Mathematics Year 4 Textbook DLP

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

Solv e 2 × 600 g ÷ 12 = g Check


100 g 12
× 1 00 g
12 1 200 g
600g 1200 g
– 1 2

× 2 00

1 2 0 0 g – 0 600
– 00
1 200 g
0
2
0
1

2 × 600 g ÷ 12 = 100 g

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 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.
194 13.2 (i) NOTES " Expose various types of Higher Order Thinking Skills (HOTS) questions involving mass.

Solve.

5 kg 280 g 2 kg 50 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 50 g
the same mass on a scale. 2 kg
Calculate the mass, in g,
for 3 boxes of biscuits.

e A packet of flour weighs 980 g less than the Beans Murukku
total mass of the two items on the left. 3 kg 620 g 640 g
What is the mass of the flour?

TEACHER’S 195
NOTES

1 Solve in standard written form.

a 2 kg 400 g + 3 kg 690 g – 1 kg 286 g = kg g

b 8 kg 720 g + 5 kg 685 g – 2 kg 405 g = kg

c 17 kg 360 g – 9 kg 847 g + 8007 g = g

d 20 kg 50 g – 16 kg 700 g + g = 9 kg

e 4 × 6 kg 80 g ÷ 5 = kg g

f 9 × 8 kg 240 g ÷ 6 = g

2 a Reduce 4 295 g from the sum of 5 kg 840 g and 6 kg 960 g.
What is the mass, in gram?

b Divide the product of 7 and 14 kg 240 g by 8.

3 How many grams more is 30 kg than the total mass of two objects
which are 13 kg 960 g and 15 kg 750 g.


4 Solve these problems.
a

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 Mother adds 50 g more of longans into the
basket. Calculate the total mass in kg and g,
2 kg 80 g of the longans if the basket weighs 350 g.

TEACHER’S
NOTES

196

14 School
VOLUME OF LIQUID

Addition and subtraction of volume of liquid

I add 200 mℓ Let me fill up this bottle
of watermelon with watermelon juice.
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 = ℓ mℓ

2 ℓ 600 mℓ 2 ℓ 800 mℓ
+ 200 mℓ – 1 ℓ 500 mℓ

2 ℓ 800 mℓ 1 ℓ 300 mℓ

2 ℓ 600 mℓ + 200 mℓ – 1 ℓ 500 mℓ = 1 ℓ 300 mℓ
The volume left in the jug is 1 ℓ 300 mℓ.

Find the difference in Watermelon juice Watermelon juice Grape
volume between the Juice
watermelon juice and 1 ℓ 500 mℓ 365 mℓ 1 ℓ 200 mℓ
the grape juice.

TEACHER’S Carry out simulation activities using liquid and measuring cylinders.
NOTES
14.1 (i)
197

2 49 ℓ – 13 ℓ 472 mℓ + 8 472 mℓ = ℓ

9 9 10 1 11 × 1 000
4 8 10 0 0 litre millilitre
3 5 ℓ 5 2 8 mℓ
4 9 ℓ 0 mℓ + 8 ℓ 4 7 2 mℓ ÷ 1 000
– 1 3 ℓ 4 7 2 mℓ

3 5 ℓ 5 2 8 mℓ 4 3 ℓ 1 0 0 0 mℓ

43 ℓ 1 000 mℓ = 43 ℓ + 1 ℓ INFORMATION

= 44 ℓ 44 ℓ



49 ℓ – 13 ℓ 472 mℓ + 8 472 mℓ =

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 = mℓ
Convert 4 ℓ 390 mℓ
1 5 15
to mℓ.
3 ℓ 9 0 0 mℓ 4 ℓ 6 5 0 mℓ

+ 7 5 0 mℓ – 2 6 0 mℓ

4 ℓ 6 5 0 mℓ 4 ℓ 3 9 0 mℓ

750 mℓ + 3 ℓ 900 mℓ – 260 mℓ = 4 390 mℓ

In the number sentence above, convert
3 ℓ 900 mℓ to mℓ. Then, solve it. Is the
answer the same?

How do you fill up 9 ℓ of water

into the green container using

both the red and blue pails?

Explain.
12 ℓ 15 000 mℓ

TEACHER’S Guide pupils with mechanical questions in short sentences using vocabulary which
means add and subtract.
198 14.1 (i) NOTES

http://www.primaryresources.co.uk/maths/docs/Capacity_Problems_Y4.doc

Materials Players
4 pupils in a group.
4 sets of volume cards, task cards,

A4 paper.

