MathematicsDLP Tahun 6

B Duration
Units of time

1 Sumitha and her father board a bus in Tanjung Malim, Perak at 0930 hours.

They are expected to arrive at Batang Kali, Selangor at 1015 hours. How long

is their journey?

BOARD ARRIVE Use a clock face.
The time ends at
5 minutes 5 minutes the time of arrival.

5 minutes 5 minutes

5 minutes 5 minutes

5 minutes

5 minutes
5 minutes

(5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5) minutes = 45 minutes
OR

9 × 5 minutes = 45 minutes

Their journey will take 45 minutes.

2 The National Day in 2016 fell on Wednesday, the fifth
week in August. Malaysia Day was celebrated on
Friday, the third week in September. How long, in weeks
and days, was the duration between the two events?

AUGUST 2016 SEPTEMBER 2016

S MTWT F S S MTWT F S
31 1 2 3 4 5 6 28 29 30 31 1 2 3
7 8 9 10 11 12 13 4 5 6 7 8 9 10
14 15 16 17 18 19 20 11 12 13 14 15 16 17
21 22 23 24 25 26 27 18 19 20 21 22 23 24
28 29 30 31 1 2 3 25 26 27 28 29 30 1

31 August, Wednesday until 6 September, Tuesday = 1 week
7 September, Wednesday until 13 September, Tuesday = 1 week
14 September, Wednesday until 16 September, Friday = 3 days

The duration between the two events was 2 weeks and 3 days.

Teacher’s Notes

Emphasise determining the correct start time, end time, and duration before
94 solving problems pertaining to time. 6.2 (i)

3 Puan Marlia attended a course from 4 March 2016 until 5 May 2016. How

long did she attend the course? State the duration in:

a days. b months and days. Use a calendar
to count.

2016

MARCH APRIL MAY

SMTWT F S SMTWT F S SMTWT F S

12345 12 1 234 5 6 7

6 7 8 9 10 11 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14

13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21

20 21 22 23 24 25 26 17 18 19 20 21 22 23 22 23 24 25 26 27 28

27 28 29 30 31 24 25 26 27 28 29 30 29 30 31

a Duration in days: b Duration in months and days:

4 March until 31 March = 28 days 4 March until 3 April = 1 month

1 April until 30 April = 30 days 4 April until 3 May = 1 month

1 May until 5 May = 5 days 4 May until 5 May = 2 days

Total = 63 days Total = 2 months

2 days

Puan Marlia attended the course for 63 days or 2 months and 2 days.

4 The THEMIS satellite was launched by NASA on
17 February 2007 to study the energy emitted
by the Earth’s magnetosphere. The duration of
the mission was 7 years, 7 months and 11 days.
When was this satellite’s operation terminated?

February Year Month Day Source: www.nasa.gov/mission_pages/
is the 2nd month. 2007 2 17 themis/main/index.html
+ 7 7 11
Sum according 20 14 9 28 AMAZING FACTS
to the units of
time. The Earth’s magnetosphere
is the magnetic field around
The THEMIS satellite’s operation was the Earth that protects
terminated on 28 September 2014. the Earth from solar wind,
harmful ultraviolet rays,
and radiation from
outer space.

6.2 (i) Teacher’s Notes 95

Get pupils to use other methods such as a timeline and diagrams to calculate the
answer.
Explain how to determine a leap year.
Emphasise the correct way to calculate the duration in days or in months and days.

5 Sali boards an express bus at 2230 hours from
Kuantan to Kota Bharu. The duration of the journey
is 5 hours 15 minutes. Calculate the time he will
arrive in Kota Bharu.

Method 1 Method 2

1 hour 1 hour 1 hour 1 hour 1 hour 15 minutes 30 minutes 4 hours 45 minutes

223203 0203300 000003 001000 130020 0023003 000330 0400 2230 0345
2300 0000 0100 0200 0300 0400

board 0345 2230 hours until 2300 hours — 30 minutes

arrive hours minutes

5 hours — 2230 hours until 0330 hours 4 75 duration
15 minutes — 0330 hours until 0345 hours
5 15
– 30

4 45

4 hours 45 minutes — 2300 hours until

Sali will arrive in Kota Bharu at 0345 hours. 0345 hours

6 Puan Marsha arrived in Taiping at 11:10 a.m.. Her journey from Kuala Lumpur

to Taiping took 4 3 hours. She stopped for 1 hour to refuel her car and rest.
4 2
At what time did she depart from Kuala Lumpur?

4 3421hhoouursr = 4 hours 45 minutes hours minutes 1 hour = 60 minutes.
= 30 minutes 10 minutes + 60 minutes = 70 minutes.
10 70 25 minutes + 60 minutes = 85 minutes.

11 10 hours minutes
– 4 45
5 85
6 25
6 25
– 30

5 55

Puan Marsha departed at 5:55 a.m. from Kuala Lumpur.

Teacher’s Notes

Discuss the conversion of time from the 12-hour system to the 24-hour system
96 and vice versa. Recall the conversion of units of time. 6.2 (i)

Discuss various calculation strategies to find the start time and the end time.

7 The following table indicates the duration and the ending time of the Space
Science Exhibition. When did the exhibition start?

Starting time Ending time Duration
10 April, 3:00 p.m. 8 days 6 hours

Method 1 Subtraction 3:00 p.m. = 1500 hours
Use subtraction.
days hours minutes
1 0 1 5 00

– 8 6 00
2 9 00

Meth od 2 Timeline 8 days

6 hours

3:00 p.m. End
2 April 3:00 p.m.
10 April

Start 8 days = 2 April, 3:00 p.m. until
9:00 a.m. 10 April, 3:00 p.m.
6 hours = 2 April, 9:00 a.m. until
2 April

2 April, 3:00 p.m.

Count back every
1 hour until 6 hours
starting from 3:00 p.m..

Why is the answer not

9:00 p.m. on 2 April? Explain.

The exhibition started at 9:00 a.m. on 2 April.

6.2 (i) Teacher’s Notes 97

Pose questions on calculating duration involving units of hours, minutes and
seconds, and days and hours. Vary the questions to calculate the start time and
end time of an event.

World time zones

1 a The whole world is divided into 24 time zones. The
calculation of time begins at 0o longitude, which is at

the Greenwich Line in England, United Kingdom.

The time in Kuala Lumpur is 8 hours The time difference between INTERNATIONAL DATE LINE
ahead of the time in London. The Kuala Lumpur and London is
time in Osaka is 1 hour ahead of 8 hours. The time difference
the time in Kuala Lumpur. between Osaka and
Kuala Lumpur is 1 hour.

London Kuala Lumpur Osaka Journey to the west
United Kingdom Malaysia Japan

12:00 noon 8:00 p.m. 9:00 p.m.
4 June 2016 4 June 2016 4 June 2016

b What is the time in Kuala Lumpur if the time BOOST
in London is 3:00 p.m.? YOUR KNOWLEDGE

Kuala Lumpur is in the east. • Make sure the country’s
The time difference is 8 hours. location is either on the west
or east.
Therefore, add 8 hours to the time in London.
• Find the time difference.
The time in Kuala Lumpur = 3:00 p.m. + 8 hours • Determine the operation. If

= 1500 hours + 0800 hours the country is located in the:

= 2300 hours

The time in Kuala Lumpur is east Add the time
2300 hours or 11:00 p.m.. difference to the time
in the country.
Why is time in the eastern
countries ahead of time in the west Subtract the time
western countries? Discuss. difference from the
time in the country.

Teacher’s Notes

98 Surf http://www.fgienr.net/time-zone/ to get the 24 time zones of the whole world. 6.2 (i)

Discuss the time difference between Malaysia and other countries and relate it

to the Earth’s orbit around the Sun.

London

Japan INTERNATIONAL DATE LINE
Malaysia

Greenwich Journey to the east
Line

st

c State the date and time in Kuala Lumpur if the time in Osaka
is 0030 hours on 31 March 2017.

Malaysia is located to the west of Osaka. The time difference is 1 hour.

Therefore, subtract 1 hour from the time in Osaka.

0030 hours = 12:30 a.m. It is the previous day
in Malaysia.

31 March 2017 30 March 2017

The time in Malaysia is 2330 hours or
11:30 p.m. on 30 March 2017.

6.2 (i) Teacher’s Notes 99

Emphasise the importance of stating the time correctly in the 12-hour system
or 24-hour system.

2 The clock tower in Auckland is 4 hours ahead of time
to the clock tower in Fraser’s Hill. What is the time in
Auckland if it is 10:15 a.m. in Fraser’s Hill?

Method 1 I add an hour repeatedly
until 4 hours.

10:15 a.m. 11:15 a.m. 12:15 p.m.

2:15 p.m. 1:15 p.m.

