to 4 000.
×2
6 2 × 3 ones The answer is
reasonable.
2 0 2 × 1 tens

0 0 0 2 × 0 hundreds
+ 4 0 0 0 2 × 2 thousands

4 026

2 013 × 2 = 4 026 Saiz sebenar

TEACHNOETRE’SS • Provide more exercises without regrouping to reinforce pupils’ 2.3.1
understanding of the multiplication process.
• Encourage pupils to check their answers using estimation method 61
and calculator.

4 596 × 10 = 5 78 × 100 =

Method 1 Method 1 78

596 × 1 tens = 596 tens × 100

= 5 960 7 800

Method 2 596 Method 2 78 × 1 = 78
× 10 78 × 10 = 780
78 × 100 = 7 800
5 960

596 × 10 = 5 960 78 × 100 = 7 800

6 10 × 1 000 = 7 9 × = 9 000
10
9 × 10 = 90
× 1 000 9 × 100 = 900
1 0 000 9 × 1 000 = 9 000

10 × 1 000 = 10 000 9 × 1 000 = 9 000

MMIINNDD What is the smallest hundreds digit if
CCHHAALLLLEENNGGEE the answer is a four digit number?

12 × 4 =

LET’S TRY

Multiply.

a 40 b 21 c 50 1 d 29
×6 ×10
×8 ×5

e 17 × 100 = f 10 × 35 = g 100 × 80 =

Saiz shebe6na×r = 6 000 i × 902 = 9 020 j 10 000 = × 1 000

AB39 TEACHNOETRE’SS • For multiplication in vertical form, encourage pupils to place larger numbers 2.3.1
on top for easier calculation.
62 • Emphasise the multiplication pattern of any number by 10, 100 and 1 000.

MORE MULTIPLICATION

1

How many books are there altogether?
15 × 3 =

tens ones tens ones tens ones SCAN THIS

tens ones 1 5
3
15 1 5
×3 ×

15 4

Multiply ones Multiply tens
3 × 5 ones = 15 ones 3 × 1 tens = 3 tens
Change 15 ones to 3 tens + 1 tens = 4 tens
1 tens and 5 ones.
Could I add 15 and 30
15 × 3 = 45 to get the answer?

There are 45 books altogether.

Is this calculation 17
correct? Explain. ×5

535

TEACHNOETRE’SS • Guide pupils to use number lines and squared paper to multiply Saiz sebenar
two numbers involving regrouping.
2.3.1

63

2 Number of passangers’ 44 people What is the total
6 × 44 = Syarikat Lim number of pupils
Jalan Damai
Selangor. in 6 buses?

44 people

tens ones Multiply ones
6 × 4 ones = 24 ones
44 24 ones is 2 tens and 4 ones.
×6

24

2 4 Multiply tens
6 6 × 4 tens = 24 tens
4 24 tens + 2 tens = 26 tens
× 4 26 tens is 2 hundreds and 6 tens.

26

hundreds tens ones Multiply hundreds
6 × 0 hundreds = 0 hundreds
22 0 hundreds + 2 hundreds = 2 hundreds

0 44
×6

2 64

6 × 44 = 264
The total number of pupils in 6 buses is 264.

3 109 × 7 =

Method 1 6 Method 2 1 09×

1 09 006 7
×7 703

763 7 63 SCAN THIS

Saiz sebe1n0a9r × 7 = 763

TEACHNOETRE’SS • Guide pupils to multiply using lattice and mental calculation methods. 2.3.1
• Encourage pupils to check their answers using estimation.
64

4 576 × 8 = 5 4 × 2 193 =

× 500 70 6 Multiply according 2 1 9 3
8 4 000 560 48 to the place value. ×
4

12

576 × 8 = 4 000 + 560 + 48 360
= 4 608
400
576 × 8 = 4 608
+8 000

8 772

4 × 2 193 = 8 772

6 Kaswini Adila
Asin

1 21 1 032× 11

1 032 00 1 1 5 1 032
×5 505 0 ×5

6 000 51 60 5 160

Whose answer is correct? Why?