Steps A 2 ℓ 720 mℓ B 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: Pupil 2:
a. Add the volumes of Card A and Card B. a. Subtract the volume of Card A from Card B.
b. Subtract the volume of Card C from b. Add the answer in a to the volume of
Card C.
the answer in a. c. Write the number sentence and the answer.
c. Write the number sentence and the answer.

Pupil 3: Pupil 4:
a. Add the volumes of Card B and Card C. a. Subtract the volume of Card C from Card A.
b. Subtract the volume of Card A from b. Add the answer in a to the volume of
the answer in a. Card B.
c. Write the number sentence and the answer. 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. mℓ
mℓ
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
d 12 ℓ 198 mℓ – 10 ℓ 662 mℓ + 22 ℓ 464 mℓ = ℓ

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

199

Multiplication and division of volume of liquid

Each bottle holds I transfer equally
1 500 mℓ of honey. 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

1 750 mℓ

1 500 mℓ 6 ) 4 500 mℓ

×3

4 500 mℓ – 4 2
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 Convert 12 ℓ 800 mℓ
to mℓ.
5 × 12 ℓ4 800 m ℓ = 5 × 12 800 mℓ
4
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 Emphasise that answers must be given in units required.
NOTES 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
836 mℓ
14 ) 87 ℓ 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 = ℓ mℓ

33 ℓ 80 mℓ 1
0 mℓ
25 ) 827 ℓ 33 ℓ 80 mℓ
+ 2 000 ×2
– 75 2 000
77 66 ℓ 160 mℓ
– 2 00
– 75 00
2
–0
0

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 Get pupils to create stories based on division number sentences. 201
NOTES

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

4 565 mℓ Half the volume of C 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 O 6 × 12 ℓ 300 mℓ ÷ 2 E

70 ℓ 600 mℓ ÷ 10 × 12 L 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 1 269 mℓ 84 ℓ 720 mℓ 36 900 mℓ

1 Calculate. ℓ mℓ b 8 ℓ 56 mℓ ÷ 8 × 9 = mℓ mℓ
a 2 × 7 ℓ 930 mℓ ÷ 5 = mℓ d 12 ℓ 640 mℓ ÷ 8 × 7 = ℓ
c 5 × 2 ℓ 884 mℓ ÷ 14 = mℓ f 9 ℓ 100 mℓ ÷ 13 × 50 = ℓ
e 3 × 7 ℓ 602 mℓ ÷ 9 =

2 a Find the product of 10 322 mℓ and 7 divided by 2. State
the answer in ℓ and mℓ.

b What is the volume when divided by 5 and multiplied by 9 gives
the answer 27 ℓ ?

202 14.1 (ii) TEACHER’S Carry out simulation to help pupils answer challenging questions.
NOTES 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?

The volume of tea drank is 27 ℓ 850 mℓ.
Given The volume of tea added is 14 ℓ 600 mℓ.
The volume of tea remaining is 520 mℓ.

The volume of tea drank.
Find

Operation Add, then subtract.

14 ℓ 600 mℓ The volume
27 ℓ 850 mℓ of tea drank

520 mℓ remainder

Solve

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

1 1 4 1 1 450

2 7 ℓ 8 5 0 mℓ 4 2 ℓ 4 5 0 mℓ
+ 1 4 ℓ 6 0 0 mℓ – 5 2 0 mℓ

4 2 ℓ 4 5 0 mℓ 4 1 ℓ 9 3 0 mℓ

1 4 1 1 450
Check
4 1 ℓ 9 3 0 mℓ 4 2 ℓ 4 5 0 mℓ
+ 5 2 0 mℓ – 1 4 ℓ 6 0 0 mℓ

4 2 ℓ 4 5 0 mℓ 2 7 ℓ 8 5 0 mℓ

27 ℓ 850 mℓ + 14 ℓ 600 mℓ – 520 mℓ= 41 ℓ 930 mℓ
The volume of tea drank was 41ℓ 930 mℓ.

14.2 (i) TEACHER’S Guide pupils to draw tables to solve problems. 203
NOTES Guide pupils to estimate the reasonable final answers.