Method 2 1415 hours =
2:15 p.m.
AMAZING FACTS
hours minutes
10 15 Auckland is a city in New Zealand
+4 which is also known as the Yacht City.
14 15 The city receives the most sunshine
with the annual total sunshine of
2 060 hours.

The time in Auckland is 2:15 p.m. or 1415 hours.

3 Argentina is located to the west of Malaysia. The time difference between
the two countries is 13 hours. Determine the time and day in Argentina if the
time in Malaysia is 9:40 a.m. on Thursday.

Argentina 1:40 a.m. 3:40 a.m. 5:40 a.m. 7:40 a.m. Malaysia
west Thursday Thursday Thursday Thursday east

9:40 p.m. 11:40 p.m. 9:40 a.m.
Wednesday Wednesday Thursday

8:40 p.m. 10:40 p.m. 12:40 a.m. 2:40 a.m. 4:40 a.m. 6:40 a.m. 8:40 a.m.
Wednesday Wednesday Thursday Thursday Thursday Thursday Thursday

The time in Argentina is 8:40 p.m. on Wednesday.

100 Teacher’s Notes 6.2 (i)

Pose more questions as in examples 2 and 3 so that pupils can explore further
the time differences between various cities and countries in the world.

SELF-PRACTICE
1 Calculate the duration from:

a 10:00 a.m. until 9:30 p.m.
b 1:00 p.m., Saturday until 3:55 a.m., Sunday.
c 0400 hours, Monday until 1000 hours, Thursday.
d 1530 hours, Wednesday until 0200 hours, Friday.

2 What is the duration, in days?
a Thursday of the second week until Saturday of the third week.
b 21 May 2014 until 18 June 2014.

3 State the duration in years, months, and days.
a April 2017 until August 2020. b 23 February 2018 until 19 March 2023.

4 Complete the travelling schedule below.

START ARRIVE DURATION
1:30 a.m. 0515 hours 4 hours 15 minutes
6 hours 30 minutes

5 The time difference between Kuala Lumpur and Sydney is 3 hours. Sydney is

located in the east. If the time in Kuala Lumpur is 1600 hours, what is the time
in Sydney?

6 The time in Malaysia is 1:30 a.m., Thursday. The time in Italy is 6:30 p.m.,
Wednesday. What is the time difference between Malaysia and Italy? Give
another similar example of the above for both countries.

BRAIN TEASERS

A digital clock shows the time, day, and month as shown below. There
are times when the clock will display each of the digits, 0 to 9.

This is not the
earliest time, day,
and month in a year!

Arrange each digit from the digits 0 to 9 to get the earliest time, day,
and month in a year.

6.2 (i) Teacher’s Notes 101

Prepare cards for a quiz involving the start time, end time, and duration of various units of
time such as hours and minutes, days and hours, months and days, years and months
including the difference of time between Malaysia and other countries.
Use an event schedule and determine the duration of the listed activities.

C Solve the Problems

1 Suresh was born on 21 March 1988. The age difference
between his brother’s and his is 9 years 8 months and
9 days. When is his brother’s date of birth?

Solution

Given Suresh was born on Asked for Suresh’s brother’s date of birth

21 March 1988. The difference

in age with his brother is Operation Addition

9 years, 8 months and 9 days.

Solve year month day Check year month day
+
1 1 1997 1 1 30
– 989
1988 3 21
9 89 1988 3 21
1 1 30
1997

Suresh’s brother was born on 30 November 1997.

2 Bee Yee was selected for squash training as Squash Training
a preparation to represent the country for the 5 Feb to 9 April 2016
Olympic Games from 5 February until 9 April 2016
as shown in the table. How long did she practice Activity Start End
in a day? Time Time

Training 0715 hours 1200 hours

Rest

Solution Training 1430 hours 1830 hours

hours minutes hours minutes hours minutes

1 1 60 18 30 4 45
+ 4 00
12 00
8 45
– 07 15 – 14 30

4 45 4 00

Check 0715 hours until 1115 hours = 4 hours Calculate the duration Bee Yee
spent at the training centre.
1115 hours until 1200 hours = 45 minutes

1430 hours until 1830 hours = 4 hours

Total = 8 hours 45 minutes

Bee Yee trained for 8 hours 45 minutes in a day.

102 Teacher’s Notes 6.3 (i)

Use other strategies such as timeline, calendar or trial and error method to solve
the problem. Recall the leap year.

Movie Show Duration
time
3 Puan Jamilah and her child want to 1 hour
2:30 p.m. 42 minutes
watch a movie. They need to return How to 3: 15 p.m.
home at 3:00 p.m.. State the movie Train Your 1 hour
and the show time that is suitable for Dragon 2 1 :35 p.m. 27 minutes
them to watch. 1 :50 p.m.
Upin and Ipin 2 hours
the Movie 45 minutes

Transformers: 12:05 p.m.

Solution Important Age of 1 :45 p.m.
information
Extinction

Show times The movie and show time that is suitable
of each movie for Puan Jamilah and her child.

Solve Estimation

Movie Show Estimated End of Estimate the
time duration show time time each movie
How to Train Your will end.
2:30 p.m. 1 hour 4:1 0 p.m.
Dragon 2 3:15 p.m. 40 minutes 4:55 p.m.

Upin and Ipin 1 :35 p.m. 1 hour 3:05 p.m.
the Movie 1 :50 p.m. 30 minutes 3:20 p.m.

Transformers: Age 12:05 p.m. 2 hours 2:55 p.m.
1:45 p.m. 50 minutes 4:35 p.m.
of Extinction

There is one movie that ends before 3:00 p.m.. The movie is Transformers:
Age of Extinction which starts at 12:05 p.m..

Check How to Train Your Dragon 2

Upin and Ipin the Movie hours minutes Transformers: Age of Extinction

2 30

hours minutes hours minutes + 1 42 hours minutes hours minutes
3 72
1 1 50 1 1
+ 1 27 + 1 – 60
1 35 4 12 12 05 1 45
+ 1 27 2 77 + 2 45
+ 1 – 60 hours minutes + 2 45
2 62 14 50
+ 1 – 60 3 17 3 15 3 90

32 + 1 – 60

4 30

+ 1 42 1450 hours = 2:50 p.m.
4 57

6.3 (i) The movie and the show time that is suitable for Puan Jamilah 103
and her child is Transformers: Age of Extinction at 12:05 p.m..

Teacher’s Notes
Instil moral values such as punctuality.
Construct questions which use trial and error and estimation strategies to solve.

4 Nurhuda and her family returned from an
overseas vacation on 24 December 2015.
She and her family were on vacation for
2 weeks and 4 days. When did they begin
their vacation?

Solution Date of return:
24 December 2015

Important Duration of the 1 week = 7 days
information vacation:
2 weeks and 4 days
Solve
Find the beginning
date of the vacation

7 days — 18 December until 24 December 2015
7 days — 11 December until 17 December 2015
4 days — 7 December until 10 December 2015

Therefore, the beginning date of the vacation is 7 December 2015.

Check 2 weeks and 4 days — 18 days

START DECEMBER 2015 Count back 18 days
from 24 December
SMTWT F S 2015. The counting
30 31 1 2 3 4 5 must include the
6 7 8 9 10 11 12 return date.
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31 1 2

END

Nurhuda and her family began their vacation on 7 December 2015.

104 Teacher’s Notes 6.3 (i)

Discuss whether the calculation of duration should take into account
the first day by giving several examples of different situations.

5 The English Premier League Football is broadcast live from England on
Saturday at 7:00 p.m.. England is located to the west of Malaysia. The time
difference between England and Malaysia is 8 hours. On which day and at
what time will Encik Rizal watch the match in Malaysia?



Solution

Important information England

England is located Malaysia
in the west and
Malaysia is located
in the east. The time
difference is 8 hours.
The time in England
is 7:00 p.m..

Find the day and time of
the broadcast in Malaysia.

Solve Greenwich Line

Malaysia is located to the east of England. Therefore, add 8 hours to the time

in England. Use subtraction to check

the answer.

England 8 hours Malaysia

7:00 8:00 9:00 10:00 11:00 12:00 1:00 2:00 3:00

p.m. p.m. p.m. p.m. p.m. midnight a.m. a.m. a.m.

Saturday Sunday

6.3 (i) Encik Rizal will watch the live broadcast of the game 105
in Malaysia on Sunday at 3:00 a.m..

Teacher’s Notes
Surf http://www.timeanddate.com/time/map/ to get the interactive time zones.
Carry out interactive activities with pupils to find the time of any city in the world.

6 Puan Rani who is in Malaysia wishes to
contact her son who is studying at a university
in New Zealand. Malaysia is located to the
west of New Zealand. Her son returns from
lectures at 5:00 p.m., New Zealand time. The
time difference between the two countries is
3 hours. At what time can Puan Rani contact
her son?

Solution

Important information

• Her son returns from lectures at Malaysia
5:00 p.m..

