DIGITAL TEXT BOOK DUAL LANGUAGE MATHS YEAR 4 MIKE POJAN 2020

Solve the problems

The picture shows the mass of a bunch
of rambutans and a watermelon. The mass of
the bunch of rambutans is 2 kg 500 g. The
mass of the pomelo is 1 kg 750 g lighter than
the watermelon. Calculate the total mass of the
bunch of rambutans and the pomelo.

Given A bunch of rambutans is 2 kg 500 g, the watermelon is 3 kg,
the pomelo is 1kg 750 g lighter than the watermelon

Find Total mass of the bunch of rambutans and the pomelo

Operation Addition and subtraction I draw a diagram.
Then, I calculate.
Total
2 kg 500 g
3 kg

1kg 750 g ?

Solve 2 kg 500 g + 3 kg – 1kg 750 g= kg g
Check
2 kg 5 0 0 g 1410
+ 3 kg 0 0 0 g 4 150 0

5 kg 5 0 0 g 5 kg 5 00 g
– 1 kg 750 g

3 kg 750 g

25 0 0 g 14
+ 30 0 0 g 4 4 10

55 0 0 g 5 500 g
– 1 750 g

3 750 g

3 750 g = 3 kg 750 g

2 kg 500 g + 3 kg – 1kg 750 g = 3 kg 750 g
The total mass of the bunch of rambutans and the pomelo is 3 kg 750 g.

TEACHER’S Guide pupils to solve problems by making tables or mantic reasoning.
NOTES
13.2 (i) 193

2 Nani’s mother bought 2 boxes of raisins. Nani gave the 600 g
raisins equally to 12 friends. What is the mass of raisins
each person got, in gram?

I draw a picture.

600 g 600 g

Solve 2 × 600 g ÷ 12= g Check

600g 10 0 g 12
×2 12 1 2 0 0 g × 10 0 g

120 0 g – 12 12 0 0 g

00

–0

00 600
–0
1200 g
0
2

1

2 × 600 g ÷ 12= 100 g

The mass of raisins for each person is 100 g.

If Nani shares 1200 g of raisins with 5 friends, whatis 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 = 14700 g b 8 kg 400 g ÷ 7 × 4 = 4 800 g

194 13.2 (i) TEACHER’S Guide pupils to solve problems by trying a simpler case and working backwards.
NOTES Simulation can be done in groups.
Expose various types of Higher Order Thinking Skills (HOTS)questions involving mass.

Solve.

5 kg 280 g 2 kg 50g

a. Puan Hayati cooked 1kg 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 10pupils. What is the mass of green beans
each pupil gets?

P R
Q

c

1kg 200 g

The mass of cake Pis 1kg 100 g heavier than cake Q. While the mass
of cake Ris 700 g lighter than cake P.
i Choose the correct number sentence to find the mass of cake R.

1kg 200 g + 1kg 100 g –700 g 1kg 200 g – 1kg 100 g + 700 g

ii What is the mass of cake Rin 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 – 1kg 286 g = kg g

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

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

e f20 kg 50 g – 16 kg 700 g + g = 9 kg

2 a 4 × 6 kg 80 g ÷ 5 = kg g
9 × 8 kg 240 g ÷ 6 = g

Reduce 4 295 g from the sum of 5 kg 840 g and 6 kg 960g.
What is the mass, in gram?
b Divide the product of 7 and 14kg 240 g by 8.

3 How many grams more is 30 kg than the total mass of two objects
which are 13kg 960 g and 15kg 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 1container?

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.

1ℓ 500mℓ

Thank you, father.

3ℓ
3ℓ

1ℓ 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 – 1ℓ 500 mℓ

2 ℓ 800 mℓ 1ℓ 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 1ℓ 500 mℓ 365 mℓ 1ℓ 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 8 100 0 litre millilitre
3 5 ℓ 5 2 8 mℓ
4 9 ℓ 0 mℓ + 8 ℓ 4 7 2 mℓ ÷ 1000
– 1 3 ℓ 4 7 2 mℓ

3 5 ℓ 5 2 8 mℓ 4 3 ℓ 10 0 0 mℓ

43 ℓ 1000 mℓ = 43 ℓ + 1ℓ INFORMATION
= 44 ℓ

49 ℓ – 13 ℓ 472 mℓ + 8 472 mℓ = 44 ℓ

Add 49 ℓ and 8 472 mℓ. Then, subtract 13ℓ 472 mℓ
from the answer. Explain.