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

Solve 3 × 2 ℓ 750 mℓ ÷ 5 = mℓ

21 1 650 mℓ

2 ℓ 750 mℓ 5 ) 8 250 mℓ
×3
–5
8 ℓ 250 mℓ 32

8 ℓ 250 mℓ = 8 250 mℓ – 30
25

– 25
00

–0
0

Check 32 2 750
22 15
1 650 mℓ
×5 8 2 5 0 mℓ = 2 750 mℓ
3
8 250 mℓ 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 Give other daily situation for problem solving involving division and multiplication.
NOTES

Solve.

a Devaki and Lisa fill up 5 ℓ 350 mℓ and 8 ℓ 950 mℓ soya drink
respectively into a container. 3 500 mℓ soya drink is served to the
guests. What is the remainder, in ℓ and mℓ , the volume of soya drink?

b Sayang Restaurant has 18 ℓ 50 mℓ olive oil. After consuming
16 ℓ 180 mℓ, an amount of 12 ℓ is added to the stock of oil. What is
the volume of olive oil, in ℓ and mℓ, in the restaurant?

c 3 ℓ 75 2 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



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 Give more standard UPSR questions involving volume of liquid. 205
NOTES

1 Calculate. mℓ
a 3 ℓ 201 mℓ + 54 ℓ – 18 ℓ 127 mℓ = ℓ mℓ
b 16 ℓ 672 mℓ – 998 mℓ + 44 ℓ 326 mℓ = ℓ
c 40 ℓ 765 mℓ + 13 ℓ 478 mℓ – 23 ℓ 499 mℓ = ℓ
d 2 × 4 ℓ 210 mℓ ÷ 4 = ℓ mℓ
e 12 ℓ 105 mℓ ÷ 15 × 3 = mℓ
f 8 ℓ 75 mℓ ÷ 5 × 7 = ℓ

2 Calculate.

a Reduce 10 ℓ 326 mℓ from the sum of 674 mℓ and 18 ℓ 78 mℓ.
Give answer in mℓ.

b Divide 29 ℓ 848 mℓ by 8 then multiply by 7. Give your answer in ℓ and mℓ.

3 Solve.

a Gobind buys 8 tins of diesel. The diesel is distributed 5 ℓ 130 mℓ
equally among him and 8 workers for the lawn
movers. What is the volume, in ℓ and mℓ,
received by each person?

b A total of 25 ℓ 500 mℓ milk from Bagus Farm and
20 ℓ 880 mℓ from Jaya Farm was collected by Encik Bakri.
He sold 43 ℓ 150 mℓ of milk. Calculate the volume of milk left,
in ℓ and mℓ.

c 3 jugs of orange juice with the volume of 2 ℓ 800 mℓ each is
poured equally into 7 bottles. What is the volume of orange juice,

in mℓ, for each bottle?

TEACHER’S

NOTES
206

15 Sekolah
SPACE

Recognise angles A triangle has
3 sides and
1 A rectangle has 4 sides. 3 angles.

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 An obtuse angle is bigger
there in the shapes above? than a right angle.

Right angle Acute angle Obtuse angle

oAfofrramig rheedtcataan tngtghleleei.s corne r tAhnana cautreigahnt galnegilse.smaller

2

Look at my arm.
What type of angle
is formed?

Right angle

TEACHER’S " Encourage pupils to recognise angles for basic shapes found at a preschool
NOTES playground or the reading corner.
15.1 (i)
207

Materials A4 paper, pencil, ruler and scissors.

Steps

1 Fold a sheet of A4 paper 2 Mark the right 3 Draw a line as in the
picture and cut it.
into two equal parts. angle.

Right Right
angle
angle
Can a right angle
be formed from this
paper? Explain.
4 Mark the acute angle Obtuse
angle
and the obtuse angle

on both paper cuttings. Right Acute
angle
Label them. angle

5 Paste the paper cuttings

in your exercise book.

1 How many angles are there in each diagram?

a b c

2 Name the angles found in the following shapes.
a b c

208 15.1 (i) TEACHER’S " Use the Geoboard to form various basic shapes and relate them to angles.
NOTES

Recognise lines

Parallel lines

Look at side a and side b a
which are opposites on the
white board. The distance 1.4 m The same distance 1.4 m
between the two is the
same. Both of these lines b
are parallel lines.

30 cm 30 cm 30 cm Both of these racks 0.6 m
show examples of
parallel lines.

30 cm 30 cm 30 cm 0.6 m

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

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

TEACHER’S " Encourage pupils to tell stories about objects or places which have a lot of
NOTES parallel lines.
15.2 (i)
a 209

Perpendicular lines b

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

Which parts of this door
are perpendicular lines?


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

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 Draw a draughtboard Draw hopscotch

210 15.2 (i) b TEACHER’S " State 10 objects in the classroom that have perpendicular lines.
NOTES

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

h

1 Count the number of perpendicular lines in the following shapes.

a b c

d e f

2 Redraw and mark: b blue lines for perpendicular lines.
a red lines for parallel lines.

15.2 (i) TEACHER’S " Prepare exercises as in questions 2(a) and (b) in the worksheets. 211
NOTES http://www/superteacherworksheets.com

Perimeter

Mummy, what is 3
the length of the
1

lace that you used?