• Time difference is 3 hours.
• Malaysia is located to the west of

New Zealand.

• Find the time in Malaysia for
Puan Rani to contact her son.

Solve

The time in Malaysia is 3 hours New Zealand
behind the time in New Zealand.

Time in Malaysia = Time in New Zealand – Time difference

= 5:00 p.m. – 3 hours

= 1700 hours − 0300 hours 1400 hours = 2:00 p.m.

= 1400 hours

Puan Rani can contact her son after
2:00 p.m., Malaysian time.

Cairo is the capital of Egypt. It is located to the west of
Malaysia. The time difference between Malaysia and
Cairo is 6 hours. State the time in Cairo, if the time in
Malaysia is 2130 hours.

106 Teacher’s Notes 6.3 (i)

Emphasise the addition and subtraction of time based on the country’s location
in the world map.
Vary the situations involving time in Malaysia compared to other countries in the
world to enhance pupils’ understanding.

7 Encik Hanif boarded an aeroplane from
Kuala Lumpur to Istanbul, Turkey on Monday at
2330 hours. Istanbul is located to the west of
Malaysia. The time difference between Istanbul
and Kuala Lumpur is 6 hours. The flight took
11 hours. On what day and at what time would
Encik Hanif arrive in Istanbul?

Solution Turkey

Important information Malaysia

• Departed from Kuala Lumpur
on Monday at 2330 hours.

• Istanbul is located to the west
of Malaysia.

• Time difference is 6 hours.
• Flight duration is 11 hours.

• Find the day and time of
arrival in Istanbul.

Calculate the time after 11 hours in Malaysia.

30 minutes 10 hours 30 minutes 11 hours

2330 1030
0000 0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100

The journey from Kuala Lumpur to BOOST
Istanbul means travelling to the west. YOUR KNOWLEDGE
Therefore, subtract 6 hours from 1030 hours.
When travelling towards east,
Time in Istanbul = 1030 hours – 6 hours add time and when travelling
= 1030 hours – 0600 hours towards west, subtract time.
= 0430 hours

6.3 (i) Encik Hanif arrived in Istanbul on Tuesday, 0430 hours. 107

Teacher’s Notes
Discuss the location of major cities in the world and construct appropriate
questions in groups.

8 Encik Hilmi wants to watch the USA Open Tennis Championship held in
Flushing Meadows, New York. The broadcast of the opening ceremony
begins at 10:00 a.m., New York time. New York is located to the west. At what
time will Encik Hilmi be able to watch the opening ceremony in Malaysia if
the time difference between Kuala Lumpur and New York is 13 hours?

Solution

The broadcast of the opening ceremony at 10:00 a.m.,
Given New York time.
New York is located to the west.
The time difference is 13 hours.


Asked for The broadcast of the opening ceremony of the championship
in Malaysia

Operation Addition

Solve Solve Use the timeline that represents world time
zones. Convert the time into 24-hour system.

New York Greenwich Malaysia
Line

1000 hours ?

13 hours

Meaa slat.yTshi eareisfor leo,ciatste tidmetom tuhset The opening ceremony broadcast time
be ad ded b ecaus e the time in Malaysia:
1000 hours + 13 hours = 2300 hours
is 13 hours ahead compared
2300 hours = 2300 – 1200 hours
to the time in New Yo rk .

= 1 100

1 1:00 p.m.

Encik Hilmi can watch the broadcast of the opening ceremony
at 2300 hours or 11:00 p.m. in Malaysia.

108 Teacher’s Notes 6.3 (i)

Emphasise the location of New York City and Malaysia.
Guide pupils to determine the operations whether to add or subtract the time.

SELF-PRACTICE
Solve the following problems.

a Anthiri and her family boarded a ferry to Pulau Langkawi Langkawi
from Kuala Kedah for a holiday. The ferry departed at
1420 hours. They reached Kuah Jetty, Pulau Langkawi at Kuala
1605 hours. Calculate the duration, in hours and minutes, of Kedah
their journey.

b Danish was born on 10 November 2004. His father was born
on 7 June 1970. What is their age difference?

c The incomplete table below shows the information about
the satellites which were launched by the United States to Landsat 5

collect images of the surface of the Earth.

Type of satellite Date launched Date ended Duration

Landsat 5 1 March 1984 5 June 2013

Landsat 7 15 April 1999 11 January 2015

i. Calculate the duration and complete the table above. Landsat 7

ii. Which satellite was longer in space and what was the difference in time?

d The train schedule shown is torn. The duration of Destination Departure Arrival
the train journey is 3 hours 45 minutes. What is the Tenom 1025 hours
arrival time?

e Kim Leong attended the PLKN Course for 3 months 5 days. His course ended
on 31 December 2016. When did the course begin?

f The time in Saudi Arabia is 1:00 a.m. when it is 6:00 a.m. in Malaysia. What
time is it in Saudi Arabia, when it is 4:00 p.m. in Malaysia?

g The 2016 Olympic Games was held in Rio De Janeiro, Brazil. The city is located
to the west of Malaysia. Brazil is 11 hours behind Malaysian time. What time is
it in Malaysia, when the opening ceremony in Rio De Janeiro is broadcast at
2:30 p.m.?

h Mr Gan boarded an aeroplane at 1630 hours from Kuala Lumpur to Vancouver,
Canada on Wednesday. The time in Kuala Lumpur is 15 hours ahead of
Vancouver. Vancouver is located to the west of Kuala Lumpur. The flight took
19 hours. At what time would Mr Gan arrive in Vancouver?

6.3 (i) Teacher’s Notes 109

Conduct a quiz or game to calculate duration in any unit of time and state the
corresponding time between Malaysia and some of the world’s capital cities.

SKILFUL MIND

1 Complete the following table:

12-hour system 9:15 p.m. 12:30 p.m. 7:10 a.m.
1805 hours 0010 hours
24-hour system 1245 hours
Duration
2 Complete the table.
6 hours 30 minutes
Start time End time 5 hours
2:05 p.m., 9 January 2015
5:15 a.m., 7 January 2015 1910 hours, Wednesday 3 days 4 hours
10:30 p.m., 20 December 2016 2 years 4 months
2130 hours, Tuesday
1:20 a.m., 6 September 2016 0515 hours

2030 hours 16 May 2017

27 August, 7:00 p.m.

3 Solve the following problems.

a Zara communicates with her Swedish friend through social media.
Sweden is 7 hours behind Malaysian time. Malaysia is located to the east
of Sweden. If she wishes to make a video call to her friend, is it proper for
Zara to contact her at 9:00 a.m., Malaysian time?

b Mr Vincent works in Korea which is located to the east. He wishes to visit
Malaysia and takes a flight at 0830 hours from Korea to Kuala Lumpur.
His flight takes 6 hours 15 minutes. The time difference between the
two countries is 1 hour. At what time is Mr Vincent expected to reach
Kuala Lumpur?

c Puan Nabihan’s itinerary in London is as follows:

Activity Start Time/Date Arrival Time/Date Duration

Flight to London 11:45 p.m., 28 February 2016 6:00 a.m., 29 February 2016 3 days
4 days
Seminar Registration in 8:00 a.m., 1 March 2016
London

Seminar in London 1 March 2016

Visits in London 4 March 2016

Return flight from London 8 March 2016, 1530 hours
(local time in London)

London is located to the west of Malaysia. The time difference between
London and Malaysia is 8 hours. The flight to London takes 14 hours 15 minutes.

i. How many days will Puan Nabihan be in London?
ii. State the date and time Puan Nabihan arrives in Malaysia.

111100 Teacher’s Notes 6.1 - 6.3

Pose challenging questions involving corresponding time of countries located
to the west and east of the Greenwich Line. For example, the comparison of
time in Malaysia and United States of America.

SELF-ASSESSMENT
A Answer all the following questions.

1 Write 1 020 409 in words. 10 10 356 × 98 − 37 005 =

2 Convert 0.37 million to a whole 11 8.4% of RM9 000 is .
number.

12 What is the fraction that can be
1
3 State the digit value of digit 6 in divided by 4 to get the answer of
6.04 million.
4 1 ?
7 4 2
4 Solve: 8 × 5 =
13 The diagram shows a number
5 1.3 million − 25 million = sequence.

6 The diagram shows four number 6, 18, 54, 162, , P
cards.
Explain how to get the value of P
403 815 4 217 863 63 094 1.034 million using a calculator.

Form a number by using the digit 14 7.5 ÷ 0.8 × 20 =

values of 4 from each of the card. 15 4 2 ÷ 18 =
5
7 Solve the following question with
a calculator. Round off the answer 16 19 032 + 73 048 × 60 =
to two decimal places. Round off the answer to the

1 456 922 ÷ 83 = nearest ten thousand.

