MATHEMATICS Y6 SK (SEMAKAN 2017)

TIME ZONES
WEBSITE

R U S TimI R eA UzonS e IinATokyo, Japan (GMT +9) SCAN ME
Tuesday, 8 March 2022, 11:12 a.m.
TIPS
LARUS KAZAKHSMTOANNGOLIA MONGOLIA
RAINE KAZAKHSTAN China uses only
one time zone
TTUURRKKMEEYNISTAN TURKMENISTAN INTERNATIONAL DATE LINE which is GMT +8.
INTERNATIONAL DATE LINE
CHINA CHINA JAPAN JAPAN (chinahighlight.com/
MYANMAR travelguide/china_time)
AFIGRHAAQNISTAN AFGHANISTAN
What is GMT?
RAN IRAN GMT is Greenwich Mean Time, the
PAKISTAN PAKISTAN local clock time at Greenwich Meridian
0° that passes through Greenwich,
YPT SAUDI London in England. This standard time
ARABIA is the basis for the 24-hour time zone
INDIA MYANMARINDIA
in the world.
AN PHILIPPINES PHILIPPINES

LIA ETHIOPIA SOMALSIARI MSARLI AYSIA MALAYSIA
LANKA
KENYA LANKA

TANZANIA I N D O N E S I AI N D O NNEEWPAGSPUUIIANAEA PAPUA SOLOMON
SOLNOEMWOGNUINEA

IA MOZAMBIQUEMADAGASCAR
GASCAR NEW ZEALAND
NEW ZEALAND
AUSTRALIA AUSTRALIA

SOUTH

AFRICA Time zone in Kuching, Malaysia

(GMT +8)

Tuesday, 8 March 2022, 10:12 a.m.

Travel to the East

Time differences between three cities from Greenwich

6 hours of difference 8 hours of difference Kuching
10:12 a.m.

Mexico Greenwich 9 hours of difference Tokyo
2:12 a.m. 11:12 a.m.
City
8:12 p.m.

Based on the timeline, discuss the time difference between:

a Kuching and Tokyo. b Mexico City and Kuching.

4.1.1 €€Discuss countries that have two or more time zones with pupils. For example, 143
4.1.2 Australia (GMT +8, GMT +9, and GMT +10) and Indonesia (GMT +7, GMT +8,
and GMT +9).

€€Scan the QR code to explore time all around the world.

3 Japan, 1707 hours
Tokyo, Japan
Malaysia, 1607 hours Sunday, 15 May 2022
Ipoh, Perak, Malaysia
Sunday, 15 May 2022

Indonesia, 1507 hours
Aceh, Indonesia
Sunday, 15 May 2022

Based on the above information, find the time difference between the cities:

a Ipoh and Tokyo. b Aceh and Tokyo.

hours minutes hours minutes

170 7 170 7

−1 6 0 7 −1 5 0 7

10 0 20 0

The time difference between Ipoh The time difference between
and Tokyo is 1 hour  . Aceh and Tokyo is 2 hours  .

Tokyo, Japan is in the east Aceh, Indonesia is in the
of Malaysia. Therefore, west of Tokyo, Japan.

the time in Tokyo is 1 hour Therefore, the time in Aceh is
ahead of Ipoh. 2 hours behind Tokyo.

144 €€Guide pupils to find the time difference between two time zones for a few popular 4.1.2
cities in the world.

€€Emphasise the importance of identifying the location of a city or a country in the

east or west to determine whether the time is ahead or behind.

4

Moscow, Russia Vladivostok, Russia
26 August 2022 26 August 2022
4:35 a.m. 11:35 a.m.

Calculate the time difference Russia has 11
between Moscow and Vladivostok. time zones.

Moscow Vladivostok

4:35 a.m. time 11:35 a.m.

difference?

hours minutes

Vladivostok time 0 11 Subtract the time in Moscow from
the time in Vladivostok because
113 5 Moscow has a later time.

Moscow time − 0 4 3 5

Time difference 70 0

The time difference between Moscow and Vladivostok is 7 hours .