I use the lace 33
according to the

length around the

pillow case.

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

3 4 cm
2 4 cm 3 cm B

A is a rectangle 5 cm

6 cm A aanngdl eBdistraiar nigghlet.


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 http://www/superteacherworksheets.com/geometry/perimeter-3_TZFFD.pdf
NOTES

4 Find the perimeter of the hexa gon.
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.

6 cm 10 cm 12 cm

8 cm 12 cm Multiplication
is repeated
Perimeter = 6 cm + 8 cm + 10 cm 12 cm addition.
= 24 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 c d

12 cm 13 cm 15 cm

T hesleid negitsh5 ocfmea ch 5 cm The length of each

8 cm side is 4 cm

15.3 (i) TEACHER’S " Carry out hands-on activities to measure perimeters of triangular and four-sided 213
NOTES objects in the school compound.

Area The area of 1 unit

1 square is 1 square

1 unit unit. It is written
as 1 unit2.
1 unit 1 unit2

INFORMATION The area of the red
rectangle is 6 square
The area of the orange square is 4 square units. units.
Area = 4 units2 Area = 6 units2

Length

Width 3 cm

Area = 15 units2 5 cm
2 Find the area of the checkerboard.
Area = Length × Width
= 5 cm × 3 cm

= 15 cm2

The area of each square of
the checkerboard is 1 cm2.

The area of the checkerboard = cm2

TEACHER’S " Carry out hands-on activities using grid book to measure areas of basic shapes.

15.3 (ii) NOTES http://www.superteacherworksheets.com/geometry/area-1_TWBDW.pd
214

3 Draw a line from 1 square forms
two triangles of the
vertex to vertex. same size.

The area of a triangle is half the area of a square.
4 cm

4 cm Width 4 cm

Length 4 cm

Area = Length × Width Are a = Area
= 4 cm × 4 cm 2
= 16 cm2
= 16 cm2
2

= 8 cm2

4 A re a = Base × Height
2

Height = 6 cm × 8 cm
Base 2
8 cm
6 cm = 48 cm2 It is written as
2
1 × Base × Height.
= 24 cm2 2

5 Are a = 1 × Base × Height
3 cm 2

4 cm = 1 × 3 cm × 4 cm
2

= 12 cm2 = 6 cm2
2

15.3 (ii) TEACHER’S " Emphasise that the height of a triangle must be measured from 215
NOTES the base to the vertex of the triangle that has the right angle.

The perimeter of a rectangle is 48 cm. This
rectangle consists of two squares. What is the
area of the rectangle?



1 Look at the diagrams in the squared grid. Answer the questions.

1 unit

1 unit
A BD

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
9 cm
8 cm 10 cm

d e 7 cm f --------

6 cm 7 cm 5 cm
8 cm 16 cm

3 13 cm P is a square. Find the area,
in cm2, of the shaded part.

P 5 cm

22116 15.3 (ii)
TEACHER’S http://www.charliefrench.com/PDF/Gr4measure2PDF

NOTES

Volume How many cubes are 12 cubes are needed
needed to fill up the to fill up the big box.
1 These small boxes space of the big box? This big box is a cuboid.

are cubes.





1 un it 1 un it Vo lume of cu be =V1oulunmite×=11u2nuint i×ts31 unit

= 1 unit3

1 unit

The volume of a cube is 1 unit The volume of a cuboid
can be determined by
cube. It is written as 1 unit3. This counting the number of
cube is known as cubic unit. cubes filled in it.

INFORMATION

2 1 cm 1 cm Volume of cube = 1 cm × 1 cm × 1 cm

= 1 cm cube
1 cm
= 1 cm3

How do you count

t he n um ber of the

hidden cubes?

There are 8 unit cubes There are 18 unit cubes
Volume = 8 units3
Volume = 18 units3

TEACHER’S " Carry out the activity to find the volume of cube and cuboid using
unit cubes.
15.4 (i) NOTES
217

3 a b

Volume = 27 cubic units Volume = 32 cubic units
= 27 units3 = 32 units3

Length Width Height Volume Length Width Height Volume

(units3) (units3)

3 33 27 4 24 32

The formula for volume of cube or
cuboid is Length × Width × Height.

Try to use the formula of volume INFORMATION
of cube and cuboid to check the
anwers for 3 a and 3 b .