LET’S TRY

Multiply. b 67 c 209 d 2 015
a 30 ×6 ×3 ×4

×2

e 65 × 8 = f 5 × 417 = g 9 × 1 108 = Saiz sebenar

AB40 TEACHNOETRE’SS • Encourage pupils to use times table as a reference. 2.3.1
• Remind pupils about the commutative law in multiplication, that is
a × b = b × a. 65

DIVISION Calculate the number of small stones
in one jar.
1 We put 24 small
24 ÷ 2 =
stones equally into
2 jars. 12

24 12
0 10 20 24

–2 –2 –2–2–2–2–2 –2–2–2–2–2

24 ÷ 2 = 12

There are 12 small stones in one jar.

21 45 ÷ 3 =

1 Divide tens
3 45 4 tens ÷ 3
= 1 tens remainder 1 tens
–3
15 Change 1 tens to 10 ones.
10 ones + 5 ones = 15 ones

15 Divide ones
3 45 15 ones ÷ 3 = 5 ones

–3 45 ÷ 3 = 15
15

–15
0

Saiz sebenar

TEACHNOETRE’SS • Guide pupils to divide numbers without a remainder using object 2.4.1
simulations, diagrams, and times tables.
66
• Guide pupils to construct a 3 times table for an easier division process.

31 628 doughnuts are packed in fours. How many
packets of doughnuts are there?

628 ÷ 4 =

1
4 628

–4
22

Divide hundreds.
Change the
2 hundreds
remainder to 20 tens.

15
4 628
–4

22
–20

28

Divide tens.
Change the 2 tens
remainder to 20 ones.

157

4 628

–4

22

There are 157 –20
packets of 28
doughnuts.
–2 8

0

628 ÷ 4 = 157 Divide ones. Saiz sebenar

TEACHNOETRE’SS • Guide pupils to divide numbers starting with hundreds, followed by tens 2.4.1
and ones.
67

4 2 100 ÷ 7 = Calculate 480 ÷ 6 =
using mental 7 200 ÷ 8 =
Method 1 Method 2 calculation.
Talk about it.
30 0
7 2100 3 × 7 = 21

–21 300 × 7 = 2 100
00
–0
00
–0
0

2 100 ÷ 7 = 300

5 5 045 ÷ 5 = 6 Blue Card Green Card

1 009 9 20 902
5 5045 8 7216 8 7216
– 72 – 72
–5
00 016 01
– 16 –0
–0
04 0 16
–16
–0
45 0

–45 Which calculation
0 is correct?

5 045 ÷ 5 = 1 009

Saiz sebenar

4A1B-42 TEACHNOETRE’SS • Provide questions involving division in the form of games or number puzzles. 2.4.1
• Guide pupils to estimate before calculating the actual answers.
68

7 690 ÷ 10 = 8 8 600 ÷ 100 =

69 86
10 6 9 0 100 8 6 0 0

– 60 – 800
90 600

– 90 – 600
0 0

690 ÷ 10 = 69 8 600 ÷ 100 = 86

9 7 000 ÷ 1 000 = 10 ÷ 10 = 204

7 000 ÷ 10 = 700 2 04 I use
7 000 ÷ 100 = 70
7 000 ÷ 1 000 = ? × 1 0 multiplication.

2 040

7 000 ÷ 1 000 = 7

2 040 ÷ 10 = 204

LET’S TRY

Divide.

a 2 36 b 3 603 c 5 840 d 6 1 200
g 180 ÷ 10 =
e 80 ÷ 4 = f 5 004 ÷ 9 =

h 4 700 ÷ 100 = i 9 000 ÷ 1 000 = j ÷ 100 = 11

AB42 TEACHNOETRE’SS • Guide pupils to check their answers using multiplication. Saiz sebenar
BA 2
2.4.1

69

MORE DIVISION I put 29 pieces
of chalk equally
1 How many pieces of chalk are
there in each box? How many into 3 boxes.
pieces of chalk are left?

29 ÷ 3 =

remainder

29 ÷ 3 = 9 remainder 2
Each box has 9 pieces of chalk.
There are 2 pieces of chalk left.

2 47 ÷ 4 =

remainder

11
4 47

–4
07

–4
3 remainder

Saiz sebenar47 ÷ 4 = 11 remainder 3

TEACHNOETRE’SS • Carry out simulation activities using objects and representatives. 2.4.1
• Guide pupils to use other division strategies such as repeated subtraction
70
according to pupils’ level of understanding.