5 Calculate the time Alor Setar, Malaysia Darwin, Australia
Friday, 24 June 2022
difference between Thursday, 23 June 2022

Darwin and Alor Setar.

Thursday Friday

Alor Setar 1 hour 30 minuteDsarwin

2310 hours 0010 hours 0040 hours

The time difference between Darwin and Alor Setar is 1 hour 30 minutes .

€€Guide pupils to identify the location before subtracting the time to find € 145
4.1.2 the time difference.

€€Surf https://timeanddate.com to get the time in two different cities €
in the world.

6 The time in Kuala Lumpur
is 5 hours ahead of
Riyadh. State the time in
Riyadh.

Change 10:00 p.m. to Kuala Lumpur Tower, Kingdom Centre,
24-hour system, which Riyadh, Saudi Arabia
Malaysia
is 2200 hours. 10:00 p.m.

22 February 2022

hours minutes

1 12 Subtract 5 hours from the time in Kuala Lumpur

2 2 0 0 because the time in Riyadh is behind by 5 hours.
− 50 0

1 7 0 0 1700 hours in a 12-hour system is 5:00 p.m.

The time in Riyadh is 1700 hours or 5:00 p.m. .

The time in Tawau is 7 hours ahead of Dublin, Ireland on 6 December 2022.
What is the time in Dublin if the time in Tawau is 1:45 p.m.?

2 hours ahead City
P

THINK City hours
SMART A

1510 hours

City
Q 3 hours behind
hours

State the time in city P and city Q.
How much is the time difference between city P and city Q?

146 €€Guide pupils to determine the time in a 12-hour system or a 24-hour system 4.1.2
correctly.

€€Encourage pupils to use an analog clock face for simulation.

LET’S DO IT

1 Wellington, New Zealand
10 May 2022
1355 hours

Kota Kinabalu, Sabah, Malaysia
10 May 2022
0955 hours

Find the time difference between Wellington and Kota Kinabalu.

2 The time in Los Angeles, The United States of America is Thursday, €

27 January 2022, 1420 hours. The time in Kota Bharu is Friday, €

28 January 2022, 0520 hours. Calculate the time difference between €

these two cities. Maluku Kuala Lumpur

3 Zahidah has arrived at Ambon Airport,

Maluku, Indonesia from Kuala Lumpur.

Calculate the time difference between

Kuala Lumpur and Maluku based on €

the picture.

4 1915 hours Paris,
24 November 2022 France

1315 hours
24 November 2022

Calculate the time difference between the two places based on the
information given above.

5 The time in Liverpool, England is 6 hours
Vientiane, Laos behind the time in Vientiane, Laos. State the
time in Liverpool when the time in Laos is as
Thursday, 17 February 2022 shown in the picture.

6 The time in Arau, Perlis is ahead of the time in Buenos Aires, Argentina by 11 hours.
State the time in Buenos Aires if the time in Arau is 1950 hours.

€€Ask pupils to refer to the time zone map to determine if the location is in the correct €
4.1.2 time zone. 147

SOLVE THE PROBLEMS

1 Ikhwan is in Malacca. He joins
an online class organised by a
university in Amman, Jordan on
23 February 2022 at 1545 hours
Malaysia time. The local time in
Amman is 1045 hours. How much
is the time difference, in minutes,
between both locations?

Solution

Understand the problem Solve hours minutes
154 5
• Malacca, 1545 hours.
• Amman, 1045 hours. −1 0 4 5
• Find the time difference in minutes.
50 0
Plan the strategy

• Subtraction.
• Convert the answer to minutes.
1545 hours – 1045 hours =

Check 5 hours = 5 × 60 minutes
= 300 minutes

60minutes 60minutes 60minutes 60minutes 60minutes

1 hour 1 hour 1 hour 1 hour 1 hour

1045 hours 1545 hours

Amman Malacca

The time difference between both locations is 300 minutes.

Ikhwan’s friend who is in Yangon, Myanmar also joined the same online
class. The local time in Yangon at that time was 1415 hours. Calculate the

time difference between Yangon and Amman.