4 1 cm 1 cm height Volume = Length × Width × Height
width = 5 cm × 2 cm × 3 cm
1 cm
= 30 cm3
length

5 Calculate the volume of the box. 20 cm
Volume = 50 cm × 30 cm × 20 cm 30 cm
= 30 000 cm3
50 cm
Can volume be calculated by multiplying
the area of base by height? Discuss.

218 15.4 (i) 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 c

unit cubes. unit cubes. unit cubes.
Volume = units3
Volume = units3 Volume = units3

2 Calculate the volume of the diagrams.

a b c d

4 cm 10 cm 8 cm 12 cm
4 cm 10 cm

4 cm 2 cm 15 cm
8 cm

10 cm

3 cm

3 Calculate the volume of the cube and cuboid.



4 cm

5 cm 8 cm
10 cm

15.4 (i) TEACHER’S http://www/superteacherworksheets.com/geometry/volume-cubes-1_TZWBB.pd.
NOTES 219

1 Draw and mark the angle on the diagram. Fill in the blanks.

Right angle Acute angle Obtuse angle A
A

2 Copy and draw: b perpendicular lines.
a parallel lines.

3 The perimeter of rectangle X is the same as the perimeter of square Y.

a Find the perimeter of diagram X. 5 cm Y
b Find the length of the sides of X
diagram Y. 3 cm
c Find the areas of the diagrams
X and Y.

4 The surface area of A is 48 cm2. A
Find the volume of this cuboid. 3 cm

5 The perimeter of the surface B is 16 cm.
B Find the volume of this cube.

6 The length of the side of square B is 4 times

of square A. How many times is the area B

of B compared to A? 2 cm A

TEACHER’S

NOTES
220

16 School
COORDINATES

Recognise position

1 The picture shows the positions of pupils of 4 Bijak.

The pupil Farah Siva May Ros Izam
in the fifth
column, row Yes,
two, are you
a new pupil? Ika Amit Shah Joseph Muaz teacher.

Wong Ain Yee Adam Nina

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 " Discuss the positions of other objects. Encourage pupils to surf the Internet to see the 221
NOTES " 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

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) TEACHER’S " Use paper foldings, tiles or grids to create square grids to show the positions
NOTES of the objects.
" 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
5

4 Bishop Knight
Pawn Castle
3

2

1

ABCDEFGH

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 is located at H3.

What can you see at E2, F4 The position of an
and B7? Discuss. object is stated by
the column first
followed by the row.

INFORMATION

16.1 (ii) TEACHER’S " Guide pupils to say locations at the horizontal axis first then at the vertical axis.
NOTES Relate the locations of objects in daily life such as seatings in a cinema.

223

The princess wants 6
to fin d he r sho e with 5
4
the condition that the 3
number of movements 2
at the horizontal axis 1
and the vertical axis are 0 1 23456
the same. What is the
colour of her shoe?

Materials MS Word Players 4 pupils 5

Steps 4

1 Each group choose a theme. 3

2 Execute MS Word. 2

3 Choose Insert Table (4 × 5 table). 1 B CD
Type the letters at the horizontal A
axis and numbers at the vertical axis. Animal
Position
4 Choose the graphics of animals from
Clip Art. Copy and paste in the

squares.

5 Create another table under the
animal grid. Complete the table.

6 Print and check your work.
Display at the Mathematics corner.

224 16.1 (ii) TEACHER’S " Diversify exercises, activities or games to recognise the positions of
NOTES objects in or outside the classroom.

Tourist attraction places in Malacca
4

3

2

1

A B C D E

Key: Crocodile Mini A Famosa
Farm Malaysia
Butterfly
Garden

Malacca Stadthuys Samudera Independence
Zoo Building Museum Memorial

Complete.
a The Independence Memorial is located at the same row as and .
b The Crocodile Farm is located at the same column with .
c At location B2 is the .
d D2 is the location of a historical building called .
e is located at A4 and is located at E3.

TEACHER’S 22255
NOTES

Determine the position

Cameron Highlands
Strawberry
5 Farm Museum and Tea
Gallery Plantation

4 Vegetable Cactus Flower
Farm Valley Garden


3
Bee Apiary


2

1

A B C D E

What is the location of the The Bee Apiary
Bee Apiary based on the is at A3.
horizontal and vertical axes?

Where are the Strawberry Farm

a nd 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.

16.2 (i) TEACHER’S " Relate the situation in the picture with the positions of the objects.
226 NOTES " Prepare grid papers and get pupils to draw objects and determine their positions.

The squirrel is searching for food at Pak Ali’s orchard.

5 1 State the positions of the following
fruits:

4 a Ciku b Papaya

3 c Durian d Guava

2 2 The squirrel does not like chillies and
bitter gourds. State the positions of
1 the chillies and bitter gourds.