3 376 ÷ 6 = 4 8 035 ÷ 9 =

62 9
6 376 9 8035
–7 2
–36
16 83
–8 1
– 12
4 25
–
376 ÷ 6 = 62 remainder 4

8 035 ÷ 9 = 9 remainder

5 682 ÷ 10 = 6 7 090 ÷ 100 =

68 70
10 6 8 2 100 7 0 9 0

–60 – 700
82 90

– 80 –0
2 90

682 ÷ 10 = 68 remainder 2 7 090 ÷ 100 = 70 remainder 90

7 8 400 ÷ 1 000 = Solve 5 230 ÷ 1 000.

8
1 000 8 4 0 0

– 8000
400

8 400 ÷ 1 000 = 8 remainder 400 Saiz sebenar

4A3B-44 TEACHNOETRE’SS • Encourage pupils to check their answers using multiplication. 2.4.1

71

8 a 9 768 ÷ 10 = 976 remainder 8
b 9 768 ÷ 100 = 97 remainder 68
What is your c 9 768 ÷ 1 000 =
answer for

c?

Fill in the blanks with the digits given.

5 9 2 3 1 7 remainder 1
3
MMIINNDD
CCHHAALLLLEENNGGEE

LET’S TRY

Divide.

a 2 45 b 3 590 c 7 8 032 d 10 607

e 92 ÷ 5 = f 702 ÷ 8 = g 1 502 ÷ 9 =

h 3 791 ÷ 10 = i 513 ÷ 100 = j 4 300 ÷ 1 000 =

Saiz sebenar

AB TEACHNOETRE’SS • Provide more exercises to reinforce pupils’ understanding. 2.4.1
44
72

CREATE STORIES 3 × 24 = 72

1 Puan Zurina distributed
bags of souvenirs to 3 group
leaders. Each group leader
received 24 bags. The total
number of bags is 72.

2 8 × RM1 000 = RM8 000

8 pupils won the robotic
competition. Each pupil received
RM1 000. The total amount of
money received is RM .

3 There were 675 boxes of food
675 ÷ 9 = 75
distributed to orphanages.
4
3 740 ÷ 100 Each orphanage received
= 37 remainder 40
boxes.

key chains are put into
100 boxes. Each box contains
37 key chains. The remainder
of the key chains are .

LET’S TRY b 7 × 1 000 = 7 000

Create stories.

a 16 × 4 = 64

c 528 ÷ 6 = 88 d 643 ÷ 100 = 6 remainder 43 Saiz sebenar

4A5B-46 TEACHNOETRE’SS • Guide pupils to create stories based on the pictures and number sentences. 2.7.1 73
• Provide suitable keywords to help pupils create stories.

SOLVE THE PROBLEMS

1 Darren’s mother bought 4 boxes of strawberries. Each box
has 15 strawberries. What is the total number of strawberries?

Given bought 4 boxes of strawberries
A box has 15 strawberries.

Find total number of strawberries

Method I draw
pictures.

15 strawberries 15 strawberries

15 strawberries 15 strawberries

4 × 15 = I use repeated
addition to check
2
the answer.
15
×4 4 × 15 = 15 + 15 + 15 + 15
= 30 + 30
60 = 60

Saiz sebenar 4 × 15 = 60

TEACHNOETRE’SS The total number of strawberries is 60. 2.7.3

74 • Guide pupils to solve problems using various methods such as models
and number lines.

• Provide more practise in constructing number sentences orally based on
story cards.

2 Farm Bee Tin’s father Jarjit’s father

Number of 1 670 3 times the number of
cocoa trees trees Bee Tin’s father has

How many cocoa trees are there on Jarjit’s father’s farm?

Method Bee Tin’s father’s farm 1 670

Jarjit’s father’s farm 1 670 1 670 1 670

3 × 1 670 = Check your answer
using repeated
22 addition.

1 670
×3

5 010

3 × 1 670 = 5 010

The number of cocoa trees on Jarjit’s father’s farm is 5 010.

3 Hajar puts 96 packets of dodol equally
into 4 containers. How many packets
are there in each container?

Given 96 packets of dodol Find number of packets of
dodol in each container
4 containers
24
Method 96 packets of dodol 4 96

?? ? –8
96 ÷ 4 = ? 16

– 1 6
0

96 ÷ 4 = 24

The number of packets of dodol in each container is 2S4a.iz sebenar

4A7B-49 TEACHNOETRE’SS • Guide pupils to underline important points and understand the questions. 2.7.3 75
• Guide pupils to solve problems using number lines and encourage them
to check their answers.