€€Remind pupils to solve problems using Polya’s method. 4.2.1
148

2

Putrajaya London
2315 hours
10 March 2022

Johari returns to London for work. As soon as he arrives in London at €
11:15 p.m., he sends a short text message to his mother who is in Putrajaya.
The time in Putrajaya is 7 hours ahead of London. State the time in
Putrajaya at that moment.

Solution

Given Asked for

• London, 11:15 p.m. • Time in Putrajaya.

• Time in Putrajaya is 7 hours ahead

of London. The 7-hour time

Solve 11 12 1 11 12 1 difference is
10 2 10 2 because the time

93 93 in Putrajaya is
ahead of the time in
84 84
76 5 76 5 London.

Check

Johari 1:15 a.m. 3:15 a.m. Johari’s
11 March 2022 11 March 2022 mother
London
11:15 p.m. 5:15 a.m.
10 March 2022 11 March 2022 Putrajaya

12:15 a.m. 2:15 a.m. 4:15 a.m. 6:15 a.m.

11 March 2022 11 March 2022 11 March 2022 11 March 2022

The time in Putrajaya is 6:15 a.m., 11 March 2022.

Johari’s father is in Bangkok, Thailand. The time in Bangkok is 1 hour
behind Putrajaya. Does his father's watch show 7:15 a.m. at that
moment? Discuss.

€€Guide pupils to understand day conversion by doing simulation. 149
4.2.1

3

National Stadium
of Bukit Jalil, €
Kuala Lumpur
2045 hours

29 August 2022

−1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12

Naypyidaw, Myanmar Perth, Australia Jakarta, Indonesia Osaka, Japan
1 hour behind 1 hour ahead
1.5 hours behind 2045 hours
GARISAN TARIKH ANTARABANGSA
FINLAND
ND NORWAAYfSoWEoDtEbN all match is broadcast live frRomUtheSNaItionAal Stadium of Bukit Jalil, €
Kuala Lumpur. The pictures above show fans who are watching the match €

UNITED from their respective countries.

RELAND aKINGDOM POWRLhANyDBAaLrAeRUtShe fans in Perth watch the match at the same time as in €
JERMAN KuaUlaKRLAIuNEmpur?
PERANCIS KAZAKHSTAN MONGOLIA

SEPANYOL bITALI State the time of the match in Naypyidaw, Myanmar and Jakarta, Indonesia.
cGR EIEsCEit trueTUtRhKaI t the faTnURsKiMnENOIAsaka,
RTUGAL Prove it. IRAQ Japan watch the match at 194J5EPhUNours? €
+3½ AFGANISTAN CHINA

AGHRIBI IRAN +4½ betw+5¾een
+5½
ALGERIA d L IBCYAalcMuElaSIRte theARtAimB e differeIRnANce Naypyidaw, Myanmar, and Osaka, Japan.

SAUDI +6½

ITANIA MALI NIGAR CHAD INDIA MYANMAR

NIGARIA SolutioSUnDAN Kuala Lumpur,
Malaysia
a Perth isHAlKBoESNYcAYaAH tSeOdMALinIA the SRI
sCOaNmGO e time zone as LANKA
GABON

Kuala TLAuNZmANpIAur. SOLOMON

ANGOLA

TheZArMeBfIoA re, theMAfaDAnGAsSCinARPerth
MOZAMBIQUA
NEW ZEALAND
NAMIBwIA atch the match at the same

AtiFmRIKeA as in Kuala Lumpur, Perth, Australia
SwELAhTAicNh is at 2045 hours.

€€Carry out a simulation to understand the situation. 4.2.1
150 €€Use the clock face display to show the time difference between two cities.

b The time in Naypyidaw is 1.5 hours behind the time in Kuala Lumpur.

1.5 hours = 1 hour 30 minutes hours minutes
Naypyidaw time
= Kuala Lumpur time – Time difference 1 10
= 2045 hours – 1 hour 30 minutes
= 1915 hours 204 5
− 13 0

191 5

The time of the match in Naypyidaw is at 1915 hours.

The time in Jakarta is 1 hour behind the time in € hours minutes
Kuala Lumpur.
1 10
Jakarta time = Kuala Lumpur time – Time difference
= 2045 hours – 1 hour 204 5
= 1945 hours − 10 0

194 5

The time of the match in Jakarta is at 1945 hours.

c The time in Osaka is 1 hour ahead of the time in Kuala Lumpur.

