Mathematics Year 4 Textbook DLP

7 State the currency and country for the following notes.

a Specimen b Specimen c Specimen

d Specimen e Specimen f Specimen

8 Name the country that uses the following currencies.

a Pound Sterling b Won c Renminbi

d Naira e Rupiah f Riel

g Baht h Kyat i Peso

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

Daily situations Payment
Buying fish and vegetables at the market. instrument

Using card to call a friend.
Buying airline ticket to go on a tour.
Giving donation to fire victims.
Buying electrical items at a supermarket.

TEACHER’S
NOTES

11444

11 School
TIME

Recognise time The earth rotates
on its axis in 1 day.
Day and hour
1

Sundial Water Clock





Hourglass Analogue Yes, the complete
Clock rotation takes
24 hours.
Ancient people used
various instruments to

d etermine the time.

1 day = 24 hours

Day and night
----------------------------------------------------
Sun rays Direction of 2 days is equal to
rotation how many hours?

 Day 2 days = hours

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

11.1 (i) 2 days = 48 hours 145
a
Axis

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

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

3 days = hours

24 hours 24 hours 24 hours

0 1 2 3

1 How many hours
24 hours in 5 days?

×3

72 hours

3 days = 72 hours

3 96 hours = days


96 ÷ 24 = days

4 x 24
24 96 day hour
– 9 6 ÷ 24
0
INFORMATION
96 hours = 4 days

4 6 days 7 hours = hours • Convert 6 days to hours.

6 days 7 hours = 6 days + 7 hours 6 × 24 hours = 144 hours

= 144 hours + 7 hours

= 151 hours

6 days 7 hours = 151 hours How many days and hours in
100 hours? Explain.

11.1 (i) TEACHER’S " Relate days and hours based on the situation given.
a NOTES

146

Week and day

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

4 weeks = days Remember the 31
7 times table.
National Day
4 × 7 days = days

4 × 7 = 28



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

2 Aisyah and her family went for a holiday in a village for 41 days.
How many weeks and days were they there?

41 days = weeks days ×7
5 weeks 6 days
5 week day
7 41
– 35 ÷7
6
INFORMATION
41 days =

They were in the village for 5 weeks 6 days.

In the life cycle process of a butterfly, takes about

10 days to transform into . State the time in

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

TEACHER’S " Relate weeks and days based on the life cycle of insects such as the cockroach, the
NOTES fly and others.
11.1 (i) b
147
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/time/
index.htm

Year and month Father Mother
45 years 6 months 42 years
1 Study Kak Ngah’s family chart.
How old is Usu in months?

5 years = months

Kak Long Kak Ngah Abang Chik Usu
12 15 years 10 years 8 years 5 years
7 months 5 months 3 months
×5
60

5 years = 60 months Whose age is the same
Usu’s age in months is 60 months. as 504 months? Explain.

2 187 months = years months
1 5
1 2 1 8 7 × 12

– 12 year month
67
÷ 12
–60
7

185 months = 15 years 7 months INFORMATION

Time taken by planets to make one
complete rotation around the sun.

Jupiter 12 years

Uranus 7 times the time taken by Jupiter

State the time, in months, taken by Uranus.



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

TEACHER’S " Emphasise that leap year and normal year have the same number of months, but
different number of days.
148 11.1 (i) c NOTES " Guide pupils to identify the leap years.

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

Players 4 persons Materials 21 pieces of time cards

(10 pairs of cards, 1 piece of stork card)

Steps 3
1 Distribute 21 pieces of cards to all players.

2 Determine the players turn. The player with the most

cards gets the first turn.

3 Pull out a card from each player according to turns.
4 If there are matching cards, the 2 cards are taken out. 4

5 Repeat steps 3 to 4 until all matching cards are

taken out.

6 The player who gets the stork card wins the game.

1 Convert.

a 9 days = hours b 8 days 5 hours = hours

c 37 hours = days hours d 6 weeks = days

e 2 weeks 4 days = days f 84 days = weeks

g 10 years 3 months = months h 9 years = months

i How many hours in 7 days? j State 14 months in years
and months.


2 How many weeks and days are
there in May 2014?


3 The first Prime Minister of Malaysia, the late Tunku Abdul
Rahman Putra Al-Haj served for about 13 years.

State his term of service in months.

11.1 (i) TEACHER’S " Prepare a few sets of time cards for enrichment activity.
a,b,c NOTES Game like “Happy Family” is encouraged.

149

Addition of time

1 a The picture shows the 1 day 9 hours 1 day 8 hours
handicraft products of the
disabled. Find the total time days hours
taken to finish the baskets
and shell crafts. 2 days 16 hours

1 day 9 hours + 1 day 8 hours =

day hour

1 9
+ 1 8
17
2

1 day 9 hours + 1 day 8 hours = 2 days 17 hours

The total time taken to finish the baskets and shell crafts
is 2 days 17 hours.

b How many hours does it take to finish all the handicraft
products above?

1 day 9 hours + 1 day 8 hours + 2 days 16 hours = hours

da y h our 4 days = 4 x 24 hours
= 96 hours
2
4 days 33 hours = 96 hours + 33 hours
1 9 = 129 hours

1 8

+ 2 16

4 33

1 day 9 hours + 1 day 8 hours + 2 days 16 hours = 129 hours

The time taken to finish all the handicraft products above
is 129 hours.

150 11.2 (i) a TEACHER’S " Use time line for addition operation.
NOTES " Emphasise the conversion of units from hour to day.

2

Pulau Redang Belum Rainforest FRIM
4 weeks 2 days 6 weeks 1 day 1 week 5 days

The photography association shot films at the locations above.

a Calculate the time taken for shooting films at Pulau Redang
and Belum Rainforest.

4 weeks 2 days + 6 weeks 1 day = weeks days
week day

4 2
+ 6 1

1 0 3

4 weeks 2 days + 6 weeks 1 day = 10 weeks 3 days

The time taken for shooting films at Pulau Redang and
Belum Rainforest is 10 weeks 3 days.

b Calculate the duration taken for filming at the three locations.
4 weeks 2 days + 6 weeks 1 day + 1 week 5 days

= weeks days

week day

4 2 11 weeks 8 days
6 1
+ 1 5 + 1 –7

11 8 12 weeks 1 day

4 weeks 2 days + 6 weeks 1 day + 1 week 5 days
= 12 weeks 1 day
The duration taken at the three locations is 12 weeks 1 day.