3 750 mℓ + 3 ℓ 900 mℓ – 260 mℓ = mℓ

1 5 15 Convert 4 ℓ 390 mℓ
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?

12 ℓ 15000 mℓ How do you fill up 9 ℓ ofwater into the
green container using both the red
and blue pails?
Explain.

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

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

Materials Players

4 sets of volume cards, task cards, 4 pupils in a group.
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. Subtractthevolumeof CardAfromCardB.
b. Subtract the volume of Card Cfrom the b. Add the answer in a to the volume of

answer in a. Card C.
c. Writethenumbersentenceand theanswer. c. Writethenumbersentenceandtheanswer.

Pupil 3: Pupil 4:
a. Add the volumes of Card Band Card C. a. SubtractthevolumeofCardCfromCardA.
b. Subtract the volume of Card A from b. Add the answer in a to the volumeof

the answer in a. Card B.
c. Writethenumbersentenceandtheanswer. c. Writethenumbersentenceandtheanswer.

3 Discuss the task among members in the group.
4 Keep the task in Mathematics file.

1 Calculate.

a 5 ℓ 550 mℓ + 4 ℓ 340 mℓ – 1ℓ 240 mℓ = ℓ mℓ

b 6 ℓ 78 mℓ – 988 mℓ + 3 ℓ 885 mℓ = mℓ

c 368 mℓ + 17ℓ 120 mℓ – 2 ℓ 388 mℓ = ℓ

d 12 ℓ 198 mℓ – 10 ℓ 662 mℓ + 22 ℓ 464 mℓ = ℓ mℓ

2 Reduce 36 712mℓ from 86 ℓ. Then, add the answer to 712mℓ.

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
1500 mℓ of honey. into 6 small bottles.

1500 mℓ 1500 mℓ 1500 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

1500 mℓ 6 )4 500 mℓ
×3
–4 2
4 500 mℓ 30

3 × 1 500 mℓ ÷ 6 = 750 mℓ – 30
00

–0
0

The volume of honey in each small bottle is 750 mℓ.

2 5 × 12 ℓ 800 mℓ ÷ 4 = ℓ

3 200 Convert 12ℓ 800mℓ
to mℓ.
5 × 12 ℓ 800 mℓ = 5 × 12800 mℓ
4 4
1

= 16000 mℓ

16 000 mℓ = 16 ℓ
1000

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

6ℓ 274 mℓ 63
836 mℓ
14 )87 ℓ 6 ℓ 274 mℓ

– 84 + 3000 ×9

3 3 836 54 ℓ 2 466 mℓ
–2 8

1 03

– 98 54 ℓ 2 466 mℓ = 54 000 mℓ + 2 000 mℓ + 466 mℓ

56 = 56 466 mℓ

– 56

0

87 ℓ 836 mℓ ÷ 14 × 9 = 56 466 mℓ

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
+ 2000 ×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.

TEACHER’S Get pupils to create stories based on division number sentences.
NOTES
14.1(ii) 201

A B Find the volume of
4 565 mℓ Half the volume of C C water in ℓ and mℓ

in container B.

4 times the volume of A

Answer the puzzle. Complete the answer with the matching letter in the
blanks below.

3 × 2 ℓ 115mℓ ÷ 5 T 35 ℓ 280 mℓ ÷ 7 × 9 O 6 × 12ℓ 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?

10090 mℓ 45 360mℓ 1ℓ 269mℓ 1269mℓ 84 ℓ 720 mℓ 36 900mℓ

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

2 a Find the product of 10322 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?

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

The volume of tea drank.

Operation Add, then subtract.

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

520 mℓ remainder

Solve

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

11 4 1 1450

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 1ℓ 9 3 0 mℓ

Check 1 4 1 1450

4 1ℓ 9 3 0 mℓ 4 2 ℓ 4 5 0 mℓ
+ 5 2 0 mℓ – 14 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.
NOTES Guide pupils to estimate the reasonable final answers.

203

2 Encik Lingam bought 3 bottles of goat milk with
the volume of 2 ℓ 750 mℓ in each bottle.Then,
he poured equally into 5 containers for his
children. What is the volume of milk, in mℓ,
for each container?