Osaka time = Kuala Lumpur time + Time difference hours minutes
= 2045 hours + 1 hour 204 5
= 2145 hours + 10 0

Incorrect. The fans in Osaka watch the 214 5
the match at 2145 hours.

d Naypyidaw 1.5 hours Kuala Lumpur Osaka
1 hour

How many hours difference?

1.5 hours + 1 hour = 2.5 hours
= 2 hours + 0.5 hour
= 2 hours + (0.5 × 60 minutes)
= 2 hours 30 minutes

The time difference between Naypyidaw, Myanmar and€
Osaka, Japan is 2 hours 30 minutes.

4.2.1 €€Provide various problem-solving strategies such as using a timeline and a clock 151
model.

TRY IT OUT OUR WORLD CLOCK CRAFT

Tools/Materials Cardboards or manila cards, pens, scissors, €
small nuts, and screws.

Participants 5 pupils in a group.

Task 1 Each pupil cuts the cardboard according to their Kuala Lumpur
creativity to create a clock face, hour hand, and € 0900 hours

minute hand. London
2 Complete the clock face by writing the numbers in a€ 0200 hours

12-hour system or a 24-hour system. Brisbane
3 Assemble the hour hand and minute hand using a 1100 hours

small nut and screw.
4 Label one of the clock display according to the time in

Kuala Lumpur.
5 Label another four clock displays according to the time

in four other different cities.
6 Display the best top five world clock created in the

class.

Riyadh Osaka
0400 hours 1000 hours

LET’S DO IT

Solve the following problems.
a Puan Winnie Mawan is from Miri, Sarawak. She works at a telecommunication

company in Kawasaki, Japan. The current time in Kawasaki, Japan is 4:20 p.m.
Meanwhile, the current time in Miri is 1520 hours. Find the time difference between
these two cities.

b Encik Emir works at the Turkey Embassy in Malaysia. He receives a short text
message from his brother in Istanbul, Turkey while having his lunch at 12:30 p.m.
The time in Kuala Lumpur is 5 hours ahead of the time in Istanbul. What is the local
time in Istanbul at that time?

c Father is having a conversation with his brother who is currently in Florida, The United
States of America via a video call. The time in Kuala Lumpur is 12 hours ahead of
Florida.

i S tate the time in Florida when father’s watch shows 10:30 p.m., 5 February 2022.

ii A t what time will father contact his brother if he wants to talk to him at €
0900 hours, Florida time?

152 €€Surf https://www.timeanddate.com/time/map/ or other suitable websites to 4.1.2, €
check the time for the selected cities in the Try It Out activity. 4.2.1

LET’S PRACTISE

1 What is the total number of the world time zones?

2 Calculate the time difference between these two cities on 3 March 2022 according to
the timeline below.

Rio de Janeiro Madrid
11:30 p.m. 3:30 p.m.

Greenwich Mecca Labuan Gold Coast
2:30 p.m. 5:30 p.m. 10:30 p.m. 12:30 a.m.

3 Lahad Datu, Sabah Medina, Saudi Arabia Based on the information given,
Saturday, 16 April 2022 Saturday, 16 April 2022 calculate the time difference
3:23 p.m. 10:23 a.m.
between Lahad Datu and Medina.

4 The clock shows the time in Seremban. The time in
Seremban is 1.5 hours ahead of the time in town P. State

AM the current time in town P.

5 Solve the problems below.

a FINAL FOOTBALL The time in Johannesburg, South Africa is 6 hours
MATCH behind the time in Malaysia. At what time will the
football fans in Malaysia start watching the live
Venue: Johannesburg broadcast of the final match?
Time: 1700 hours

b M aheshwaran works in Bern, Switzerland since January 2022. His family stays in
Dungun, Terengganu. The time difference between Bern and Dungun is 7 hours.
Maheshwaran makes a video call to his family starting at 1135 hours, the time in Bern.

i At what time does the video call in Dungun start?
ii T hey talk for 25 minutes. When does the video call in Bern end?

c A n international conference is broadcast live on 9 February 2022 from Putrajaya
International Convention Centre (PICC) to a few countries. The conference starts

at 0930 hours, Malaysia time.
i T he time in Putrajaya is 5 hours ahead of the time in Helsinki. State the time
when the conference starts in Helsinki, Finland.
ii M rs Smith who is currently in London watched the delayed broadcast of the
conference for 40 minutes. The time in London is 7 hours behind the time in
Putrajaya. State the time Mrs Smith watched the delayed broadcast.