8 1, 13, 25, 37, .... 4, 13, 22, 31, .... 17 1 hundred thousand + 240 360 ÷ 40 =

Look at the two sets of number 18
sequence above. Number 13
appears in both the number a.m. a.m.
sequences. State another number
which appears in both the London Malaysia
number sequences above. 8/4/2016 8/4/2016

State the time in London if the

time in Malaysia is 7:00 p.m..

9 State two prime numbers that have 19 7 1 × 4 =
a total of 20. 5 9

20 List eight prime numbers which
lies between 20 and 60.

111

21 Given, A ÷ 1 = 8. 30 Complete the table below.
3
1
Solve (A ÷ 3 ) × 2 = . Item Cost Selling Discount Percentage

price price (RM) of

22 The diagram shows a number (RM) (RM) discount (%)
line.
Telephone 900 765
1 1 1 3 P 2 1 Q Camera 1 200 300
2 4 2 Laptop 3 600
25

Calculate P × Q.

23 34 × 8.96 ÷ 7 = 31 The incomplete invoice below shows
Mr Gan’s order. Calculate:
24 Write the number sentence a. the goods and service tax (GST).
involving the product of a proper b. the total to be paid.
fraction and a proper fraction
based on the diagram below. INVOICE
Syarikat Ambang Sdn. Bhd.
➙
To: Gan Huat Trading, Invoice Number: PR26601
A-20, Prisma Square, Date: 29 April 2016
43100 Gombak,
Selangor.

25 2.054 ÷ 1.3 × 9 = ÷ 10 No. Items Quantity Price per unit Total
Find the value in the box. (RM) (RM)
26 Convert the time into
1. Toaster 20 45.00
the 12-hour system. 0010 hours
2. Hairdryer 15 98.00

3. Vacuum cleaner 10 230.00

Total
GST 6%
Total amount to be paid

27 2015 2016

October ➙ January 32 Calculate the dividend received
after investing for a year.
13 6
Value of investment: RM50 000
Find the duration in months and Dividend: 6.5% per year.
days between the two dates
above.

28 Give examples of two types of: 33 Find the selling price of the car and
a. assets. b. liabilities. house shown.


 

29 Complete the table below.

Start time End Time Duration
 

7 April, 9 April, Cost price: RM58 920 Cost price: RM296 880

1845 hours 0630 hours Loss: RM12 630 Profit: RM25 720

29 June, 8 July,

1950 hours 0530 hours

112

34 Housing Project Phase 1 40 Solve.
Start: 23 September 2012
Complete: 8 August 2015 8 ÷ 4 ÷ 5 × 2
15 5➙ 6➙ 3➙
How long does it take for the
project to be completed? Compare the final answer with the

35 Based on the information given, first fraction. Explain.
what is the possible number of 2-D
and 3-D movie tickets sold? 41 6 2 × Q = 30.
3

What is the value of Q?

Price of 2-D tickets Price of 3-D tickets

RM10 RM18 42 Find 28.4% of RM1 500.

Total sale of tickets = RM1 580 43 4 1 hours + 2 hours 56 minutes
4
36 Use a calculator to complete the
blanks. = hours minutes

4.081 million + 0.919 million 44 Determine whether the calculation
below is correct. If not, correct it.
÷

× 11 2

a. 5 × 5 = 1 b. 5 × 6 = 7
88 9 7 10

45 Solve. 3

37 Calculate 6 250 000 – 3.09 million. 1 1 × 1 = 1 ÷ 1 =
Round off the answer to the 2 3 2 3
nearest hundred thousand.
141 ÷ 3 = 3 × 141 =
38 Use a calculator to find the 8 10
answer. State the number pattern.
46 Complete the following table.
1 ÷ 11 = 0.0909
2 ÷ 11 = 12-hour 24-hour Duration
3 ÷ 11 = system system
4 ÷ 11 =
5 ÷ 11 = 8:20 a.m.
to
39 Business Hours
11:00 a.m. – 9:30 p.m. 10:45 a.m.
Find the duration of the business
1700 hours
hours. to

1930 hours

.... to 7 hours

0810 hours 50 minutes

113

B Solve the following problems.

1 The number of residents in a town 7 An express bus departed from

is 0.107 million. The number of Kuala Lumpur to Kangar at
adults is 65 000 and the rest are
children. How many children are 10:10 p.m., on Tuesday. The
there in the town?
journey took 7 3 hours. When did
4
the bus arrive at Kangar?

2 The selling price of a watch is 8 The estimated number of vehicles

RM2 640 and the profit is 10%. that passed a toll plaza for two

Calculate the cost price of the watch. days continuously is between

3 A total of 37 marbles is filled into 0.018 million to 0.019 million. The
3 containers. Each container has a number of vehicles that passed
different number of marbles and the toll plaza on the first day was
each value is a prime number. 2 times the number of vehicles
How many marbles are there in on the second day. Estimate the
each container? number of vehicles that passed the
toll plaza on the second day.

4 Asraf bought a pizza. He gave 9 The table below shows the
number of Year 6 boys in a
a38teof61thoef pizza to Sarah and he school. Each class has 40 pupils.
the remaining pizza. Calculate the percentage of
Year 6 girls in the school.
Calculate the fraction of pizza left.
Class 6S 6K 6D

5 Mr Kumaran invests RM100 000 Number of boys 26 20 20
in a company. The dividend he
receives from the investment 10 The total price of a smartphone
is 7.8% per year. What is the and its cover is RM2 000. The price
dividend that he receives after of the smartphone is RM1 760
a year? more than the price of its cover.
Calculate the price of the cover.

6 Sin Yi completed 1 of his project 11 The sum of two numbers is
6 the duration 0.5 million. The difference
1
in 2 3 days. Calculate

he took to complete his project. between the two numbers is

1 million. Find the value of the
5
two numbers.

114

12 The time allocated for a test is an 15 The following is the nutritional
facts for a type of biscuit.
hour. Amalin completed the test

1 hour earlier than the time given, Nutritional facts for a serving (50 g)
4

whereas Rina took 5 minutes more Energy 14 g Protein 3.5 g

than Amalin. Calculate: Fat 5.5 g Carbohydrate 27 g

a. the percentage of time taken Calculate the percentage of each
nutrient.
by Amalin.

b. the time taken by Rina to

complete the test. 16 The table below shows the departure
time of a train from Town A and the
13 An advertisement shows the arrival time at Town B.
prices of 3 pianos and the
discounts during a promotion. Train Departure Arrival
Which is the cheapest model
after discount? State its price. 1 8:35 a.m. 10:05 a.m.

2 9:05 a.m. 10:30 a.m.

3 9:30 a.m. 11:10 a.m.

Zailan missed the first train by

1 hour and she had to take the
4

Model A Model B Model C second train. Calculate the total

RM12 400 RM12 600 RM13 500 time taken by Zailan from the time

Discount 10% Discount 15% Discount 20% she arrived at Town A until she

14 The diagram shows the volume arrived at Town B.
of orange juice in a jug.

1 1 ℓ 3 ℓ 17 Aida has booked an overseas
5 10 flight ticket and she will depart
on 5 August. She must make a
How many 3 ℓ glasses are payment at least 3 weeks prior to
10 the date of departure. What is the
due date for the payment of
her ticket?

needed to fill in all the orange

juice?

115

18 The time in Thailand is 1 hour 22 Khalidah and her family went for a
earlier compared to Malaysia. If dinner. The bill was RM119.50. They
the time in Thailand is 1630 hours, were charged 6% for the service.
Monday, state the day and time
in Malaysia. a. How much was the service
charge?
19 A company distributed 18 400
bottles of mineral water to two b. How much change will she get
flooded districts respectively. The if she paid 3 pieces of RM50?
company also distributed 20% of
the total contribution of mineral 23 A temporary worker works for
water to another flooded district. 9.5 hours and gets paid RM61.75.
Calculate the number of bottles If the rate of payment is the same
of mineral water for the three for each hour, calculate his
flooded districts. payment for a duration of 4.5 hours.

20 Puan Ina bought a cake. Half 24 The table shows an incomplete bill.
of the cake was given to her
neighbour. The remaining half Price Total
was shared equally among 8 Quantity Item per unit
family members. What fraction
of the cake did each family 5 Milk RM29.80
member get? packets powder

4 Cooking RM14.70
bottles oil

6 kg Rice

21 The diagram shows the distance Encik Nordin paid RM250 and

from Prakash’s house to the received a balance of RM27.50.

 
  temple via th2e 0b.a42n5k0..k4m5 km
a. What is the selling price of a
kilogram of rice?

20.45 km b. State the items from the table

that can be bought with the


 
 
 
 
 
  balance.
KSuuPri lerhaKSsokuhuuarPissleehras’shkaBsBahanknwkBoarknskin Temple
the bank. 25 The time difference in Moscow and
The Malaysia is 7 hours. Moscow is

distance from his house to the located to the west. If the time in
temple is 5 times the distance Malaysia is 3:40 a.m. on

from his house to the bank. 22 August 2016, what is the date

Calculate the distance from the and time in Moscow?
bank to the temple.