Given Bought 3 bottles of goat milk.
The volume of 1bottle of goat milk is 2 ℓ 750 mℓ.
Poured equally into 5 containers.

Find The volume of goat milk for 1container, in mℓ.

Operation Multiply, then divide.

Milk Milk Milk

2 ℓ 750 mℓ 2 ℓ 750 mℓ 2 ℓ 750mℓ

Solve 3 × 2 ℓ 750 mℓ ÷ 5 = mℓ

21 1650 mℓ

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

8 ℓ 250 mℓ = 8 250mℓ – 30
25

– 25

Check 00
–0

0

32 275 0
22 15
1650 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.

TEACHER’S Give other daily situation for problem solving involving division and multiplication.
NOTES
204 14.2 (i)

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

c 3 ℓ 752 mℓ Mak Jah gave 3 containers of
equal amount of porridge to
3 ℓ 752 mℓ 8 neighbours. Find the volume
of porridge, in mℓ, received by
each neighbour.

3 ℓ 752 mℓ

d. A school provided 4 ℓ 720 mℓ cooking oil for a cooking competition.
The oil was given to 8 groups that were competing. Calculate the
volume of oil received by 5 groups. Choose the correct number
sentence and solve it.

4 ℓ 720 mℓ ÷ 5 × 8 = 5 × 4 ℓ 720 mℓ ÷ 8=

e. The volume of paint from a container is poured in equal amount
into 9 small tins. The volume of paint in 2 small tins is 2 ℓ 700 mℓ.
Calculate the volume of paint in the container at the beginning.

TEACHER’S Give more standard UPSRquestions involving volume of liquid.
NOTES
205

1 Calculate.

a 3 ℓ 201 mℓ + 54 ℓ – 18ℓ 127mℓ = ℓ mℓ

b 16ℓ 672 mℓ – 998 mℓ + 44 ℓ 326 mℓ= ℓ

c 40 ℓ 765 mℓ + 13ℓ 478 mℓ – 23 ℓ 499 mℓ= ℓ mℓ

d 2 × 4 ℓ 210 mℓ ÷ 4= ℓ mℓ

e 12ℓ 105 mℓ ÷ 15× 3 = mℓ

f 8 ℓ 75 mℓ ÷ 5 × 7= ℓ

2 Calculate.

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

b. Divide29 ℓ 848mℓ by 8 thenmultiply by 7.Giveyour answerinℓ and mℓ.

2 Solve. 5 ℓ 130mℓ

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

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

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

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

A right angle is An acute angle is smaller
formed at the corner than a right angle.
of a rectangle.

2

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

Right angle

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

207

Materials A4 paper, pencil, ruler and scissors.

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

Right Right
angle angle

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

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? c
ab

2 Name the angles found in the following shapes.
a bc

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

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 0.6m

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

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

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

209

Perpendicular lines b

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

Can you point to the Which parts of this door
perpendicular lines in the are perpendicular lines?
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.

ab c

Draw a flag Draw a draughtboard Draw hopscotch

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

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

h

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

d ef

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 3
1 lace that you used?

I use the lace 3
according to the
length around the 3
pillow case.
The length of the lace is 12
2 4 cm units. The 12units isthe
6 cm A perimeter of the pillow case.

Perimeter:
3 + 3 + 3 + 3 = 12 units

A is a rectangle 3 4 cm
and Bis a right 3 cm B
angled triangle.
5 cm

Perimeter A: Perimeter B: =
4 cm + 6 cm + 4 cm + 6 cm = 20 cm ++

Draw the shapes of a square, a rectangle and triangles with the
perimeters of 12 cm.

TEACHER’S http://www/superteacherworksheets.com/geometry/perimeter-3_TZFFD.pdf
NOTES
212 15.3 (i)

4 Find the perimeter of the hexagon. The length of each
side is 3 cm.
Perimeter = 3 cm + 3 cm + 3 cm + 3 cm + 3 cm + 3 cm
= 18 cm

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 + 10cm 12cm addition.
= 24 cm
12 cm INFORMATION

Perimeter= 12cm + 12cm + 12cm + 12cm

= 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 bcd

12cm 13cm 15cm

The length of each The length of each
side is 5cm
5 cm 8 cm side is 4 cm

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

213

Area The area of 1unit
square is 1square
1 unit. It is written
as 1unit2.
1unit

1unit 1unit2

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 = 15units2 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 1cm2.