A BCDE

Letter Grid Card

Players 2 pupils in each group. 5jc f nt
4s k q bz
Materials Letter Grid card (except x), 3d og vl
questions on the position of letters 2r a i ew
using MS Word, A4 paper. 1 pmh yu
Steps

1 Distribute the letter grid A BCDE
card to each pair.

2 Teacher flashes the questions on the position of letters.
Example:

B3 A4 C1 A2 D2
3 Write the letters on an A4 paper based on their positions.

4 Rearrange the letters to form a word.

Example: h o r se

C1 B3 A2 A4 D2

5 The fastest group with accurate answers is given 5 marks.

6 Repeat steps 2 to 5.

7 The group with the highest score wins.

TEACHER’S " Diversify game methods based on creativity.
NOTES
16.2 (i)
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.

1 d State the shapes seen at the
locations:

A B C D E F i B1 ii D4 iii A3

2 Answer these questions based on the grid.

5 a Choose a method how you would
4 explain the location of .

3 i First the digit 5 followed by the letter D.
2 ii First the letter D, second the

1 digit 5.
A B C D E F b State the location of .

3 56 a el o Look at the locations of the letters
in the grid. Answer this riddle:
4t y Which box cannot be lifted?

3b x E1 D6 B2 A6 D5 B4 G4
2n

1p

A B C D E F G C3 F5 G2

4

4 3 State the coordinates of these objects:

2 a b c

1

0 1 234

22228 TEACHER’S
NOTES

17 School

RATE KANCIL BOOk STORE SPECIAL OFFER

Rates SPECIAL OFFER PINTAR BOOKSTORE

1

I want to buy 6 pens.
Which is cheaper?

Kancil Bookstore Price at
RM0.75
The price of a p en Kancil Bookstore:

2 ) RM1.50 is RM0.75.

– 0 6 × RM0.75 =

15 4 3
RM0.75

– 1 4 × 6

10 RM4.50

– 10

0 RM0.75 × 6 = RM4.50

Pintar Bookstore Price at

RM0.60 The price of a p en Pintar Bookstore:

3 ) RM 1.80 is RM0.60. 6 × RM0.60 =

– 0 3
RM0.60
18

– 1 8 × 6

00 RM3.60

– 0

0 RM0.60 × 6 = RM3.60

The price of at Pintar Bookstore is cheaper, RM3.60.

17.1 (i) TEACHER’S Carry out simulation activities like buying and selling. Inculcate 229
NOTES 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

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
0 264

The number of passengers carried by 6 buses

is 264 persons.

b How many buses are needed to carry 220 passengers?

44 passengers 1 bus
220 passengers 220 ÷ 44

5 220 ÷ 44 = 5 buses

44 ) 220

– 220
0

220 passengers

5 buses are needed to carry 220 passengers.

How many buses are needed to carry
110 passengers? Discuss.

Fazlin wants to buy 12 storybooks for
her friends. Help her to spend wisely.


2 books 3 books
RM15.00 RM21.60

230 17.1 (i) TEACHER’S Diversify questions involving money, time and units of measurement.
NOTES 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 100 g
1 marble 100 g ÷ 20
5
5g
20 ) 100 7 × 5 g = 35 g

– 100
0

1 marble
7 marbles

The mass of 7 marbles is 35 g.

What is the mass, in g of 25 marbles of
the same size? Discuss.

4 180 km ? km

AB 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 ÷ = km

3 hours × km = km

The distance from Town B to Town C is km.

17.1 (i) TEACHER’S Guide pupils to find a value involving unitary. Pose various types of questions
NOTES 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:

What is the mass of 24 cm 6 boxes 600 paper clips
7 similar balls? 4 boxes ?
Find the length of
5 similar squares.

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 20 pieces 240 g
50 sen coins of the same size?

c A car can travel for a distance of 112 km by consuming 7 ℓ of petrol.
What distance can it travel with 10 ℓ of petrol?

d In an evening, the shadow of a 30 cm plant is 60 cm. What is the
length of the shadow of a 45 cm plant?

TEACHER’S Prepare enough sets of cards for pupils. Customise activities according to pupils’
creativity and ability.
232 17.1 (i) NOTES

Hasrul lost in a garden. Find the way out by colouring the answer for each
question in order.