State 2 locations which take 42 days for filming.

11.2 (i) b TEACHER’S " Emphasise the conversion of units from day to week. 151
NOTES " Encourage pupils to talk about their school activities in weeks and days like
Reading Campaign and sports practice.

3 Calculate the duration of service for Service Record

Cikgu Sarah at the three schools based Name Duration
on the service record.
of school

4 years 9 months + 3 years SK Baiduri 4 years 9 months
8 months + 10 years 4 months SK Angkasa 3 years 8 months

= years months SK Aman 10 years 4 months

year month
2
4
3 9 21 months ÷ 12 = 1 year 9 months
+ 1 0
17 8

4 17 years 21 months = 17 years + 1 year + 9 months

21 = 18 years 9 months

4 years 9 months + 3 years 8 months
+ 10 years 4 months = 18 years 9 months

The duration of service for Cikgu Sarah at the three schools is
18 years 9 months.

Interview a few teachers at your school. Record their durations of service at
your school and others. Create an appreciation card for their contributions
and state the durations of service at your school.

1 Add.

a 3 days 7 hours + 2 days 6 hours = days hours

b 12 years 1 month + 8 years + 20 months = months

c 9 weeks 3 days + 5 weeks 6 days = weeks days

d 5 days 8 hours + 4 days 10 hours + 12 hours = hours

2 Find the total of 40 weeks 2 days, 15 days and 8 weeks 4 days.
Give answer in weeks.

11.2 (i) TEACHER’S " Diversify questions using a calendar.
a, b, c NOTES

152

Subtraction of time 4 days 17 hours
3 days 12 hours
1



Calculate the difference in time taken by the rabbit and the
tortoise to reach Sang Kancil’s house.

4 days 17 hours – 3 days 12 hours = days hours
day hour

4 17
– 3 12

1 5

4 days 17 hours – 3 days 12 hours = 1 day 5 hours

The difference in time taken by the rabbit and the tortoise to reach
Sang Kancil’s house is 1 day 5 hours.

2 5 days 5 hours – 2 days 9 hours – 14 hours = days hours



day hou r da y hour • 9 hours can be subtracted
54 259 2 21 100 from 5 hours.

– 2 9 – 1 4 • Convert 1 day to 24 hours.

2 2 0 2 6 24 hours + 5 hours = 29 hours

5 days 5 hours – 2 days 9 hours – 14 hours = 2 days 6 hours

Add 2 days 9 hours and 14 hours. Then, subtract the sum from
5 days 5 hours. Is the answer the same? Explain.

11.3 (i) a TEACHER’S " Find the difference by doing simulation activities. 153
NOTES " Do subtraction by counting down.

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/
maths/timetables/index.htm

3 What is the difference, in weeks and Mural A
days to complete mural A and mural B? 2 weeks 6 days

2 weeks 6 days – 1 week 5 days Mural B
1 week 5 days
= weeks days

week day

2 6
– 1 5

1 1

2 weeks 6 days – 1 week 5 days = 1 week 1 day
The difference in time to complete mural A and mural B is 1 week 1 day.

Solve by changing the unit from week
to day first. Is the answer the same?

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

week day week day

18 7 13 11

1 9 0/ 1 4 4/
– 4 3 – 6

14 4 1 3 5

19 weeks – 4 weeks 3 days – 6 days = 13 weeks 5 days



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

3 weeks 3 months

11.3 (i) TEACHER’S " Do subtraction by counting down.
b NOTES

154

5 Find the difference of life span

between the orang-utan and the 30 years 45 years
panda. Give answer in months. 2 months

45 years 3 months – 30 years 2 months = months 3 mo nt hs

year month

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

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

6 14 years 7 months – 8 months – 2 years 3 months

= years months

11 16

– 1 24 yyeeaarrss 37 mm oonntthh ss – 1 2 y ears 4 months
8 months

1 2 years 4 months 1 1 years 8 months

14 years 7 months – 8 months – 2 years 3 months 11

= 11 years 8 months

1 Subtract. days
a 8 days 3 hours – 5 days 2 hours = days hours months
b 24 days 7 hours – 10 days 15 hours – 3 days 9 hours
= days hours
c 16 weeks 2 days – 6 weeks 5 days – 8 days = weeks
d 31 years – 12 years 8 months – 5 months = years

2 Solve.
a Find the difference between 21 weeks 4 days and 13 weeks 3 days.

Give answer in days.
b How many months more is 50 years than 23 years 9 months?

11.3 (i) c TEACHER’S " Carry out activities to find difference in age amongst friends and relatives. 155
NOTES

Multiplication of time

1 How much time, in days and hours, This wood carving
is taken by Raden to do 5 similar is done in 1 day
wood carvings? 3 hours.

5 × 1 day 3 hours = days hours

day hour

1 3
5
× 1 5

5

5 × 1 day 3 hours = 5 days 15 hours
Time taken to do 5 similar wood carvings is 5 days 15 hours.

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

2 a Shah Indra attended computer courses.
What is the total time of the two courses?

Give answer in days.

2 × 2 weeks 4 days = days

2 weeks 4 days = 14 days + 4 days
= 18 days

1

1 8 days
×2

3 6 days

2 × 2 weeks 4 days = 36 days 2 weeks 4 days

The total time of the two courses
is 36 days.

156 11.4 (i) TEACHER’S " Do multiplication using different suitable methods, like repeated addition.
a, b NOTES " Use schedules for school holidays and co-curriculum activities involving
multiplication of time.

b I attended the third course

for the same duration.

Calculate the duration of
t he thr ee courses. State the

answer in weeks and days.

3 × 2 weeks 4 days = weeks days

2 weeks 4 days

× 3
6 1 2

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

3 × 2 weeks 4 days= 7 weeks 5 days
The duration of the three courses is 7 weeks 5 days.

3 4 × 10 years 7 months = years months

ye ar mo nth
10 7

× 4

4 0 2 8



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

= 40 years + 2 years + 4 months

= 42 years + 4 months

4 × 10 years 7 months = 42 years 4 months


11.4 (i) TEACHER’S " Guide pupils to build conversion of units chart. 157
b, c NOTES

Players 4 to 6 persons. 1. Q2Fwi.3un2T.id1eothh3fsy=ea2t×etihd_poap1e_iarnf0usf_tiepro.y_Criotleesaayfanleirpsrcdaasue3grp4seimn.ilmsooafongntehtsh.s

Materials Pupil’s register book, question cards.