4 A factory produces 9 507 bottles of soursop juice So So SoJuuircseop sop op
in one day. 8 bottles are packed in each box. Ju Ju ice ce
How many boxes of soursop juice are there?
What is the remainder of bottles?

Given There are Method 9 507 ÷ 8 = remainder
9 507
1 188
bottles of

juice. Each 8 9507

box has 8 – 8 I check by using
bottles. multiplication.
15

Find number of –8
boxes and 70
remainder
of bottles –64
67

–64

3

9 507 ÷ 8 = 1 188 remainder 3

1 188 boxes of juice are produced. The remainder is 3 bottles.

LET’S TRY

Solve these.

a Rita arranges 18 flowers in a vase. Calculate the total

number of flowers in 6 vases.


b A charity organisation distributes 840 storybooks

equally to 5 orphanages. How many storybooks does

each orphanage get?


c There are 2 008 packets of batteries. Each box has

100 packets of batteries. How many packets of batteries

Saiz sebeanraer not in the boxes?

AB TEACHNOETRE’SS • Working backwards is an easy way to check whether the answers are 2.7.3
49 reasonable or not.
76
• Guide pupils to check the answers of division involving remainders.

RECOGNISE MORE UNKNOWN

1 Each comic has the same
number of pages.
I have read
3 series of Wow! You have
this comic. read 150 pages.

The number of pages for each comic is the unknown.
3 comics times the certain number of pages is 150 pages.
3 multiply unknown is equal to 150.

Number sentence 3 × = 150
unknown

2 There are 100 pieces

several jars of
biscuits in this
box. The total

number of
biscuits is
1 200 pieces.

100 pieces

Several jars is the unknown.

Number sentence × 100 = 1 200

unknown Saiz sebenar

TEACHNOETRE’SS • Carry out simulation activities using story cards to identify the unknown. 2.6.1 77
2.6.2
• Provide a variety of unknown symbols in teaching and learning process.

For example ▲ and ★ .

3 Puan Siti hands out 20 pieces of coloured paper
equally to several pupils. Each pupil receives
5 pieces of coloured paper.

Identify the unknown. Write the number sentence.

Several pupils is the unknown.

20 divided by the unknown is equal to 5.

20 ÷ =5

4 Please distribute all

these food packs Each class

equally to 4 classes will get 30

of year 3. packs of

food.

State the unknown. Write the number sentence.

The unknown is .

Saiz sebenar ÷ 4 = 30

78 AB TEACHNOETRE’SS • Carry out simulation activities to identify the unknown. Encourage pupils 2.6.1
50 to relate the multiplication with division. 2.6.2

MMIINNDD The total mass of
CCHHAALLLLEENNGGEE several similar cakes
is 4 000 g. State the
unknown. Write the
number sentence.

LET’S TRY

Identify the unknowns. Write the number sentences.

a Jamit has several files. He keeps 20 certificates
in one file. There are 40 certificates altogether.

b Mogan’s mother buys a quantity of apples.
She puts 6 apples into each plastic bag and
sells them. She has 30 bags of apples.

c Habsah’s textile factory donated 400 pieces
of batik and pelekat sarong to several
charities. Each charity received 80 pieces.


d 35 schools take part in the
Muafakat Johor Run. Each
school is represented by
a number of pupils. The total
number of pupils participating
in the run is 3 500.

Saiz sebenar

TEACHNOETRE’SS • Guide pupils to identify the unknown based on several situations inside and 2.6.1 79
outside the classroom. 2.6.2

FUN TIME

COLLECT CHIPS

Tools/Materials dice, A4 paper, pencil, 2 markers,
12 red chips, 12 blue chips

Participants 2 players and 1 referee

START 4 032 + 564 = 6 170 + 298 + 79 =
8 034 – 2 157 =
FINISH 4 135 3 473 3 × 819 =
2 180 8 720 ÷ 4 =
Rani has 1 430 stamps. The 6 547 4 596
number of stamps Rani has 1 264 3 783
 
5 877 2 457
is 5 times more than 286 MISS A TURN
Dayang’s stamps. How many 7 150 2 107 6 032 – = 1 897
stamps does Dayang have?