The area of the checkerboard = cm2

214 15.3 (ii) TEACHER’S Carry out hands-on activities using grid book to measure areas of basic shapes.
NOTES http://www.superteacherworksheets.com/geometry/area-1_TWBDW.pd

3 Draw a line from 1square forms two
vertex to vertex. triangles of the
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 Area = Area
= 4 cm × 4 cm 2
= 16cm2
= 16 cm2
2

= 8 cm2

4 Area = Base × Height
Area 2

Height 8 cm = 6 cm × 8 cm
6 cm 2
Base
5 = 48cm2 It is writtenas
2
1 × Base × Height.
= 24 cm2 2

= 1× Base × Height 2

4 cm = 1×23 cm × 4 cm

3 cm = 12 cm2 = 6 cm2
2

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

215

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.
1unit

1unit BD
A

C
a. Find the areas of A, B, Cand D.
b. State the shapes having the same areas.

2 Calculate the areas of the coloured diagrams. c
a b 4 cm 12 cm
9 cm
5 cm

8 cm 10 cm

d e 7 cm f
3 6 cm
8 cm 7 cm --------5 cm
13cm 16 cm

P 5 cm P is a square. Find the area,
in cm2, of the shaded part.

TEACHER’S http://www.charliefrench.com/PDF/Gr4measure2PDF

216 15.3 (ii) NOTES

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

are cubes.

1unit Volume = 12units3
1unit
Volume of cube = 1unit × 1unit × 1unit
1unit = 1unit3

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

INFORMATION

2 1cm Volume of cube = 1cm × 1cm × 1cm
= 1cm cube
1cm = 1cm3

1cm

How do you count
the number of the
hidden cubes?

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

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

217

3a b

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

Length Width Height Volume Length Width Height Volum
(units3) 4 e
(units3)
3 3 3 27
2 4 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 1cm 1cm height Volume = Length × Width × Height
width = 5 cm × 2 cm × 3cm
1cm = 30 cm3

length

5 Calculate the volume of the box. 50 cm 20 cm
Volume = 50 cm × 30 cm × 20 cm 30 cm
= 30 000 cm3

Can volume be calculated by multiplying
the area of base by height? Discuss.

TEACHER’S Encourage pupils to draw nets to differentiate areas and volumes.
NOTES
218 15.4 (i)

Discuss.
a. Can 2 boxes with the same base area produce different volume?

Explain.

b. Can 2 boxes with different base area produce the same volume?
Explain.

1 State the number of unit cubes. Calculate the volume of the diagrams.

ab c

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

2 Calculate the volume of the diagrams.

ab 10 cm c d

4 cm 8 cm 12 cm
4 cm
10 cm
4 cm
10 cm 2 cm 15 cm
8 cm

3 Calculate the volume of the cube and cuboid. 3 cm

4 cm

5 cm 10 cm 8 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. Fillin 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
X
b Find the length of the sides of Y

diagram Y. 3 cm

c Find the areas of the diagrams

X and Y.

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

3 cm

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

6 The length of the side of square Bis 4 times

of square A. How many times is the area B

of Bcompared 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 in Farah Siva May Ros Izam
the fifth
column, row Yes,
two, are you
a newpupil? 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.

Thetoy 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

3

2

Pawn Castle

1

A BC D EFG H

The letters A to H are located at the horizontal axis.
This axis shows the locations at the column.

At the location C2, we can see the white bishop.
At G8, we can see the black knight.

is located at A4 and 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.

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

223

The princess wants to 6
find her shoe with the 5
condition that the 4
number of movements 3
at the horizontal axis 2
and the vertical axis are 1
the same. What is the 0 12 34 56
colour of her shoe?

Materials MSWord Players 4 pupils 5 CD

Steps 4 Animal

1 Each group choose a theme. 3

2 Execute MSWord. 2
3 Choose Insert Table (4 × 5 table).
1
Type the letters at the horizontal AB
axis and numbers at the vertical axis.
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 CD E

Key: Crocodile Mini A Famosa
Farm Malaysia
Butterfly
Garden

Malacca Stadthuys Samudera Independence
Zoo Building Museum Memorial

Complete.

a TheIndependence 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 eD2 is the location of a historical building called .

is located at A4 and is located at E3.