116

7

A Measurement of Length, Mass, and Volume of Liquid

Let’s calculate Medical Purpose
check-up
1 Ajay, your mass is 36 kg. To determine the
Ajay, your height is 1.4 m. Height and pupils’ diet status for
mass check-up an ideal body mass

or obese.

BMI Guide

< 14.8 = Underweight
14.8 – 21.6 = Ideal weight
21.6 – 25.2 = Overweight risk
25.2 or higher = Obese

Way to calculate Body Mass Index (BMI)
BMI = Body mass (kg)
Height (m) × Height (m)

megnogSviu.rmam-ytbu/eibnru:dhhe-txti3Bp,dp0MC:e/hTaaIa/ipnplrt.=/aaghmTsutgiB1onmmr8isa.lgep(.<lie5dagmb2eJnal1iii5n–/s)hg8n9iem.–2i=65rr(4aa37B=Kb.n-0(9MIaecmgKna=I=ldaee)dt)rainbKakJneni.iu-egsPkhPrig(sgaamakeeinn×Jngmmdidbkg)sjPaieauesiuaemnridasknmimkaainjhisjsninbesaaBimiaraumMtidannkmIagbsnengaamudamslaptnaunutrnuidysMSaspeeeiebnommaebanaebstskuad.akniapanenrlukan Source: Surat Pekeliling Ikhtisas Bil. 4/2008,
Standard Kecergasan Fizikal Kebangsaan
mass? untuk Murid Sekolah Malaysia (SEGAK).

Does Ajay have an ideal body

BMI = Body mass (kg) (m) 2 My brother’s mass is 30 kg
Height (m) × Height but his height is only 1 m.

= 36 Your brother is
1.4 × 1.4 overweight or obese.
He must control his diet
and do more exercises.

= 36
1.96

= 18.36

18.36 is between the range of 14.8 and 21.6. BMI = 30
Therefore, Ajay has an ideal body mass. 1×1

What is your BMI? Discuss = 30
ways to maintain an ideal
body mass.

7.1 (i) Teacher’s Notes 117

Instil good practices such as nutritious diet and exercise to obtain good
Body Mass Index.
Surf http://www.myhealth.gov.my/index.php/bayikanak-kanak/umum/
perkhidmatan-kesihatan-sekolah

3 The picture below shows the volume of water in two containers, R and S.

1 1 ℓ R
2

S

450 mℓ

Mrs Jim wants to prepare some syrup. She dissolves 180 g of sugar in
container R. How much sugar, in g, should be dissolved in container S so that
both the containers have the same concentration of syrup?

1 1 ℓ = 1 500 mℓ
2

Method 1 Method 2

Volume Mass 1 500 mℓ 180 g
of water of sugar 1 mℓ
180 g
1 500 mℓ 180 g 450 mℓ
÷ 10 ÷ 10 1500 mℓ
18 g
150 mℓ ×3 180 g × 3 mℓ = 54 g
×3 1500 mℓ
450

1

450 mℓ 54 g

The mass of sugar that should be dissolved in container S so that both
the containers have the same concentration of syrup is 54 g.

If the mass of sugar is 0.9 kg, what is the volume of
water, in ℓ, needed to prepare the same concentration
of syrup as in the example above?

BRAIN TEASERS

ℓ × 46 < 900 mℓ
What is the largest possible value in the box?
Give your answer to 3 decimal places.

118 Teacher’s Notes 7.1 (i)

Pose various questions involving other operations learned in Year 4 and Year 5.
Make sure the levels of questions are easy, followed by average, and then complex.
Surf http://www.onlinemathlearning.com/measure-liquid-volume.html

4 The diagram on the right shows the 6 cm
mass of a pandan cake in the shape of
a cuboid. The pandan cake is cut into 2 cm
several pieces of the same size. The mass
of each piece of cake is 200 g. Determine 4 cm
the measurement for each piece of cake.

1.2 kg = (1.2 × 1 000) g 1.2 kg ÷ 200 g = pieces
= 1 200 g
6
1 200 g
1.2 kg ÷ 200 g = 200 g

1

= 6 pieces

The measurement of each piece of pandan cake is probably:

a First way of cutting: Get the size of each piece of cake:

2 cm 2 cm

4 cm 2 cm
2 cm
6 cm
Get the size of each piece of cake:
b Second way of cutting:

2 cm 2 cm

4 cm 4 cm
1 cm
6 cm

Discuss the different ways to cut
the cake. State the size of each
piece of cake.

7.1 (i) If 100 g of the same type of cake contains 380 calories, how 119
much of calories found in each piece of cake? Discuss.

Teacher’s Notes
Discuss the calories needed by children based on gender, age, height, and level
of physical activities. For example, the calories needed by children between the
age of 10 to 12 years old is about 2 000 calories.
Surf http://www.mod.gov.my/phocadownload/panduannilai_kalori.pdf

Solve the problems

1 Maria’s body mass is 68 kg. She is obese based on her
mass, height, and age. She tried to reduce her body mass by
cycling 3 km and jogging 2.5 km every day for four weeks.
Then, her body mass decreased by 5%. Calculate Maria’s
new body mass.

68 kg

Solution

Given Original mass 68 kg
Decreased 5% of body mass

Asked for New body mass

Operation Subtraction and multiplication

Solve Original mass = 100% Check

New mass = 100% − 5% 5 × 68 kg = 0.05 × 68 kg
100
95 = 95%
95 100 × 68 kg = 0.95 × 68 kg
95% = 100 3
4
53
74 0.05

0.95 × 68 kg

× 68 kg 0 40

1 + 03 00

7 60 3.40 kg

+ 5 7 00 68 kg − 3.4 kg = 64.6 kg

64.60 kg

Maria’s new body mass is 64.6 kg.

Which is the correct number sentence to calculate Maria’s total distance of
cycling and jogging activities in 4 weeks? Discuss and solve it.

(3 + 2.5) km × 4 = (3 + 2.5) km × 28 =

120 Maria wants her body mass to be 51 kg. How many weeks 7.1 (i)
does she need to achieve it?

Teacher’s Notes
Discuss other daily situations involving mass and height such as growth of children.
Emphasise that pupils need to underline important information.

2 Puan Ina buys a piece of cloth measuring 14 m in
length that costs RM210. The cloth is cut into 7 pieces of
equal lengths. She uses 3 pieces of the cloth to make a
tablecloth. What is the length of cloth, in m, used to make
the tablecloth? Calculate the cost of the tablecloth.

Solution Important information

➙ ➙

14 m of cloth — RM210 Length of the tablecloth — ?
14 m of cloth is cut equally to 7 pieces. The cost of the tablecloth — ?
3 pieces are used to make a tablecloth.

Solve 14 m

3 to make a tablecloth.
7

The length of the tablecloth The cost of the tablecloth

3 × 14 m = 3 × RM210 =
7 7
RM30
3 × 2 m = 3 ×2 m 3 × = 3 × RM30
7 = 6 m 7 RM210
14
1
1 = RM90

3 × 14 m = 6 m 3 × RM210 = RM90
7 7

Check 14 m ÷ 7 × 3 = 6 m RM210 ÷ 7 × 3 = RM90

The length of the cloth used to make the tablecloth is 6 m and the cost is RM90.

Puan Ina used the remaining cloth to sew 10 pillowcases of
equal size. What is the length of cloth used for each pillowcase?
Estimate the cost.

7.1 (i) Teacher’s Notes 121

Use other strategies such as conducting simulation to solve the problem.
Surf http://www.onlinemathlearning.com/adding-lengths.html

3 The diagram below shows the position of three locations along a
straight road.

15 km

5 km

Haziq’s house Mosque Shopping complex

Haziq drives from his house to the shopping complex. On the way home,
he stops to pray at the mosque. Haziq used 2 litres of petrol for the distance
travelled. If he drives at constant speed, how many litres of petrol is needed
for a distance of 1 km?

Solution

15 km

5 km ? km

Calculate the distance from the mosque to the shopping complex and the total distance
travelled by Haziq.

The distance from the shopping complex to the mosque: 15 km – 5 km = 10 km

The total distance travelled by Haziq is: 15 km + 10 km = 25 km

25 km 2 ℓ
1 km 2 ℓ ÷ 25 =

Divide 2 ℓ by 25 to 0.08 ℓ Use a calculator
25 2.00 ℓ to check the
get the answer. answer.
–0
20

–0
200

– 200
0

Haziq used 0.08 ℓ of petrol for a distance of 1 km.

The speedometer in Haziq’s car recorded a distance of 36.9 km. After
prayers, he drove home. What is the reading on the speedometer when
he reached home? Discuss.