Yap has 1 860 marbles.
Rina has 247 marbles
less than Yap. How many
marbles do they have

altogether?

6 004 – 1 237 – 984 = 1 407 – 208 + 65 =

Method

1 Throw the dice. The first player moves the marker according
to the number on the dice.

2 Answer the question. Show your calculation to the referee. If it is
correct, put a chip on the answer in the middle.

3 If the marker stops on the flower, put a chip on any answer in
the middle.

4 The next player takes his/her turn. Repeat steps 1 to 3. If the marker
stops on a question answered correctly, throw the dice again.

Saiz se 5beTnhaer player with the most chips wins.

80 A51B-52 TEACHNOETRE’SS • Provide copies of the game for pupils. 2.1.1, 21..51..21 , 2.2.1,
• Ask pupils to determine their turns before the game starts. Players 2.2.2, 2.3.1, 2.4.1,
2.5.1, 2.7.3
should take a set of coloured chips and a marker.
• Instil cooperation, honesty, and trustworthiness while playing.

FRACTIONS, DECIMALS,
AND PERCENTAGES

Reduced to
1
2 price

discount The tip of this pen
is 0.7 millimetre.
20%
50%
2
5 price cut

RM100
only RM50

NOTEBOOK

2 of these
5 notebooks
are yellow.

Saiz sebenar

TEACHNOETRE’SS • Discuss fractions, decimals, and percentages shown in the picture above. 3.1.1, 3.2.1 81
• Ask pupils to state several daily situations related to fractions, decimals, 3.3.1, 3.3.2
and percentages.

PROPER FRACTIONS

1 3 of the 4 3 of 4 is
mouses are red. three over four.

Three over four
is written as

3 numerator
4 denominator

3 is a proper fraction.
4
The numerator is smaller than the denominator.

2 4 of the 5 pencils Look at the diagram.
Do the red parts have
are not green. the same fractions?
Discuss.

MMIINNDD
CCHHAALLLLEENNGGEE

LET’S TRY

State the fractions
4 of 5 is four over five. of the balloons:

Four over five is written a red.
as 4 .
5 b blue.

Say other c yellow.

proper fractions. d purple.

Saiz sebenar • Carry out activities of stating various proper fractions from a group of objects

82 5A3B-54 TEACHNOETRE’SS where the denominator is up to 10 using flash cards. 3.1.1
• Explain that the value of a proper fraction is less than 1.

• Surf http://www.mathinenglish.com/worksheetview.php?id=3079&stid

=10020

EQUIVALENT FRACTIONS

The blue parts of the 1 × 2 = 2
3 × 2 6
1 two diagrams have
the same size. 1 1
33

211 1 = 2
6 66 3 6

1 is equal to 2 . These
3 6
are equivalent fractions.

EQUIVALENT FRACTIONS

Two different fractions that have equal value.
1 2
For example, 2 is equivalent to 4 .

2 Is 2 equivalent to 1 ?
10 5

Method 1 1 2 The green parts of these two
10 10 diagrams have the same size.
2 parts of are .

21 1
10 10 10

1
5

Method 2 2 ÷ 2 = 1
10 ÷ 2 5

2=1
10 5

2 is equivalent to 1 . Saiz sebenar
10 5
3.1.2
TEACHNOETRE’SS • Use the same size and same coloured paper to colour parts that make
equivalent fractions. 83

• Reinforce pupils’ understanding of equivalent fractions by simulation using
a fraction kit, paper strips, and transparencies.

3 What is the equivalent fraction of 1 ?
2

Look at the parts FRACTION CHART

1

with the same 2
size as 1 . 1
2 3

21 1

44 4

1 11

5 55

31 1 1

66 6 6

41 1 1 1

88 8 8 8

51 1 1 1 1

10 10 10 10 10 10

Which fraction is 1 = 2 1 = 3 1 = 4 1 =
1 2 4 2 6 2 8 2
equal to 2 ?

The equivalent fractions of

1 are 2 , , and .
2 4

Give examples of
equivalent fractions based

on the chart above.