TEACHER’S NOTES

22255

Determine the position

Cameron Highlands

Strawberry
Farm Museum and
5 Tea

Gallery Plantation

4 Vegetable
Farm

3 Cactus Flower
Bee Apiary Valley Garden

2

1

AB C DE

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 and Cactus Valley located?

The Strawberry Farm is located at C5 and the Cactus Valley

is at D2. The Vegetable Farm is located at .

The Tea Plantation islocated 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. 5j c f n t
4s k q b z

Materials Letter Grid card (except x), 3d o g v l
questions on the position of letters 2r a i e w
using MSWord, A4 paper.

Steps 1 pmh y u

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

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 Fis located at axis.

2 c 1to 4 is located at axis.
1
d State the shapes seen at the
A BCD EF
locations:

i B1 ii D4 iii A3

2 Answer these questions based on the grid.

5 BCDEF a. Choose a method how you would
4 explain the location of .
3 i Firstthedigit5 followedby theletterD.
2 ii First the letter D, second the
1
digit 5.
A b. State the location of .

3 6a e o Look at the locations of the letters in
l y the grid. Answer this riddle: Which
5 box cannot be lifted?
4t

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

1p
A B C D E F G C3 F5 G2

4 State the coordinates of these objects:
43 abc

2

1

0 1234

22228 TEACHER’S
NOTES

17 School

RATE KANCIL BOOk STORE S P EC IAL OF F ER

Rates S PECIA L PINTAR BOOKSTORE
O FFER
1

I want to buy 6 pens.
Which is cheaper?

Kancil Bookstore Price at

RM0.75 The price of a pen Kancil Bookstore:
is RM0.75.
2 )RM1.50 6 × RM0.75 =

–0 43
15
RM0.75
– 14 ×6
10
RM4.50
– 10
0 RM0.75 × 6 = RM4.50

Pintar Bookstore Price at

RM0.60 The price of a pen Pintar Bookstore:
is RM0.60.
3 )RM1.80 6 × RM0.60 =

–0 3
18
RM0.60
– 18 ×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 moral 229
NOTES 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 1320 passengers. Each bus carries the same number
of passengers.

a What is the number of passengers carried by 6 buses?

Number ofpassengers for Total number of passengers for

44 6 × 44 =

30 )1320 22

– 120 44
120 ×6

– 120 264

0

The number of passengers carried by 6 buses is

264 persons.

b How many buses are needed to carry 220 passengers?

44 passengers 1bus
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 110passengers? Discuss.

Fazlin wants to buy 12storybooks 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. Thetotal mass
of the marbles is 100 g. Calculate the
mass of 7 marbles.

20 marbles 100 g
1marble 100 g ÷ 20
5
5g
20 )100 7 × 5 g = 35 g

– 100
0

1marble
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 Bto Town Cwith the same speed.
Calculate the distance from Town Bto Town C.

2 hours 180 km

1hour 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 7 24 cm 6 boxes 600 paper clips
similar balls? 4 boxes ?
Find the length of
5 similar squares.

2 Show the calculation steps to find the answers on anA4 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 112km 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 isthe
length of the shadow of a 45 cm plant?

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

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 bc

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

d 15minutes 420words e 120 stamps 6 envelopes

7minutes words 100stamps envelopes

f 4glasses 1ℓ
10glasses mℓ

TEACHER’S 233
NOTES

1 Solve. b c
a
45 cm

4 books cost 3 packets of sweets Calculate the
RM30 weigh 900 g height of 4 boxes.

How much does Find the mass of
3 books cost? 7 packets.

2 Solve.

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

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
1hour produces
600 greeting cards 112hours produces 900 greeting cards

A businessman wants to buy a printing machine. He chooses
printing machine A with the reason that the machine prints more
greeting cards. Is his reason right? Prove it.

e

12 m

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 12m ÷ 3 × 4

TEACHER’S NOTES

234 9.1(i)

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 LiSarjit Ajol
Friends’ names
represents 2 books

Pictograph

1 My Friends’ Storybooks Title
Akif
In apictograph, 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 × =

1. (i)a TEACHER’S Who has the most number of 235
2. (i)a NOTES storybooks?

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

2

The Sales of Mangosteens for 4 Days

Complete the table.