122 Teacher’s Notes 7.1 (i)

Inculcate the moral values of using unleaded petrol to minimise air pollution.
Discuss daily situations involving volume and distance. For example, the use of
insecticide and the area of the farm, watering trees along the road by the district
municipal council and the distance.

4 Puan Nora bought 6 packets of organic

vegetables with a total mass of 6 500 g. Spinach Bitter gourd Cabbage
The mass of each packet of vegetable 900 g 1 kg 1 200 g

is shown in the pictures on the right.

She bought at least one packet of each

type of vegetable. How many packets

of each type of organic vegetable did RM4.80 RM5.60 RM3.90
she buy?

Solution Trial and error Total mass of 6 packets — 6 500 g
First Trial
1 kg = 1 000 g

Spinach Bitter gourd Cabbage 3 100 g
900 g 1 000 g 1 200 g

6 packets 1 000 g 1 200 g 2 200 g

1 000 g + 1 000 g

Second Trial Total mass 6 300 g
3 100 g
Spinach Bitter gourd Cabbage
900 g 1 000 g 1 200 g

6 packets 1 000 g 1 200 g 2 200 g

The second trial is accurate. Explain 1 200 g + 1 200 g
how to check your answer. Total mass 6 500 g

Puan Nora bought 1 packet of spinach, 2 packets of bitter gourd, and
3 packets of cabbage.

7.1 (i) Calculate the balance received by Puan Nora if she paid 123
RM50 to the cashier.

Teacher’s Notes
Use other methods such as creating a table and logical reasoning to solve
problems.

5 The pupils in group A are given a task to make Sugar
ice cream. Two of the main ingredients used are 140 g
sugar and full-cream milk as shown. If they want to
use a carton of milk with a volume of 1 ℓ, what is the Full-cream milk
mass of sugar needed?

250 mℓ 250 mℓ

Solution

Method 1 Pattern The volume of 4 cartons of 250 mℓ milk is equal to 1 ℓ.
Therefore, the mass of sugar needed for 1 ℓ of milk is
1ℓ = 1 000 mℓ 4 times the original mass.

1 carton 250 mℓ The mass of sugar needed
2 cartons 500 mℓ for 1 ℓ milk:
4 cartons 1 000 mℓ
1

140 g
×4

560 g

Method 2 Simulation

250 mℓ 250 mℓ 250 mℓ 250 mℓ 1 000 mℓ

250 mℓ 250 mℓ 250 mℓ 250 mℓ

140 g 140 g 140 g 140 g 560 g

If 1 ℓ of milk is used, the mass of sugar needed is 560 g.

The pupils of Group B use 700 g of sugar. Calculate the volume,

in mℓ, of milk needed by them to make ice cream based on the
same recipe.

124 Teacher’s Notes 7.1 (i)

Ask pupils to solve problems using other suitable methods such as proportion.
Remind pupils to check their answers.

6 The diagram shows 120 ℓ of water which is

1 of the volume of the tank. When water is
3

at a constant flow, the time taken to fill 120 ℓ 120 cm
50 cm
of water is 30 minutes. What is the time taken

to fill up the tank? 1
3
120 ℓ

Solution 60 cm

1 of the volume of the tank is 120 ℓ.

➙➙ 3
Important information 120 ℓ took 30 minutes.

➙ Volume of a full tank = ? hours ? minutes

Firstly, calculate the 1 of the volume of the tank = 120 ℓ
volume of a full tank. 3
1 1
× of the volume of the tank = 120 ℓ × 3
3 3

1 Volume of 1 tank = 360 ℓ

Method 1 Method 2

120 ℓ 30 minutes 120 ℓ 30 minutes
×3 ×3 1 ℓ
➙ 360 ℓ 1
➙ 30
1 20 minutes

360 ℓ 90 minutes 4
90
90 minutes = 1 hour 30 minutes 1 minutes
4 minutes × 360 = 90

1

90 minutes = 1 hour 30 minutes

1 hour 30 minutes is needed to fill up the tank.

If the volume of water is 180 ℓ, what is

the height of the water level? Discuss.

7.1 (i) Teacher’s Notes 125

Surf http://www.learner.org/courses/learningmath/measurement/session3/
part_b/liquid.html

7 Pak Abu mixes 800 g of coffee powder for sale each day. Mr Lim mixes
150 g of coffee powder less than Pak Abu. Pak Abu sells between 12 ℓ to 16 ℓ
of coffee each day. Mr Lim sells 75% of the volume of coffee sold by Pak Abu.

a What is the mass, in g, of coffee powder mixed by Mr Lim each day?

b What is the biggest difference in volume, in ℓ, of coffee sold between them
each day?

Solution

a Seller Mass of coffee powder each day
Pak Abu 800 g

Mr Lim 800 g − 150 g = 650 g

The mass of coffee powder mixed by Mr Lim each day is 650 g.

b The volume of coffee sold by Mr Lim:

The lowest volume: The highest volume:

75% of 12 ℓ 75% of 16 ℓ

3 3 3 4

75 × 12 ℓ = 9 ℓ 75 × 16 ℓ = 12 ℓ
100
4 100
4
1
1

Seller Pak Abu Mr Lim

The lowest volume of coffee sold 12 ℓ 9 ℓ

The highest volume of coffee sold 16 ℓ 12 ℓ

The biggest difference in volume, in ℓ = Highest volume − Lowest volume
= 16 ℓ − 9 ℓ
=7ℓ

Use a calculator to check the answer.

The biggest difference in volume of coffee sold is 7 ℓ.

126 Teacher’s Notes 7.1 (i)

Surf http://www.superteacherworksheets.com/measurement/milliliters_
TWWFQ.pdf

8 The diagram on the right shows 1.6 ℓ of
water in an aquarium. The height of the

water level is 2 cm which is 20% of the

height of the aquarium. Calculate the

height, in cm, of the aquarium and the
volume of water when the aquarium is full. 2 cm

1.6 ℓ

Solution Create a table

Relate 20% with 100%. We must do
Therefore,multiply each value with 5. multiplication for the
given information.

Percentage Height of Volume

(%) water level (cm) of water (ℓ)

20 2 1.6

20 × 5 = 100 2 × 5 = 10 1.6 × 5 = 8.0

Check

Firstly, calculate the height of the water level and the volume of water
for 1%. Then, multiply the value by 100 to get the answer.

Percentage Height Percentage Volume

20% — 2 cm 20% — 1.6 ℓ
1% — 2 cm ÷ 20 = 0.1 cm 1% — 1.6 ℓ ÷ 20 = 0.08 ℓ
100% — 0.1 cm × 100 = 10 cm 100% — 0.08 ℓ × 100 = 8 ℓ

The height of the aquarium is 10 cm and the
volume of water in the aquarium is 8 ℓ.

If the volume of the water is at the height of 8.5 cm, what is the
percentage of the height of aquarium which is filled with water?

7.1 (i) Teacher’s Notes 127

Show various problem-solving strategies such as drawing a diagram or
conducting simulation to achieve Performance Level 5.

SMART PROJECT

Participants 5 pupils in a group

Task

Download traditional kuih recipes from the Internet. Construct questions from
the recipe involving length, mass, and volume of liquid. You can request your
friends to find the answers or discuss.

KUIH SERI MUKA RECIPE

Ingredients for 1 tray: 22 cm
• 300 g of glutinous rice

• 150 g of sugar

• 2 eggs 22 cm

• 1 coconut (squeeze 150 mℓ of thick coconut

milk and 400 mℓ of diluted coconut milk)

• 3 tablespoons of flour

• 1 tablespoon of cornflour

• 10 pieces of pandan leaves (blend with water to get 150 mℓ of pandan juice)

• a pinch of salt

Examples of questions based on the Kuih Seri Muka recipe.

1 Calculate the total mass, in kg, of glutinous rice and sugar.

2 Find the difference in volume, in ℓ, of the thick coconut milk and diluted
coconut milk.

3 If you want to prepare 3 trays of Kuih Seri Muka of the same size, what is
the volume of pandan juice needed?

4 The Kuih Seri Muka is cut into 25 squares. What is the length of sides for
each piece of kuih?

5 The cost of a tray of Kuih Seri Muka is RM10. The seller wants a profit of
50%. Calculate the selling price of:

a a tray of kuih.
b a piece of kuih.

6 The mass of a packet of sugar is 1 kg. What is the percentage of the mass
of sugar left after preparing 4 trays of Kuih Seri Muka?

128 Teacher’s Notes 7.1 (i)

Choose other types of traditional kuih recipes. Construct questions and solve
them in groups.

FUN ADVENTURE

FIRST COME, FIRST SERVE

Tools/Materials mugs, measuring containers, string, a pair of scissors, ruler,
weighing scale, keyword cards, task cards, measuring tape

Participants 5 pupils in a group Keyword cards

Ground floor

There are 4 stations in the game. At each station, there are Block A
2 similar tasks for 2 groups. Tools and materials are provided.
At each station, there are also 2 judges to monitor the Near the
2 groups of participants. school hall

Between the
white pot and

the red pot

Station 1 Station 2

Task Card Task Card

Pour 2 mugs Use the measuring
of water into tape to measure
a measuring the length and
container. Find the width of the
total volume of reading corner.
water.