LET’S TRY

Choose and say the following equivalent fractions.

a2 b4 c3 d 6
9
3 54

4 1 88 46 2 3
6 5 10 88 3 2
6
• Emphasise that to find an equivalent fraction, multiply or divide the 3.1.2
Saiz sebenar denominator and numerator by the same number.
• Explore the number pattern of the numerator and denominator for
84 AB55 TEACHNOETRE’SS equivalent fractions.
• Surf www.mathfox.com/topics/fractions/ for reinforcement exercises.

FRACTIONS IN THE SIMPLEST FORM

1 2 equals 1 .
4 2
2 and 4 can be
Which fraction shows the simplest form? divided by 2.

2 2 ÷ 2 = 1
4 4 ÷ 2 2

1 2 = 1
2 4 2

1 is the simplest form of 2 .
2 4

2 State 3 in the simplest form.
9

3 3 ÷ 3 = 1
9 9 ÷ 3 3

1 3 = 1
3 9 3

3 in the simplest form is 1 .
9 3

3 4 4 1
8 8 2
Simplify .

4 ÷ 4 = 1
8 ÷ 4 2

4 = 1
8 2
Saiz sebenar
TEACHNOETRE’SS • Emphasise that to simplify a fraction, the numerator and the denominator
must be divided by the same number. 3.1.3
• Emphasise that the simplest form of fraction has the smallest value for the
85
numerator and denominator, and can only be divided by 1.

4 There are 10 hula There What is the
hoops altogether. are 4 simplest form
and 6 . of fraction for
each of these
coloured hoops?

a The fraction of is 140. 11 11 4 2
10 10 10 10 10 5
41 1 1 1 1 1
10 10 10 10 10 10 10 1 1
21 1 1 5 5
55 5 5

The simplest form of 4 is 2 .
10 5

b The fraction of is 160. The simplest form

6 6÷ of 6 is .
10 10 ÷ 10

MMIINNDD How many parts should
CCHHAALLLLEENNGGEE Ailee colour so that it is
equal to Dina’s?

Dina Ailee

LET’S TRY

Simplify.

a 2 2÷ b 4 4÷ c 8 8÷
Saiz sebe6nar 6 ÷ 8 8÷ 10 10 ÷

86 AB56 TEACHNOETRE’SS • Surf www.kidsmathtv.com/video-by-topic/fractions-ratios-and-percentages/ 3.1.3
to watch a video of fractions in the simplest form.

IMPROPER FRACTIONS AND
MIXED NUMBERS

1 How many

parts does
this pie have?

one one 11
over four 4

There is one and one over four pie.

One and one over four is written as 1 1 .
4
1
1 4 is a mixed number. mixed number

1 is a whole number. 1 1
4
1 is a proper fraction. whole proper
4 number fraction

There is 1 1 pie.
4

2 There are

2 1 two and one over two
2 chocolate fingers.

Give other examples
of mixed numbers.

Saiz sebenar

TEACHNOETRE’SS • Use various objects such as fraction kits to show mixed numbers. 3.1.7
• Explain that the value of a proper fraction is less than 1 and the value
87
of a mixed number is more than 1.

3 Two hexagons are divided into 6 equal parts.
What is the fraction of 11 parts?

111 11 The numerator
666 66 is larger
111 111 than the
666 666
denominator.

65 11 improper
6 fraction
66

11 parts of 1 is 161.
6
11
6 is an improper fraction.

The fraction of 11 parts is 161.

6 is also an improper fraction. Discuss.
6

4 State 2 2 as an improper fraction.
9

1 12
9 Overlap the transparent plastic.
2 2
9

9 92 20 parts of 1 is 20 .
9 99 9 9
20
9 2 2 = 20
9 9
Saiz sebenar

88 AB57 TEACHNOETRE’SS • Carry out paper folding activities to show the relationship between mixed 3.1.7
numbers and improper fractions.
• Explain that an improper fraction has a numerator larger than or equal to the

denominator.

5 Monday Improper Fractions and Mixed Numbers 4/3/2019

This is an 5 2 21 5 2
improper 3 1 3
fraction. 2

9 2 41 13 2 53
4 5

8 1 1 What can you tell about
7 7 these two fractions?