Day Number of Mangosteen

Monday 3 × 10= 30

Tuesday 5 × 10= 50

Wednesday 3 × 10=

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

The sales of mangosteens on Monday is 30.
The highest sale of mangosteens is on Tuesday, which is 50.

Thesales 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 calculatethe 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.

18.1(i) a TEACHER’S Use various types of pictographs to retrieve information and create questions.
236 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 showdata.

The horizontal axis shows the types of musical instruments.
The vertical axis shows .

10 pupils like to play the flute, 16 like to play thedrum, the like to play

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?

1. (i)b TEACHER’S Ensure the distance of each marking is the same. Relate questions to everyday life to
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 101520 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.
Clu
b

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

Materials MSExcel, data set. 1 Players In pairs.

1 HKeCGaehiagcyothhhoienlsfirrgediedha4nattdttadyapiainnoetntaMsh,tSeohcfecEhlhxahocosooesbbsl..bbeiieetssh.eoHSfoRwbeibmaHiedmosinibngobgfyPupoilNf5s1Pu2oumfpb4ilesCrerdas 2

2 menu Insert and click Column. Hobbies of Pupils of4 Cerdas
3 Choose Chart Layout and click

3

2-D Column.

4 Type the title and label the Hobbiesof Pupilsof4Cerdas 4
horizontal axis and the
vertical axis. Hobbies of Pupils of 4 Cerdas

5 Discuss the outcomes.

TEACHER’S
NOTES

2388

Pie 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

40%

INFORMATION

The percentage of pupils who like to eat nasi lemak is 30%. The most

liked breakfast is bread which is .

The least liked breakfast is which is .

1. (i)c TEACHER’S Relate the percentages of pie chart to fractions. Emphasise the total percentage of a 239
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.

Savings of 4 a. saves RM2. .
Pupils b. saving is the most, which is .
c. The difference between Faizal’s and
Faizal
Sivam’s saving is .
Ai Lin d. The totalsavingof the four pupils is

Sivam

Esha

Key: represents 50 sen

2 Answer the questions based on the bar chart.

Time to Answer a State the time taken to answer the

Mathematics Test Mathematics test.

Time in minute60 --------------------------------------------------------------------------------------- i Ina ii Ho
50
40 iii Ajay iv Dayang

30 b. Arrange the names in order of speed in

20 answering.

10 c. The difference in time taken between

0 and is 15minutes.

Ina Ho Ajay Dayang

Name

3 Look at the pie chart and answer the questions.

Types of Flowers in Painting a The percentage of jasmine is .

Chrysanthemum b The and the have the same
20% percentage.

Rose 10% Jasmine c The total percentage is .
50%
Ylang d Thepercentage of the flowers,excluding
20%
chrysanthemum is .

224400 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
Steps pie chart, number of pupils.

numbered question cards.

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

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

8

4

0
Reading Internet Swimming Singing surting
Hobby

2 Put the question cards on the magnetic board. PiWeotfCohtahhstaecihrsptoutohple?ilpsewrcaelknintagge likeInttopeurrpepneaielFrsdtciwnbaedonnhtBtodohakatelghisrkeo.dCesibfhtefeoeatwrsrwetuhenroecf tenhitnehe

3 The group representative takes the numbered Pictograph
question card in turn and answer the question Who borrows the most
orally. number of books from
the library?
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.

Sales of Ice Cream for 4 Days a. How many ice creams are sold on
Sunday Sunday?

Monday b. Calculate the total numberof ice
creams sold in 4 days.
Tuesday
c. What is the difference in sales of the
Wednesday ice creams on Tuesday compared to
Key: Sunday?
represents 20 ice creams
d costs RM2.Calculate the sales

of the first two days.

2 Answer the questions based on the bar chart.

Scores of 4 Sport Teams a Green Teamcollects marks.

Blue b Thetotal scoreof and
Red
Green Teams is the same as the score
Yellow

0 5 10 1520 25 30
Mark
Sport Team of RedTeam.

---------------- c Red Team needs more marks to

equalise the marks of Green

Team.

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

Items Recycled a. Thepercentage of glass and
aluminium tins that are recycled
Paper Aluminium is .
Tins
Glass 45% b. Thepercentage of paper that is
25% recycled is .
Plastic
10% c Thedifference in percentage
between the items most
recycled andthe least is .

TEACHER’S
NOTES

24422