Steps

1 Teacher retrieves information about pupil’s age
from the register book and give the data to pupils.
2 Distribute question cards to each group.
3 Pupils answer the questions in the allocated time.
4 The group that answers all the questions correctly

in the shortest time wins the game.
5 The group that makes mistakes needs to
make corrections.

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

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

b 9 × 8 weeks 4 days = days

Show the simplest method.
c Calculate the product for 8 and 10 years 9 months.

11.3 (i) c TEACHER’S " Relate multiplication of time in everyday life.
158 11.4 (i) NOTES " Inculcate moral values such as valueing time during group activity.

a,b, c

Division of time Quantity Type of house Duration

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

6 days 15 hours ÷ 3 = days hours

2 days 5 hours Welcome
3 6 days 1 5 hours

– 6 – 15

00

6 days 15 hours ÷ 3 = 2 days 5 hours

The time taken to complete the model of a single-storey house is
2 days 5 hours.

b Calculate the time taken to complete a model of a double-storey
house. State the answer in hours.

9 days 4 hours ÷ 4 = hours

2 days 7 hours

4 9 days 4 hours

–8 + 2 4 2 d ay s 7 hours = 24 hours + 24 hours + 7 hours
1 – 2 8 = 48 hours + 7 hours
2 8 = 55 hours
0

9 days 4 hours ÷ 4 = 55 hours

The time taken to complete a model of a double-storey house is
55 hours.

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

11.5 (i) a TEACHER’S " Guide pupils to divide units of time by subtracting consecutively. 159
NOTES

2 14 weeks 4 days ÷ 6 = weeks days

2 weeks 3 days Convert the remainder
2 weeks to 14 days.
6 1 4 weeks 4 days

– 12 + 14

2 18

– 18

0

14 weeks 4 days ÷ 6 = 2 weeks 3 days

3 12 years ÷ 9 = months

1 year 4 months

9 1 2 years 0 months

–9 + 36

3 36 1 year 4 months = 12 months + 4 months
– 36 = 16 months

0

12 years ÷ 9 = 16 months

1 Divide. b 8 9 weeks 1 day
a 2 18 days 20 hours

c 4 13 years 8 months d 5 22 days 7 hours

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

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

11.5 (i) TEACHER’S " Expose various calculation and conversion of units strategies to pupils.
b, c NOTES

160

Solve the problems

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

Multipurpose shop Duration of operation
Era
Whole day

Kota 8 hours

Given Duration of operation of Era is whole day or 1 day.

Duration of operation of Kota is 8 hours.

Find Difference in time



Operation Subtraction



Solve 1 day – 8 hours = hours


1 day = 24 hours

24 hours – 8 hours = hours

1 14

2 4 hours

– 8 hours
1 6 hours

Check 16 hours + 8 hours = 24 hours

1 day – 8 hours = 16 hours Beza masa
kedua-dua

The difference in time the two shops operate is 16 hours.

If another multipurpose shop operates 2 hours more
than Kota, calculate the duration the shop operates.

11.6 (i) TEACHER’S " Solve daily problems by drawing diagrams or making tables. 161
NOTES

2 In a year, a book exhibition is held in 3 stages. Each stage is held for
1 week 4 days. Calculate the total time for the 3 stages of the exhibition.

1 week 4 days 1 week 4 days 1 week 4 days
Total

3 × 1 week 4 days = weeks days

Check.

1 week 4 days 1 w eek 4 days = 11 days
× –12537 day s ×3 1 331 dd aayyss
3 4
7 33
+1 – 28
4 weeks 5

3 × 1 week 4 days = 4 weeks 5 days
The total time for the 3 stages of the exhibition is 4 weeks 5 days.

3 Four similar phases of housing projects should be completed
in 9 years. Calculate the time in years and months to complete

one phase.

9 years ÷ 4 = years months

2 years 3 months 9 years

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

1 12 How do you check the answer?
Explain.
– 1 2

0

9 years ÷ 4 = 2 years 3 months

The time taken to complete one phase is 2 years 3 months.

162 11.6 (i) TEACHER’S " Underline the key information before solving the problem.
NOTES

A

Solve. 2 days 9 hours B
a How much time boat A
sails more than boat B as 1 day 3 hours
given in the information?

b A group of pupils made a study about the school history
for 3 weeks 4 days. The folio study was completed in

1 week 5 days. Find the total time taken by them.

c The table shows the duration Project Duration
of time taken by Fong to finish History 10 hours
three projects. Find the total Science 9 hours
time needed to finish all the English 7 hours
projects. Give your answer in
days and hours.

d The life span of a jungle cat is about 5 years.
While the life span of a tiger is 3 times a jungle
cat. Calculate the life span, in months, of the tiger.

e The table below shows the age of two pupils.

Pupil Age

Alia 13 years 6 months

Danisha 7 months younger than Alia

How old is Danisha?

f Kim attended a course in Putrajaya for 24 days. Calculate
the duration of the course in weeks and days.

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

TEACHER’S 11633
NOTES

1 Convert.

a 7 days = hours b 144 hours = days

c 8 weeks 3 days = days d days = 17 weeks

e 12 years = months

f 92 months = years months

2 Solve.

a 3 days 8 hours + 15 hours = days hours

b 10 years 8 months – 2 years 9 months – 3 years 7 months

= years months

c 6 × 4 weeks 6 days = weeks days

d 11 days 6 hours ÷ 5 = days hours

3 Solve.
a Change 8 days 10 hours to hours.

b 1 6 w e eks = days Which is the correct conversion of unit?
16 × 7 days or 16 × 10 days

c Multiply 4 by 7 weeks 2 days.
d 28 years divided by 8. State the answer in months.

4 Solve the following problems.
a A writer takes 1 year 2 months to complete a novel.
A collection of short stories is completed 4 months earlier
compared to the novel. How long does it take to
complete the collection of short stories?

b Nuriz did a scrapbook in 3 weeks 1 day. While Aziah
took half the time taken by Nuriz. Calculate the time

taken by Aziah, in days.

c Mala is 8 years 9 months. The difference in age between
Mala and her brother, Bala is 2 years 5 months.