Station 3 Station 4

Task Card Task Card

Cut the string into Weigh the mass of
4 equal parts. a packet of sand
Measure the and a packet of
length of each marbles. Calculate the
string. difference, in mass, of
a packet of sand and
a packet of marbles.

Rules of the game

1 When the game starts, 2 groups will go to each station.
2 The participants complete the task by writing a number sentence.
3 The judges will check the answers. For every correct answer, the judge will

award a keyword card to the leader of the group.
4 The keyword card will be used to locate the mystery gift.

7.1 (i) Teacher’s Notes 129

Modify the tools and materials in each station involving calculation of length,
mass, and volume of liquid.

SELF-PRACTICE

Solve the following problems.

a The diagram below shows the calories of several foods in the breakfast menu.

2 pieces of wholegrain 1 egg 1 cup of yogurt
150 mℓ
bread 60 g 55 g 90 calories
70 calories
140 calories

Source: http://www.moh.gov.my/images/gallery/publications/makan/Panduan_Penyajian.pdf

Asiah eats 2 pieces of wholegrain bread, an egg, and 2 cups of yogurt.
Calculate the total calories consumed.

b 200 mℓ of green tea without sugar contains 0 calories. When 5 g of sugar is

added into the green tea drink, it contains 20 calories. Mr Lau gets 8 calories

when he drinks 200 mℓ of the tea. How many grams of sugar is added to the

drink?

c 120 km

K L MN

Based on the above diagram, town K, L, M and N are situated along a straight

road. The distance of KL is equal to the distance of MN. The distance of LM is

4 times the distance of KL. The journey from L to M uses 3 ℓ of petrol. What

is the volume of petrol needed, in ℓ, for the journey from K to N via L and M?

d The incomplete table below shows the estimated mass for one ream of
paper. There are two types of paper shown.

Type of paper A4 A3

Paper size 21 cm × 29.7 cm 42 cm × 29.7 cm

Estimated mass (kg) 2.4 kg ?

Each ream of paper contains 500 sheets. What is the estimated mass, in kg,
for one ream of A3 paper?

e The diagram on the right shows the mass of oats used to make a
nutritious drink of 4.4 ℓ.Aina’s sister wants to prepare 22 ℓ
of the drink.

i. What is the mass of oats, in kg, needed?

ii. If Aina’s sister has 3.2 kg of oats, how many litres of
nutritious drink can she prepare?

130 Teacher’s Notes 7.1 (i)
Construct similar questions and get pupils to solve them.

SKILFUL MIND 1ℓ

Solve the following problems.

a A bottle filled with 1 ℓ of water has a mass of about 1 kg.
Calculate the mass, in g, of water in a jug shown if half
the volume of water has been consumed.

b The average growth of the fingernail is 0.1 mm in a day. What is the length,
in cm, of the growth of the fingernail in a week?

Source: http://www.bbc.com/future/story/20130526-do-your-nails-grow-after-death

c Diagram A shows the original volume of water in a

measuring cylinder. Diagram B shows an increase in 400 400

volume of water when two marbles are added. The 300 300

total mass of the marbles added is 10 g. What is the 200 200

reading of the water level if 50 g of marbles are added 100 100

to measuring cylinder A?

d The table shows the distance from Kuala Lumpur to A B

two destinations. PERLIS THAILAND
Destination
Kangar BUKIT KAYU HITAM Kota
Bharu
Distance (km) Alor Setar KEDAH

Port Dickson 90 PULAU Georgetown KELANTAN Kuala
Bukit Kayu Hitam 510 PINANG PERAK Terengganu

Ipoh TERENGGANU

Source: http://malaysiavacationguide.com/distance-chart.html PAHANG Kuantan

SELANGOR

Mr Goh uses 6 ℓ of petrol to travel from Kuala Lumpur U KUALA LUMPUR
to Port Dickson. What is the volume, in ℓ, of petrol used
Shah Alam NEGERI
SUMATERA
SerembanSEMBILAN
if he travels from Kuala Lumpur to Bukit Kayu Hitam? (INDONESIA)
PORT DICKSON MELAKA

Melaka JOHOR

PETUNJUK Johor Bahru
Jalan raya utama SINGAPURA

Lebuh raya Utara-Selatan

e The diagram shows the volume of concentrated

coconut milk in a jug. 1 of the volume of the coconut
4

milk is mixed with 120 g of cendol to prepare

cendol. What is the volume of coconut milk, in 2 400 mℓ
mℓ, needed for 600 g of cendol with the same

concentration?

7.1 (i) Teacher’s Notes 131
Surf http://lamar.colostate.edu/~hillger/common.html

f Darus’ father drives from Bintulu to Mukah, Sarawak.
The diagram here shows the speedometer of the car.
His father takes 2.5 hours to reach his destination.
Calculate the distance, in km, from Bintulu to Mukah.

g 100 km 170 km 90 km
CD
AB

The above diagram shows the location of four towns along a straight road.
Khan left Town A at 8:00 a.m. He drives at a constant speed of 90 km
per hour. At what time will Khan reach Town D?

h Mr Tan buys a sack of basmati rice with a mass of 40 kg. He sells 75% of the
rice to Encik Budi and 50% of the remaining mass of rice to Mak Limah.

i. What is the mass of rice left in the sack?

ii. Mak Limah wants to prepare biryani rice. She uses 1 ℓ of evaporated milk
5
for 1 kg of the basmati rice. What is the volume of evaporated milk needed

to cook the biryani rice?

i The diagram on the right shows the measurement
and the mass of a gift box. When Ali’s mother 4 cm

arranged a few of the gift boxes into Box P, the 4 cm 500 g

total mass became 4.3 kg. Calculate the mass, in 4 cm P
kg, of an empty Box P. State the length, width, and

height of Box P.

j Saiful’s father wishes to paint the wall. He needs 3.8 ℓ of paint to paint 38 m2
of the inside wall. The outside wall needs 3.8 ℓ of paint for 24 m2. The volume
of paint used differs due to the difference in wall surfaces. Saiful’s father has

used 19 ℓ of paint. State the area of wall painted, both inside and outside of
the house.

132 Teacher’s Notes 7.1 (i)

Surf http://www.k-5mathteachinresources.com/support-files/metric-conversion-
word-prpblems.pdf

8

A Draw and Recognise Polygons

Triangle Look! The objects
1 around us have
different types of
triangular surfaces.

A triangle is a polygon with 3 sides, b Mark the midpoint between points
3 corners, and 3 angles. Let us P and Q. Draw a perpendicular line
draw the shape. from the centre of PQ.

a Mark the point P. Count
8 units to the right and mark
the point Q. Join the points.

P 8 units Q P Q

c Count 8 units from P and from d Place the centre of a protractor on point P.

Q. Mark the point of intersection, Measure angle P and label the value of

R. Join all the points. angle P. Repeat for points Q and R.

R angle R corner
60o
8 units 8 units
60o

P 8 units Q 60o
PQ
All sides of this triangle are
equal. The values of each Why is the value of
angle are equal too. each angle equal?

8.1 (i) Teacher’s Notes 133
8.1 (ii)
Guide pupils to place the protractor correctly to measure angles. Reinforce the
method to measure angles and the names of polygons learned in Year 5.
Show different methods to draw triangles with a ruler and squared paper.

2 There are many types of triangles that can be drawn as shown in the

following pictures.

a Mark Join the Measure the Label the

3 points. points. angles. angles.

b

c

Add the values of all 70o BOOST
the angles in each 70o 40o YOUR KNOWLEDGE
triangle. Compare.
33o Characteristics of a triangle
57o 3 straight sides
3 corners
3 angles

134 Teacher’s Notes 8.1 (i)
Use grid paper. 8.1 (ii)
Surf http://www.mathsisfun.com/triangle.html.

Quadrilateral The surface of this table is a
square. Let us draw two types
1 of quadrilaterals.

Mark four
points.

Join all the
points. Then,
measure
each angle.

Why is the 105o
value of each 75o
angle in the
square 90o?

90o

Characteristics of a What are the similarities
quadrilateral between the two quadrilaterals
drawn above? What are the
4 straight sides differences? Discuss.
4 angles
4 corners

8.1 (i) Teacher’s Notes 135
8.1 (ii)
Surf http://www.mathsisfun.com/quadrilaterals.html to know the
characteristics of a quadrilateral.
Use a geoboard and Geometer’s Sketchpad (GSP) software to form and draw
several polygon shapes.