LET’S TRY

1 Write the mixed numbers and improper fractions.
a b cd

2 2 1 6 3 2 9 1 4 7 14 15
4 6 9 4 5 387

a Say the improper fractions.

b Say the mixed numbers. Saiz sebenar

AB58 TEACHNOETRE’SS • Prepare suitable examples of improper fractions and mixed numbers 3.1.7
involving the denominators up to 10 using shapes for identifying activities.
89

ADDITION OF FRACTIONS

1 1 + 2 = The denominator is
5 5 the same. Just add

1 11 the numerator.
5 55

1 + 2 = 3
5 5 5

21 Add 1 and 1 .
4 4
2
1 + 1 = Simplify 4 .
4 4
1 + 1 = 2
4 4 4
1
4 1 = 2 ÷ 2
2 4 ÷ 2
1
4 = 1
2

1 + 1 = 1
4 4 2

3 4 + = 7 Look at the number line.
9 9
+?
What are two other fractions
7
0 1234567 which give a total of 9 ?
9999999

4+ 3 = 7
Saiz seben9ar 9 9

90 AB59 TEACHNOETRE’SS • Use paper strips, paper discs, transparencies, and picture cards to simulate 3.1.5 (i)
addition. Emphasise that to add fractions of the same denominator, pupils
only have to add the numerators.

4 1 + 1 = Different denominators.
2 4
Look at the fraction chart.

Method 1 Method 2 1 = 2 .
2 4

1 11 1 1
14 44 2 2
2 1 11 11
4 44 44

1 + 1 = 2 + 1
2 4 4 4

1 + 1 = 3 = 3
2 4 4 4

5 1 + 1 = 6 2 + 1 =
2 6 3 6

1 + 1 = 1×3 + 1 The simplest 2 + 1 = 2 × 2 + 1
2 6 2×3 6 form of 3 6 3 × 2 6
4 is 2 .
= 3 + 1 63 = + 1
6 6 6

= 4 ÷ 2 =
6 ÷ 2

= 2 2 + 1 =
3 3 6

1 + 1 = 2
2 6 3
Add these.

1 + 1 = 1 + 3 = 1 + 4 =
2 8 2 10 3 9

Saiz sebenar

TEACHNOETRE’SS • Guide pupils to construct a fraction chart to find equivalent fractions when 3.1.5 (ii) 91
adding two fractions of different denominators. 3.1.5 (iii)

• Emphasise that in order to add two fractions of different denominators, they
must find a common denominator for both.

7 2 + 3 = 3 + 1 =
5 10 4 8

2 + 3 = 2 + 3 3 + 1 = 3 × 2 + 1
5 10 10 10 4 8 4 × 2 8

= 5 ÷ 5 = 6 + 1
10 ÷ 5 8 8

= 1 = 7
2 8

Look at the calculations
above. Which one is correct?

Discuss.

Show the workings 3 + = 7
for this answer. 8 8

MMIINNDD
CCHHAALLLLEENNGGEE

LET’S TRY

Solve these.

a 1 + 1 = b 2 + 4 = c 5 + 2 =
3 3 7 7 9 9

d 3 + 1 = e 2 + 2 = f 3 + 1 =
5 5 3 9 8 2

g 4 + 1 = h 1 + = 5 i 1 + = 7
5 10 8 8 9 9

Saiz sebenar

92 AB60 TEACHNOETRE’SS • Surf https://solvemymaths.com/2015/02/06/adding-and-subtracting- 3.1.5
fractions-worksheet/
• Guide pupils to add fractions of the same denominator involving an

unknown.

SUBTRACTION OF FRACTIONS

1 There are 2 out of 3 parts of a
bread roll. I’m going to take 1 part.

What is the remaining part
of the bread roll?

2 – 1 = The denominator
3 3 is the same.
Just subtract
2 – 1 = 1
3 3 3 the numerator.

The remaining part of the bread roll is 31 .

2 Subtract 3 from 7 . 4 ÷ 4 = 1
8 8 8 ÷ 4 2
Simplify the
7 – 3 = answer.
8 8

7 7 – 3 = 4
8 8 8 8

= 1
2
7 3 1
8 – 8 = 2

3 What is the difference between 4 and 6 ?
7 7

6 – 4 = 0 1234567
7 7

7777777

– 4 6 – 4 = 2
7 7 7 S7aiz sebenar

AB61 TEACHNOETRE’SS • Emphasise that to subtract fractions of the same denominator, pupils 3.1.6 (i) 93
should subtract the numerator only.

• Surf www.superteacherworksheets.com/fractions-subtracting.html
• Emphasise that answers must be written in the simplest form.