Calculate Bala᾽s age.

TEACHER’S
NOTES

11664

12 School
LENGTH

Recognise units of length

1 The length of the pencil 0.5 mm

lead is 75 millimetres. 5 mm

247p5encmil lmead Millimetre is used to state
the length of small and short
Long objects. The symbol is mm.

2

The distance from
Merdeka Square to
Petronas Twin Towers
KLCC is 3.5 kilometres.

Kilometre is used to state
the distance between two
places. The symbol is km.

What unit will you use to state:
(i) the thickness of a textbook?
(ii) the distance between Kota Bharu, Kelantan and Kangar,

Perlis? Explain.

12.1 (i) TEACHER’S Encourage pupils to explore the usage of mm and km in every day life.
a, b NOTES Use search engines and type the key word “location map” to retrieve various
information related to distance in kilometres.
165

Relationship between centimetres and millimetres

The length of the blue 1 cm
line is 1 cm or 10 mm.
cm
× 10
0 12345 cm mm
0 mm 10 20 30 40 50
÷ 10

10 mm 1 cm = 10 mm INFORMATION

1 6 cm = mm 2 120 mm = cm

6 cm = 6 × 10 mm 120 mm = (120 ÷ 10) cm

= 60 mm = 12 cm

6 cm = 60 mm 120 mm = 12 cm

3 3 cm 7 mm = mm 4 83 mm = cm mm

3 cm 7 mm = 30 mm + 7 mm 83 mm = 80 mm + 3 mm

= 37 mm = 8 cm + 3 mm

= 8 cm 3 mm

3 cm 7 mm = 37 mm 83 mm = 8 cm 3 mm

Is 120 mm longer than 19 cm? Discuss.

Complete the following. b 631 mm = 63 cm mm
a 152 mm = cm 2 mm d 71 mm = cm mm
c 4 cm mm = 49 mm f 34 mm = 3 cm mm
e cm 9 mm = 909 mm

12.1 (ii) TEACHER’S http://www.ixl.com.math/grade-3/compare-and-convert-metric-units-of-length
a NOTES

166

Relationship between kilometres and metres

Saiful will run 100 m back So, Saiful will run a × 1 000
and forth 5 times for distance of 1 000 m. This km m
training today. distance is equal to 1 km. ÷ 1 000

0 metre 100 metres

INFORMATION

1 km = 1 000 m

1 8 km = m 2 16 000 m = km

8 km = 8 × 1 000 m 16 000 m = (16 000 ÷ 1 000) km

= 8 000 m = 16 km

8 km = 8 000 m 16 000 m = 16 km

3 71km 900 m = m 4 25 300 m = km m

71 km 900 m = 71 000 m + 900 m 25 300 m = 25 000 m + 300 m

= 71 900 m = 25 km + 300 m

= 25 km 300 m

71km 900 m = 71 900 m 25 300 m = 25 km 300 m

5 km 25 m equals to 5 250 m. Explain.

Complete the following.

a 12 km = m b 78 000 m = km
c 3 km = m d 90 km = m
e 8 km m = 8 407 m f 50 km m = 50 021 m

12.1 (ii) TEACHER’S Carry out activities at the school track or field for simulation distance of 1 000 m or
b NOTES 1 km to reinforce pupils’ understanding.

http://www.math- Grills.com/measurement/matric_meters_kilometers_001.html 167

Measure length of objects good
luck
30 mm
Start measuring from 0 mm. The length of the
Read the measurement at ERASER eraser is 30 mm.
the other end.

DICTIONARY

The thickness of the dictionary is . The width of the bookmark is .

Y
X

Z

mm

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

1 What is the length of necklaces X, Y and Z?
2 Which necklace is the longest and which is the shortest?
3 What is your conclusion about the length of necklaces X and Y? Explain.

1 State the length of each object. (ii)
a b (i)

mm i mm ii mm

168 12.2 (i) TEACHER’S Carry out activities to estimate lengths of objects in mm and measure actual
NOTES lengths using measuring tape, thread, paper strip and ruler. Record the
measurements in a table.

http://www.vendian.org/mncharity/dir3/paper_rulers/

Estimate distance The estimated
distance from
Chalet jetty to chalet is
about 1 km.
Jetty 1 km
Jetty Health
Centre

Robotic X
Museum
Amusements
Centre

1 What is the estimated distance The estimated
from the chalet to the health centre? distance is 2 times
more than 1 km.
Jetty 1 km Chalet

Chalet Health Centre

Estimated distance = 2 km

The estimated distance from the chalet to the health centre is about 2 km .

2 State the place that is located almost 4 km from X .
The health centre is located almost 4 km from X.

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

Jetty Chalet Amusement centre
5 km
Estimated distance = 5 km 1 km

The estimated distance from the jetty to the amusement centre is about 5 km .

A digital library will be built within 3 km from the jetty.
Where is the suitable location? Explain.

12.2 (ii) TEACHER’S Create more questions on estimation of distances based on the above map.
NOTES Discuss the importance of estimation in daily life.

169

You and three friends found a treasure map X
showing a treasure placed at X . The estimated
distance from the arrow to the cactus A
area is 1 km. Complete the table below to
estimate the distance that you will pass B
through. C

1 km

Route A B C Use thread to

Estimated measure the curved
distance route. Compare with
the given estimated
(km)
distance of 1 km.

Discuss the route that you have chosen and give reasons.

The diagram below shows the estimated distances from Nelly’s house

to a few surrounding places. Library

Library

Nelly’s

House 1 km School
Internet
Bus Station

Bus Station

Centre

a Choose the correct answer.

i The distance from Nelly’s house to the school passing through

the library is (more than, less than) 10 km.

ii Nelly wants to go to the library, the distance is

(more than, less than) 5 km.

b What is the estimated distance from Nelly’s house to the Internet

Centre? Discuss and give reasons for your answer.

170 12.2 (ii) TEACHER’S Guide pupils to determine the estimated distances between two places based on
NOTES a given reference.