2 There are various types of quadrilaterals. The shapes are drawn as below
and have angles with certain values.

a

90o

b

124o 56o
56o 124o

c

110o 124o
70o 56o

d 89o
110o 110o
136
51o

Sum all the values of the
angles for each quadrilateral
above. What do you get?

Teacher’s Notes 8.1 (i)
8.1 (ii)
Use grid paper for the activities above.
Discuss the fact that the sum of angles in each quadrilateral is 360° and relate it
to the number of triangles in a quadrilateral.

Pentagon AMAZING FACTS

This is The Pentagon Pentagon originates
from a Greek word.
in the United States Pente means five and
of America. Do gonia means angle.
you know why the
building is named
The Pentagon?

STEP 1 STEP 2 STEP 3
Mark 5 points. Measure each angle.
Join the points
using straight lines.

108o

This is also a pentagon. 140o 45o
Draw a pentagon and 110o
measure the angles. 270o 45o
110o
Characteristics of a pentagon DISCMTIAORNTARY
 5 straight sides
 5 corners Diagonal Diagonals
 5 angles
A straight line
that joins two
non-adjacent
corners.

BRAIN TEASERS

Draw diagonals in a pentagon that do not intersect. How many triangles
are formed?

8.1 (i) Teacher’s Notes 137
8.1 (ii)
Surf http://www.mathsisfun.com/geometry/pentagon.html. Draw a pentagon with
a 5-point star or trace it from a folded paper.
Surf www.youtube.com/watch?v=ikaSgNDnrv0 for learning activities with a
geoboard.

Hexagon

Look at this beehive.
The surface is a
hexagon.

Characteristics of a hexagon

 6 straight sides
 Number of angles
 Number of corners

AMAZING FACTS Is this a hexagon?
Measure each of
Any closed shape with its angles.
6 straight sides is a
hexagon. Hexa
means six.

Heptagon This is my The surface of
heptagon. this container is
I drew this in the shape of a
heptagon. heptagon.

Draw a heptagon and
measure its angles.

Characteristics of a heptagon

 7 straight sides
 Number of angles
 Number of corners

AMAZING FACTS

Any closed shape with 7 straight sides is
a heptagon. Hepta means seven.

138 Teacher’s Notes 8.1 (i)
8.1 (ii)
Guide pupils to draw and measure the angles of the polygons.
Discuss the differences of the angles in the six-sided and seven-sided polygons,
and relate them to the number of triangles in the shape.
Surf http://www.mathsisfun.com/geometry/hexagon.html to draw the hexagon
interactively and know its characteristics.

Octagon AMAZING FACTS
Octagon is any closed
The shape of the shape with 8 straight
signboard and the clock sides. Octa means eight.

STOPis an octagon. STEP 3
Measure each angle.
Let’s draw an octagon and measure its angles.

STEP 1 STEP 2
Mark 8 points. Join the points.

135o

An octagon has 8 straight sides, Draw another
8 corners, and 8 angles. octagon.

SELF-PRACTICE

1 Name the polygons and measure the value of x.

a b c

xo xo xo

Triangle

2 Draw the following polygons and measure their angles. Write the
characteristics of the polygons.

a Quadrilateral b Triangle c Hexagon

d Octagon e Pentagon f Heptagon

8.1 (i) Teacher’s Notes 139
8.1 (ii) Get pupils to create a scrapbook of various polygons.

BRAIN TEASERS

The number of triangles in a pentagon is half of the number of triangles in
an octagon. Prove it. What is the sum of the interior angles in an octagon?


SMART PROJECT

POLYGON MIND MAP Participants pairs or
groups
Tools/Materials grid paper, ruler, various
coloured pens, poster sheets

Task

1 Draw polygons on grid paper.

2 Colour and cut each shape. Measure the angles in the polygons
and label them.

3 Paste the shapes on a poster sheet and label them.
Create a mind map based on the characteristics of each polygon.
Example:

3 straight sides TRIANGLE Types Equilateral
3 corners Isosceles
3 angles Right-angled

QUADRILATERAL HEPTAGON

POLYGONS

PENTAGON OCTAGON

HEXAGON

4 Present your work. Conduct a gallery walk.

140 Teacher’s Notes 8.1 (i)
8.1 (ii)
Assist pupils to draw various graphic organisers complete with the characteristics
of each polygon.

B Solve the Problems involving Perimeter and Area

1 Encik Zahin wants to decorate the roof of his 4.7 m
house with multi-coloured lights. What is the
length of the lights that he needs? If 1 m of
the lights costs RM10.50, how much is the cost
of the lights?

Solution 3.9 m

Given Perimeter of the roof 3.1 m
Cost of 1 m of the lights is RM10.50

Asked for The length of the multi-coloured lights and the cost

Operation Addition and multiplication

Solve 3.1 m 3.9 m The length of the
opposite sides is
the same. Why?

4.7 m 4.7 m

3.9 m

3.1 m

Perimeter: 3.1 m + 3.9 m + 4.7 m + 3.9 m + 3.1 m + 4.7 m = 23.4 m
Cost: 1 m — RM10.50
23.4 m — 23.4 × RM10.50 = RM245.70

Check Perimeter: 2 × (4.7 m + 7 m) = 2 × 11.7 m

= 23.4 m

Cost: (23.4 × RM10) + (23.4 × RM0.50) = RM234 + RM11.70

= RM245.70

8.2 (i) The length of the multi-coloured lights is 141
23.4 m and the cost is RM245.70.

Teacher’s Notes
Provide various composites of two-dimensional shapes to train pupils to find
perimeter.
Surf http://www.primaryresources.co.uk/maths/mathsE4.htm

2 May Lyn arranged several cards as shown 5 cm 1 cm
in the diagram to form attractive patterns. 1 cm

3 cm
Pattern 1 Pattern 2
All the triangles are of the same size. If she 5 cm
5 cm
arranged the shapes to form Pattern 1 and 4 cm

Pattern 2, calculate the perimeter and area

of each pattern. What is the difference, in the

perimeters and areas, of the two patterns?

Solution Label the length of the Pattern 2

Pattern 1 outer sides of Pattern 1 3 cm 4 cm

5 cm and Pattern 2. 4 cm 3 cm

5 cm 5 cm 4 cm

3 cm

5 cm 4 cm 3 cm

Perimeter: Perimeter:
5 cm + 5 cm + 5 cm + 5 cm = 20 cm 7 cm + 7 cm + 7 cm + 7 cm = 28 cm
Area: 5 cm × 5 cm = 25 cm2
Area: 7 cm × 7 cm = 49 cm2

Measurement Perimeter (cm) Area (cm2)

Pattern 2 28 49

Pattern 1 20 25

Difference 8 24

The difference between the two perimeters is 8 cm.
The difference between the two areas is 24 cm2.

If the length of all sides of the triangles and squares for

Pattern 1 and Pattern 2 is 2 times the original length, what will
happen to the area and perimeter of the patterns? Discuss.

BRAIN TEASERS

Two squares are overlapped as shown in the 10 cm 6 cm 6 cm

diagram. The length of each side is 10 cm. Calculate 7 cm
the perimeter and area of the purple region. 7 cm

Teacher’s Notes

142 Guide pupils to label the outer side correctly and then calculate the perimeter 8.2 (i)
and area.

3 A carpet is laid in an office as shown in the shaded 10 m
region in the diagram. The area that is covered with 10 m
carpet is 80% of the whole area of the office floor.
Calculate the area which is not covered with carpet.
Estimate the length of the wooden skirting when the
carpet is laid.

Solution Important information 12 m

The length of the floor: 12 m The area that is covered with
The width of the floor: 10 m carpet is 80% of the floor area.

Solve Wooden skirting

Area of the floor: 12 m × 10 m = 120 m2

Area covered with carpet: 80 × 120 m2 = 8 × 12 m2 Not covered
100 with carpet

= 96 m2

Area of the floor without carpet = 120 m2 – 96 m2 = 24 m2

The estimated length and width of the region without carpet: 12 m

Length (m) 12 8 6
Width (m) 2 3 4

The estimated length and width are 6 m and 4 m.

The length of the wooden skirting:
12 m + 10 m + 12 m + 10 m + 6 m + 4 m + + =

The area of the floor without carpet is 24 m2. .
The length of the wooden skirting when the carpet is laid is

Can the length of 8 m and the width
of 3 m be a possible answer? Discuss.

BRAIN TEASERS 2 cm 1
1 cm 2
Arrange the rectangles as shown in the diagram up 1 cm 3
to 10 rows. Calculate the perimeter of the composite 4
arrangement of the rectangles. 143

8.2 (i) Teacher’s Notes

Surf www.bgfl.org/.../client_ftp/ks2/maths/perimeter_and_area/index.html,
http://mathplease.com/Geometry/Geometry%20201213/Unit%201/Chapter%201/
perimeter_of_composite.pdf and http://www2.kprdsb.ca/cdciw/departments
math/9Academic/72CompositeShapes.pdf