START RM1.20

RM1.50 RM31.50 RM32.40 8 pieces

10 pieces 9 pieces

205 words 196 words 182 words

4 envelopes 250 mℓ R

2 500 mℓ 5 envelopes 2 050 mℓ

P Q
Hasrul’s way out is at
.

a b c

10 units RM1.50 5 kg RM17.50 12 m 3 pieces
9 kg 40 m pieces
8 units

d 15 minutes 420 words e 120 stamps 6 envelopes

7 minutes words 100 stamps envelopes

f 4 glasses 1 ℓ

10 glasses mℓ

TEACHER’S 233
NOTES

1 Solve. b c
a
45 cm

4 books 3 packets of sweets
cost RM30 weigh 900 g

How much does Find the mass of Calculate the
3 books cost? 7 packets. height of 4 boxes.

2 Solve.

a 8 children have 336 stamps. Each person has an equal number
of stamps. Calculate the number of stamps for 9 children.

b The total number of paper clips in 7 boxes is 455. Each box
contains the same number of clips. How many paper clips are

there in 5 similar boxes?

c A tank was filled with tap water at the rate of 90 ℓ per 15 minutes.
Calculate the volume of water, in mℓ, filled in 2 hours.

d Printing Machine A Printing Machine B
1 hour produces
1 1 hours produces 900 greeting cards
600 greeting cards 2

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

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

234 9.1 (i) TEACHER’S
NOTES

18 School
DATA HANDLING

Recognise and compare information

These are three methods MATHEMATICS CORNER PIE CHART
of presenting data. My Friends’ Storybooks
BAR CHART
PICTOGRAPH Number of books My Friends’ Storybooks Ajol
My Friends’ Storybooks 10%
Akif 10
8 ------- Sarjit Akif
Hui Li 6 --------------------- 30% 40%
4 --------------
Sarjit 2 ---------------------------- Hui Li
0 20%
Ajol
Key: Akif Hui Li Sarjit Ajol
Friends’ names
represents 2 books

Pictograph

1 My Friends’ Storybooks Title
Akif
In a pictograph, pictures are
used to represent data.

Hui Li Picture Akif has 8 storybooks.
Sarjit 2 + 2 + 2 +2 = 8
Ajol 4×2=8

Key: Hui Li has storybooks.
represents 2 books

Key × =

18.1 (i) a Who has the most number 235
18.2 (i) a of storybooks?

TEACHER’S " Emphasise that pictures must be appropriate with the title of the pictograph.
NOTES http://urbrainy.com/get/1507/interpreting-pictograms-6273

2 Complete the table.

The Sales of Mangosteens for 4 Days Day Number of Mangosteen
Monday
3 × 10 = 30

Tuesday 5 × 10 = 50

Monday Tuesday Wednesday Thursday Wednesday 3 × 10 =
Key: represents 10 mangosteens
Thursday 2 × 10 =

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 TEACHER’S " Use various types of pictographs to retrieve information and create questions.
18.2 (i) a NOTES http://urbrainy.com/get/2304/more-pictogrms-7825

Bar chart

Vertical axis Musical Instruments Played Title
by a Group of Pupils

Markings 20 ----------------------------------------------------
18
Number of pupils 16 --------------------------
14 ---------------------------------------
12
10 -------------
8
6
4
2

0 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, like to play
the angklung and like to play the piano.

The difference between the number of pupils who like to play the drum
and the piano is .

The total number of pupils is .
10 + 16 + 14 + 20 =

What is the most favourite musical instrument? Why?

18.1 (i) b TEACHER’S " Ensure the distance of each marking is the same. Relate questions to everyday life to
18.2 (i) b NOTES enhance pupils’ understanding.

http://urbrainy.com/get/1508/interpreting-bar-charts-6922 237

Club Attendance of Year 4

Taekwondo

Silat

Robotic

Cultural

0 5 10 15 20 25 30 35 40
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.
Club

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

Materials MS Excel, data set. Players In pairs.
1 2
1 Gather data on the hobbies
of each friend in the class. HoRbebaHideoisnbgobfyPupoilNfs uPomufp4bilesCrerdas
Choose 4 types of 12
hobbies.
Swimming 5
2 Key in data in MS Excel.

3 Highlight data, choose the 3 Hobbies of Pupils of 4 Cerdas
menu Insert and click Column.
Hobbies of Pupils of 4 Cerdas 4
Choose Chart Layout and
click 2-D Column. Hobbies of Pupils of 4 Cerdas

4 Type the title and label the
horizontal axis and the
vertical axis.

5 Discuss the outcomes.

22338 TEACHER’S
NOTES

P ie chart Shida’s Pocket Money
1

Savings Food
30% 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 Nasi lemak
10% 30%

Fried noodles The total percentage
20% of a pie chart is 100%.