Addition of length After
3 days
1 Based on the picture, what is the
height of the seedling after 3 days? Increased by
2 cm 3 mm
5 mm

5 mm + 2 cm 3 mm = cm mm

cm mm
5

+2 3

2 8

5 mm + 2 cm 3 mm = 2 cm 8 mm
The height of the seedling after 3 days is 2 cm 8 mm.

2 Add 32 cm 5 mm and 40 cm 9 mm. mm
32 cm 5 mm + 40 cm 9 mm = cm
cm mm

32 5
+ 40 9

14

Convert 14 mm to
1 cm 4 mm.

cm mm

1 5
9
32 4
+ 40

73

32 cm 5 mm + 40 cm 9 mm = 73 cm 4 mm

TEACHER’S http://www.k5learning.com/free-math-worksheets/fourth-grade-4/measurement
NOTES
12.3 (i) 171
a

3 Calculate, in mm the total length of the ropes P, Q and R below.

P 18 cm 2 mm
Q 16 cm 5 mm

R 17 cm 8 mm

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

cm mm cm mm

21

1 8 2 18 2

1 6 5 16 5

+ 17 8 + 17 8

1 5 52 5

52 cm 5 mm = 520 mm + 5 mm

= 525 mm

18 cm 2 mm + 16 cm 5 mm + 17 cm 8 mm = 525 mm
The total length of the ropes P, Q and R is 525 mm.

4 Day Distance of cycle
First 76 km 433 m
Second 10 km 662 m

Calculate the total distance in the
cycling competition for the two days.

76 km 433 m + 10 km 662 m = km m

km m km m

76 433 1 433
+ 1 0 6 6 2 662
76 095
1 095 + 10

87

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

The total distance in the cycling competition is 87 km 95 m.

12.3 (i) TEACHER’S Drill pupils on conversion of units using flash cards.
a, b NOTES

172

5 Add 8 km 240 m, 20 km 790 m and 5 km 125 m.
Give the answer in m.

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

km m km m

1 11 1

8 2 4 0 8 240

20 790 20 790

+ 5 125 + 5 125

1 155 3 4 1 5 5

34 km 155 m = 34 000 m + 155 m

= 34 155 m

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

1 Calculate.

a cm mm b km m c cm mm d km m
51 8 3 1 28
34 7 14 261 10 3 11 492
7 1 01
+ 22 9 + 82 972 + 41 +7



2 Add. m
a 12 cm 3 mm + 4 mm = cm mm
b 15 cm 4 mm + 7 mm + 21 cm 9 mm = cm
c 65 km 28 m + 12 km 903 m = km m
d 25 km 114 m + 47 km 201 m + 665 m = km

3 Solve.

a What is the total length, in cm and mm, when 125 mm

is added to 40 cm 8 mm? P 7 200 R
b The distance from Q to R is 642 m
m

more than the distance from P to Q.

What is the distance, in km and m, from P to R? Q

12.3 (i) TEACHER’S Drill conversion of units using flash cards. 173
b NOTES

Subtraction of length

1 What is the difference of length between the two keys shown in the
pictures below?

5 cm 6 mm – 3 cm 2 mm = cm mm

cm mm 5 cm 6 mm 3 cm 2 mm
56
–3 2


2 4

5 cm 6 mm – 3 cm 2 mm = 2 cm 4 mm
The difference of length between the two keys is 2 cm 4 mm.

2 28 cm 6 mm – 8 mm – 13 cm 5 mm = mm

Method 1 Method 2

cm mm cm mm 7 16 2 7 8 mm
27 – 1 3 5 mm
28 16 27 8 2 8 6 mm
–13 5 – 8 mm 1 4 3 mm
– 6
2 7 8 mm
8

2 7 8 14 3


14 cm 3 mm = 140 mm + 3 mm

= 143 mm

28 cm 6 mm – 8 mm – 13 cm 5 mm = 143 mm

Which method would you choose? Why?

3 78 km 607 m – 23 km 179 m = km m

km m

9
5 10 17
78
– 23 607

1 79

5 5 4 2 8

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

12.4 (i) TEACHER’S Encourage pupils to check the answers using addition.
a, b NOTES

174

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

km m km m

13 1 2 5 9 7 9 km 182 m = 9 000 m + 182 m
6 3 12 – 3 4 1 5 = 9 182 m

1 2 7 4 2

– 1 4 5

1 2 5 9 7 9 182

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

5 32 km 720 m
15 km 785 m
8 km 950 m
AB C D

What is the distance from C to D based on the diagram above?

32 km 720 m – 8 km 950 m – 15 km 785 m = km m

km m km m Convert 1 km to 1 000 m.

2 11 16 12 22 16 16 10
31 17 2 0 17 7 0
23
32 7 2 0 – 15 770

–8 9 5 0 785

23 770 7 985


32 km 720 m – 8 km 950 m – 15 km 785 m = 7 km 985 m

The distance from C to D is 7 km 985 m.

First, add 8 km 950 m and 15 km 785 m. Then, subtract the
answer from 32 km 720 m. Is the answer the same?

Calculate.
a 94 cm 9 mm – 2 mm = cm mm
b 90 km 898 m – 47 km 288 m = km m
c 1 071 km – 67 km – 192 km = km
d 76 cm 3 mm – 33 cm 5 mm – 7 mm = mm
e 77 km 28 m – 9 km 35 m – 11 km 943 m = m

TEACHER’S http://www.bbc. uk/bitesize/ks2/maths/shape_space/measures/read/2/
NOTES
12.4 (i) 175
b

Multiplication of length

1 Ribbon Length

Pink 32 cm 2 mm

White 61 cm 5 mm

The table above shows the lengths of ribbons for two

types of bows.
a What is the length of ribbon needed to make 3 pink bows?

3 × 32 cm 2 mm = cm mm

cm mm
32 2
×3



9 6 6

3 × 32 cm 2 mm = 96 cm 6 mm
The length of ribbon needed for 3 pink bows is 96 cm 6 mm.

b Calculate the total length of ribbon, in cm, for 8 white bows.

8 × 61 cm 5 mm = cm

Method 1 Method 2

cm mm cm mm

6 1 5 6 1 5

× 8 × 8

4 8 8 4 0 488 40

+ 4 – 4 0 4 × 10 mm
48 8 c m 40 mm == 4489 82 ccmm + 4 cm
492 0

8 × 61 cm 5 mm = 492 cm

The total length of ribbon, in cm, for 8 white bows is 492 cm.

176 12.5 (i) TEACHER’S Drill multiplication of length, with or without conversion of units.
a NOTES Carry out activities like quiz and cross number puzzle to reinforce pupils’
understanding.

2 The distance of 1 round of go-kart circuit is 5 km 602 m. Calculate
the distance covered in 4 rounds.

4 × 5 km 602 m = km m

km m km m

2

5 6 0 2 5 602
×4
× 4
22 408
2 4 0 8

4 × 5 km 602 m = 22 km 408 m
The total distance covered in 4 rounds is 22 km 408 m.

3 6 × 8 km 278 m = m

1 44

8 km 278 m = 8 000 m + 278 m 8 278m
×6
= 8 278 m

4 9 6 6 8 m


6 × 8 km 278 m = 49 668 m

Multiply first. Then, convert km to m.
Is this method easier?

Solve.

a 2 × 9 cm 3 mm = cm mm b 6 × 36 cm 4 mm = mm
km
c 5 × 18 cm 2 mm = cm mm d 8 × 61 km 24 m = m
km m
e 3 × 4 km 118 m = m f 7 × 35 km 302 m =

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

12.5 (i) TEACHER’S Drill multiplication using flash cards and check the answers using calculator. 177
b NOTES

Division of length

1 What is the length of one part of the wood?

72 cm 9 mm ÷ 3 = cm mm

2 4 cm 3 mm A wood which is 72 cm 9 mm
3 ) 7 2 cm 9 mm long is cut into 3 equal parts.

– 6 –9

1 2 0

– 12

0

72 cm 9 mm ÷ 3 = 24 cm 3 mm

The length of one part of the wood is 24 cm 3 mm.

2 59 cm 4 mm ÷ 9 = mm

6 cm 6 mm 6 cm 6 mm = 60 mm + 6 mm
4 mm
9 ) 5 9 cm

– 5 4 + 5 0 = 66 mm

5 54

– 5 4 First, convert 59 cm 4 mm

0 to mm. Then, divide by 9.

59 cm 4 mm ÷ 9 = 66 mm Is this method easier?

3 The total distance taken by Jane to music class for 7 days
is 49 km 721 m. Calculate the distance taken by Jane in a day.

49 km 721 m ÷ 7 = km m

7 km 1 0 3 m
7 ) 4 9 km 7 2 1 m

– 49 – 7

0 0 2

– 0

21

– 21

0 49 km 721 m ÷ 7 = 7 km 103 m

The distance taken by Jane in a day is 7 km 103 m.

12.6 (i) TEACHER’S Remind pupils to give answers in the required units.
a, b NOTES

178

4 SEJAHTERA SUPERMARKET MURNI

PETROL STATION

MeGA SUPERMRKET

79 km 464 m

Murni Petrol Station is located 79 km 464 m ÷ 2 = km m

PbWaeenhttdrwaoMtleSiesetangtthiSaoeenSjdatuoihsptMteeaerrnamgcaSeauSrfpkruoeepmtre.mrmMaarukrreknetit? 2–) 3 9 km 732m
7 9 km 464m
6 000
1 9 + 1 464
1

– 18 – 14

79 km 464 m ÷ 2 1 06

= km m –6

04
How do you solve this problem –4

to give the answer in m? 0

79 km 464 m ÷ 2 = 39 km 732 m

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

60 km 600 m

The distance from P to R is 60 km 600 m. The Q R
distance from Q to R is 3 times the distance P

from P to Q. What is the distance, in m, from P to Q?

Solve.

a 16 cm 8 mm ÷ 2 = cm mm b 9 cm 2 mm ÷ 4 = cm mm

c 62 cm 5 mm ÷ 5 = mm d 21 km 819 m ÷ 7 = km m

e 79 km 200 m ÷ 6 = km m f 5 km 715 m ÷ 3 = m

12.6 (i) TEACHER’S Prepare question cards for division and carry out a quiz activity in groups. 179
b NOTES

Solve the problems

1 Zarul built 3 aeroplane models for Creativity
Club. For models A, B and C, Zarul used
cardboards measuring 15 cm 2 mm,
23 cm 5 mm and 13 cm 8 mm. Calculate
the total length, in mm, the cardboards used.

Given Cardboard A 15 cm 2 mm, Cardboard B 23 cm 5 mm,
Cardboard C 13 cm 8 mm.

Find Total length of cardboards in mm.

Operation Addition Draw a diagram.

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

Solve Total length mm

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

cm mm

1 1 2
5
15 8
5
2 3 52 cm 5 mm = 520 mm + 5 mm
= 525 mm
+ 1 3

5 2

Check cm mm cm mm

5 1 15

52 5 38 7
8 – 23 5
– 1 3
7 15 2
3 8

180 12.7 (i) 15 cm 2 mm + 23 cm 5 mm + 13 cm 8 mm = 525 mm

The total length of cardboards used is 525 mm.

TEACHER’S Guide pupils to solve problems using tables.
NOTES

2 The distance from Mr Jagdish’s house to the meeting venue is
47 km 850 m. After driving for 998 m, he stops to fill petrol. He

continues his journey for another 35 km 810 m and stops again
at a rest area. What is the remaining of his journey, in km and m?

Given Distance from Mr Jagdish’s house to the meeting venue is
47 km 850 m. Driving a distance of 998 m and stops
to fill petrol. Driving 35km 810 m and stops at rest area.

Find The remaining journey in km and m.

Operation Subtraction Total distance : 47 km 850 m

998 m 35 km 810 m Remaining
distance

Solve 47 km 850 m – 998 m – 35 km 810 m = Meeting venue

km m

km m km m

46 17 14 10 46 852
18 5 0 – 35 81 0
47
– 8 5 0
9 9 8


4 6 8 5 2 1 1 42

Check 47 km 850 m 48 km Estimate the
answer to the
998 m 1 km nearest km.

35 km 810 m 36 km

48 km – 1 km – 36 km = 11 km

11 km 42 m is close to 11 km.
The answer is reasonable.

47 km 850 m – 998 m – 35 km 810 m = 11 km 42 m

The remaining distance of Mr Jagdish’s journey is 11 km 42 m.

12.7 (i) TEACHER’S Guide pupils to underline information or keywords based on the given problem and
NOTES solve it with various strategies.