Bread INFORMATION

40%

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 TEACHER’S " Relate the percentages of pie chart to fractions. Emphasise the total percentage of a 239
18.2 (i) c NOTES pie chart must be 100%.

" Tell the history of the first pie chart created by William Player in 1801.
http://www.superteacherworksheets.com/graphing/pie-graph-simple-
2_TWNWR.pdf

1 Study the pictograph and complete the answers.

a saves RM2.
SavPinu gpsilsof 4
b saving is the most, which is .

F aiza l c The difference between Faizal’s and

Sivam’s saving is .
A i Lin
d The total savingof the four pupils is .

Si vam

Esha

Key: represents 50 sen

2 Answer the questions based on the bar chart.

Ti me to Answ er a State the time taken to answer the

Time in minute M ath ema tics T est Mathematics test. ii Ho
564000 ---------------------------- ----------------------- ----------------- ------------ ------- i Ina iv Dayang
iii Ajay

30 b Arrange the names in order of speed in

20 answering.

10

0 c The difference in time taken between
Ina Ho Ajay Dayang
Nam e and is 15 minutes.

3 Look at the pie chart and answer the questions.

Typ es of Flow ers in Painti ng a The percentage of jasmine is .

b The and the have the same

Chry sant hemu m percentage.
20% c The total percentage is .
d The percentage of the flowers, excluding
R1o0s% e J a5s0m% ine

Ylan g chrysanthemum is .

20 %

22440 TEACHER’S
NOTES

State the percentage of Gas in the Atmosphere
oxygen in the atmosphere.
Other Gases
1%

Oxygen

Nitrogen
78%

Materials Pictograph, bar chart, Players 4 groups of equal

pie chart , number of pupils.

Steps numbered question cards.

1 Display pictograph, bar chart and pie chart using MS PowerPoint.
Example:

Number of Books Borrowed Pupils’ Hobbies Ways of Going to School
Adam 24
Number of Pupils Bus
Lily --------------------------
Mira 20 ------------- 10% Bicycle
Maria 30%
16 Car
Key: represents 10 books 20%
12
Walking
8 40%

4

0
Reading Internet Swimming Singing
surting
Hobby

2 Put the question cards on the magnetic board. PiWeotfohCtahhstaceihrstpotuohple?ilps ewrcaelknintagge likeIntpoteurrppeneiaelFrstdcinawebdnnhoBdttoaohatgkelhrisekoCd.esbihfetfeaoetrwrwtsehuenorecfenthitnehe

3 The group representative takes the numbered Pictograph
question card in turn and answer the question tnhWuemhliobbrbeaorrryor?fobwosotkhsefrmomost
orally.

4 Pupil who answers correctly is given 5 marks.

5 The group with the highest score wins.

TEACHER’S 224411
NOTES

1 Study the pictograph and answer the following questions.

S ales 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.

Scores of 4 Sport Teams a Green Team collects marks.
b The total score of and
Teams is the same as the score
Blue of Red Team.
Sport Team Red Team needs more
marks to equalise the marks
---------------- of Green Team.
Red

G reen c

Yellow



0 5 10 15 20 25 30

Mark

3 Look at the pie chart. Answer the questions below.

Items Recycled a The percentage of glass and
aluminium tins that are recycled
is .
The percentage of paper that is
recycled is .
Paper The difference in percentage
b between the items most
Aluminium recycled and the least is .

Tins
Glass 45%
25% c

Plastic

10%

22442 TEACHER’S
NOTES

9. A

A Answer the following BC
questions.
State the pair of perpendicular
1. Round off RM53 247.65 to the lines.
nearest ringgit.
10. RM19 620 – RM8 765 – RM437 =

2. 63 days = weeks 11. 10 years 6 months ÷ 9

3. RM70 406.15 + RM16 319 = years months
+ RM782.90 =
12. A B

4. Convert 11 days 4 hours DC
to hours.
State all pairs of parallel lines
5. a. Convert 9 050 m to in the rectangle ABCD.
km and m.

b. Calculate 8 km 40 m ÷ 8. 13. The price of 9 kg of rice is

Give answer in m. RM22.50. What is the price of
7 kg of rice?

6. 14. 14 cm
0 cm 1 2 3 4 5 6
7 cm
State the length of the needle,
in mm.

7. Money RM100 RM50 RM20 5 sen Find the perimeter, in cm.

Number 100 80 7 9 4 cm
(pieces) 5 cm
15.

Calculate the total value of 9 cm

money. Calculate the volume of the

8. Solve: cuboid, in cm3.

6 cm 9 mm 16. 5 ℓ 80 mℓ ÷ 4 × 3 = ℓ mℓ

× 5

243