181

3 Encik Ismail needs strings to tie 6 similar parcels of the same size.

Each parcel needs 60 cm 3 mm. What is the length of string, in

cm and mm, needed to tie all the parcels?



Given There are 6 parcels.

60 cm 3 mm of string for 1 parcel.



Find Length of string needed for 6 parcels.



Operation Multiplication





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

Solve 6 × 60 cm 3 mm = cm mm

cm mm 360 cm 18 mm = 360 cm + 10 mm + 8 mm
60 3
= 360 cm + 1 cm + 8 mm
×6
= 361 cm 8 mm
360 18

6 0 cm 3 mm Check your answer
Check 6 ) 3 6 1 cm 8 mm by dividing it.

– 3 6 + 10

0 1 1 8

– 0 – 18

1 0

6 × 60 cm 3 mm = 361 cm 8 mm

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

182 12.7 (i) TEACHER’S Guide pupils to solve problems by simulation using real objects.
NOTES

4 The Jalur Gemilang Run of 10 km 500 m will
be held in conjuction with Hari Kemerdekaan.
4 runners run in a relay, carrying the
Jalur Gemilang. What is the distance, in m,
of each runner?


Given The distance is 10 km 500 m.
There are 4 runners.

Find The distance, in m, by each runner.

Operation Division Runner 1 Runner 2 Runner 3 Runner 4
10 km 500 m

Solve 10 km 500 m ÷ 4 = m

2 km 6 2 5 m
4 ) 1 0 km 5 0 0 m

– 8 +2000

2 2500 2 km 625 m = 2 000 m + 625 m
= 2 625 m
– 2 4

10

–8

20

– 2 0

0

Check

km m Check by multiplying
2 km 625 m by 4.
2 12

2 625
4
×

10 500

10 km 500 m ÷ 4 = 2 625 m

The distance of each runner is 2 625 m.

TEACHER’S Ensure that pupils check the answers and explain the importance of checking them.
NOTES
12.7 (i)
183

Solve.

a Tarmizi draws three straight lines with the lengths of 12 cm 4 mm,
8 cm 6 mm and 15 cm 9 mm respectively. What is the total length of
the three straight lines?


b Mei Chu recorded the measurements
of leaves that she brought for Science
experiment as shown in the picture.
Calculate the total length of the leaves.
7 cm 7 mm
30 mm
41 mm

c 12 km 18 m Mr Singam’s
House
Office Music Class

The diagram shows the distance between the office and the music
class. The distance from Mr Singam’s house to the music class is
3 km 120 m less than the distance from music class to the office.
What is the distance from his house to the music class?

d Rizal’s pencil is 12 cm long. Lily’s pencil is 3 cm 4 mm longer than
Rizal’s pencil. What is the total length, in mm, of their pencils?

e The table shows the distance to Taman Setia and Taman Anggerik
from Taman Kenanga.

Place Distance from Taman Kenanga

Taman Setia 10 km 217 m

Taman Anggerik ?

The distance from Taman Kenanga to Taman Anggerik is 3 times the
distance from Taman Kenanga to Taman Setia. What is the distance,

in m, from Taman Kenanga to Taman Anggerik?

f The width of a book is 3 times Dahlia’s hand span. The width of the book
is 36 cm 3 mm. What is the length of Dahlia’s hand span?

TEACHER’S
NOTES

18844

Materials Ruler, pencil, pen and Players 5 pupils in a group.

location map.

Kesuma Jaya Town is a new town. Suggest the locations for a recreational
park, a school and a mini library based on the estimated distance of 1 km
in the plan and the rules given.

Rules

a The distance of the recreational park is 1 km less than the lake so that
citizens can go fishing and cycling around the lake.
b The distance of the mini library is between 1 km to 2 km from the

community hall.
c The school is located between the recreational park and the mini

library with an estimated distance of 3 km.

KESUMA JAYA TOWN PLAN

X Multipurpose X
Shop
1 km Police Station
Community Hall
X

X

Lake

Steps

1 Mark X at the suggested location. Draw the distance and label the
name of the location.

2 Add other necessary facilities. State why do you need the facilities.
3 Discuss the outcomes of your group work.
4 Display it at the Mathematics corner.

TEACHER’S Make enough copies of the location map for each group.
NOTES
7.6 (i)
185

1 Measure the length of each object. Write the measurement.

a b

mm cm mm

2 Fill in the blanks.

a 62 mm = cm mm b 2 576 m = km m
d km 212 m = 16 212 m
c cm 5 mm = 85 mm

3 The distance of X and Y is given. Estimate the distance from Y to Z.

1 km b 4 km
a

X Y Z X Y Z

4 Complete the following.

a 26 cm 8 mm – 8 cm 8 mm = cm

b 18 cm 9 mm ÷ 9 = cm mm

c 14 cm 7 mm + 6 mm + 5 cm 5 mm = mm

d 3 × 12 cm 8 mm = cm mm

e 7 × 6 km 404 m = m

f 53 km 124 m ÷ 4 = km m

5 Solve.

a The distance from Azrul’s house to school is 3 km 742 m.
Calculate the total distance, in km and m, travelled by Azrul for
3 days, back and forth to school.

b A length of wire measuring 74 cm 5 mm, need to be cut into

5 equal parts. What is the length of one part of the wire in mm?

c P 25 cm Q The lengths of the lines X and Y
X are less than the line PQ as
80 mm shown in the diagram. Calculate

Y 120 mm the difference in length, in mm,
the lines X and Y.

TEACHER’S
NOTES

18866

13 School
MASS

Addition and subtraction of mass

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

Azim, how many grams

do you want to buy?

10 kg

0
500
1 kg 900 g 400 gram 100
300 200

Crackers
2 kg

What is the total mass of the items bought?

2 kg + 400 g – 150 g = kg g

k g g k g g

2 000 3 10
+ 400
2 400
2 400 – 1 50

2 250

2 kg + 400 g – 150 g = 2 kg 250 g
The total mass of the items bought is 2 kg 250 g.

Add the two masses of dodol. What is the 1 kg 900 g
difference in mass between the dodol and the
crackers bought?

13.1 (i) TEACHER’S " Add and subtract masses based on situations and simulation activities. 187
NOTES " Explain that adding and subtracting units of masses is the same as adding
and subtracting whole numbers.

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

kg g 450 g connot be subtracted from 80 g.

9 1 080 10 kg 80 g = 9 kg + 1 000 g + 80 g
= 9 kg 1 080 g
10 8 0

– 3 450

6 630 kg g

11

6 6 3 0 630 g + 370 g = 1 000 g
+ 2 370
= 1 kg
9 0 0 0

10 kg 80 g – 3 kg 450 g + 2 kg 370 g = 9 kg

3 26 kg + 8 760 g – kg g = 4 815 g

1 000 g 13 × 1 000
760 g 2 3 17 5 10 kg g
Convert 26 kg 26 760 g
to 26 000 g. 34 760 g ÷ 1 000

+8 INFORMATION

34 – 4 815 g
29 9 45 g

29 945 g = 29 kg 945 g

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

1 kg 500 g 1 kg 50 g 1 kg 550 g

PQ R

Determine the 2 packets of biscuits that should be mixed first.

Then, reduce 100 g so that the mass becomes 2 500 g.



188 13.1 (i) TEACHER’S " Pay attention on regrouping from g to kg.
NOTES " Emphasise on conversion for values more than 1 000 g.

Materials Weighing scale, pebbles, exercise book.

Players 4 pupils in each group.

Steps

1 The first pupil weighs a few pebbles and record its
mass.
2 The second pupil adds more pebbles and
record its mass. For example, add 600 g of pebbles.
3 The third pupil takes out some pebbles
and record the mass of pebbles left.
4 The fourth pupil writes the complete number
sentence involving addition and subtraction.
5 Discuss and solve the number sentence in groups.

1 Calculate.

a 4 kg 820 g + 5 kg 100 g – 1 kg 694 g = kg g

b 9 kg – 3 016 g + 1 kg 110 g = kg g

c 30 kg 60 g – 22 kg 445 g + 1 kg 32 g = g

d 27 kg 510 g + 7 kg 390 g – 18 kg 900 g = kg

e 16 kg 450 g – 9 480 g + 4 kg 30 g = kg

f 10 kg + 6 kg 5 g – 2 080 g = g

2 Subtract 3 510 g from the sum of 7 kg 30 g and 4 kg.

3 12 kg 9 kg 78 g 9 kg 200 g

Based on the cards above add the heaviest mass to the second
heavy mass. From the answer, subtract the lightest mass.

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

189

Multiplication and division of mass

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

Based on the picture, crisps
what is the mass of
crisps in 1 small pack? 50
4 kilogram 1
3 × 1 200 g ÷ 8 = g
32
4 5 0 g
1 200g 8 3 600 g
–3 2
× 3
4 0
3 600g – 40

00
– 0
0

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

2 8 x 2 kg 500 g ÷ 4 = kg Why subtract 1 000 g
and add 1 kg? Explain.
2 k g g
2 500
8 × 2 kg 500 g × 2
4 4 1 000
+ 1 –1 000
1 5 0



8 × 2 kg 500 g ÷ 4 = 5 kg

TEACHER’S " Guide pupils to multiply and divide units of mass through simulation or based on
given situation.
190 13.1 (ii) NOTES

3 18 kg 945 g ÷ 9 × 2 = g

2 kg 1 0 5 g kg g

9 1 8 kg 9 4 5 g 1

–18 –9 2 105
× 2
0 04
4 210
–0
4 kg 210 g = 4 000 g + 210 g
45 = 4 210 g

– 45

0

18 kg 945 g ÷ 9 × 2 = 4 210 g

First, multiply 9 by 2. Then, divide
18 kg 945 g by the product. Is the
answer the same?

4 31 kg ÷ 5 × 10 = kg

Method 1 6 kg 2 0 0 g kg g
6 200
5 3 1 kg 0g × 10
60 2000
–30 + 1000
60 kg 2 000 g = 60 kg + 2 kg
1 1000 = 62 kg

– 10 Which method do you
choose? Why?
00

–0

0 0

–0

0

M ethod 2 2

31 kg × 10
= 31 kg × 2

5
1 = 62 kg

31 kg ÷ 5 × 10 = 62 kg

13.1 (ii) TEACHER’S " Expose various strategies involving multiplication and division to enhance
NOTES pupils’ understanding.

191

200 g
4 kg

Each has the same mass. What is the mass of , in g?

Players 4 to 6 pupils. Materials Mass cards, symbol cards,
Steps number cards, envelopes.

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

8 350 g = 10 kg 20 g 6 ÷ × 5 (set 2)

2 Keep 1 set of cards in an envelope.
3 Teacher gives an envelope filled with the same set of cards to

each group.
4 Pupils arrange the cards to form a complete and correct number sentence.
5 The fastest group with the correct number sentence is given 5 marks. Other
groups are given 3 marks each.
6 Repeat steps 2 to 5 for different sets of cards.
7 The group that scores the highest mark is the winner.

Calculate.

a 5 × 8 kg 60 g ÷ 10 = kg g b 4 × 6 kg 300 g ÷ 6 = g

c 10 × 9 kg ÷ 12 = kg g d 40 kg 500 g ÷ 9 × 10 = kg

e 21 kg ÷ 5 × 3 = kg g f 19 kg 110 g ÷ 7 × 8 = g

TEACHER’S " Diversify activities involving mass for mixed operations in co-curriculum such as
cooking competition.
192 13.1 (ii) NOTES

Solve the problems

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

Given A bunch of rambutans is 2 kg 500 g, the watermelon is 3 kg,

the pomelo is 1 kg 750 g lighter than the watermelon

Find Total mass of the bunch of rambutans and the pomelo

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

1 kg 750 g ?

2 kg 500 g + 3 kg – 1 kg 750 g = kg g
Solve

2 kg 5 0 0 g 14 10
+ 3 kg 0 0 0 g 4 15 0 0
5 kg 5 0 0 g
5 kg 5 0 0 g
– 1 kg 7 5 0 g

3 kg 7 5 0 g

2 500 g 14
Check + 3 000 g 4 4 10

5 500 g 5 500 g

– 1 750 g

3 750 g

3 750 g = 3 kg 750 g

2 kg 500 g + 3 kg – 1 kg 750 g = 3 kg 750 g

The total mass of the bunch of rambutans and the pomelo is 3 kg 750 g.

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