4.1.1, 4.1.2, € €€Ask pupils to refer to the time zone map to get the answers. Carry out € 153
4.2.1 21st Century Learning activity such as Bus Stop to solve the question.

LET'S EXPLORE

Complete the crossword puzzle according to the sentences below.

17

8

2

39 10 CROSSWORD
PUZZLE AND
ANSWERS

4 11 5 SCAN ME

12
6

horizontal vertical

1 The time difference for each GMT 7 Malaysia has time zone.
is one .
8 The time difference between
2 The time difference in the world and Greenwich is 9 hours.
is because of the different time
. 9 The time is if the location is
in the west.

3 The time in Riyadh is 5 hours 10 The time in Malaysia is 8 hours
behind .
of the time in Greenwich.

4 The time is behind if the location 11 The time in Kuala Lumpur is
hours ahead of the time in
of the place is in the .
Karachi, Pakistan.
5 GMT acts as to determine

24 world time zones. 12 The time difference between
Greenwich and Rome is
6 The world time zone is calculated hours.
from Meridian, London.

154 €€Scan the QR code to check your answers. 4.1.1, 4.1.2
€€Emphasise that the answers for time difference between two cities do not involve

the daylight saving time.

5 MEASUREMENT

SOLVE THE PROBLEMS length

LENGTH AND MASS Book A Book B

1 The picture shows two books, A and B. The 2 cm width
length and width of the books are the same Mass 500 g
but the thickness is different. The thickness
of book A is 4 cm more than the thickness of
book B. Calculate the mass, in kg, for book A.

Solution

Understand the problem
Plan the strategy

• The thickness of book B, 2 cm.

• The thickness of book A is 4 cm Books B A
more than book B.
• The mass of book B, 500 g. Thickness 2 cm 2 cm + 4 cm = cm

• Calculate the mass of book A Mass 500 g kg

in kg.

Solve Check mass
thickness
The thickness of book A = 2 cm + 4 cm
= 6 cm

6 cm = 3 × 2 cm The thickness of book A 2 cm 50 0 g
is 3 times the thickness of 2 cm 50 0 g
3 × 500 g = kg book B. So, the mass of + 2 cm + 50 0 g
book A must be 3 times
500 g 6 cm 1 50 0 g
×3 the mass of book B.

1 500 g 1 500 g = 1.5 kg

(1 500. ÷ 1 000) kg = 1.5 kg Do a mental calculation
3 × 500 g = 1.5 kg for a book with 1 cm
thickness. Explain.

The mass of book A is 1.5 kg.

5.1.1 (i) €€Give pupils similar problems by changing the thickness or mass of a book. 155
Ask pupils to work in pairs to solve the problems and present their answers
to enhance their understanding.

2 Father cuts a 12 m metal rod into 3 parts of
different lengths as shown in the table below.
The mass of rod A is given.

Metal rod A B C

Length 3m 5m 4m

Mass 2.664 kg

Find the mass of the longest metal rod.

Solution Asked for

Given The mass of the
longest metal rod.
• A 12 m metal rod is cut into 3 parts, A, B, and C.
• The length of metal rod A is 3 m and the mass

is 2.664 kg.
• The length of metal rod B is 5 m.
• The length of metal rod C is 4 m.

Calculate

Find the mass for 3m Step 1 Step 2
1 m rod. 1m
2.664 kg The longest metal rod,
2.664 kg ÷ 3 = 5 m is metal rod B.

0 . 8 8 8 kg The mass of metal rod B
5 × 0.888 kg =
3 2 . 6 6 4 kg
−0 4 44
26
−2 4 0 . 8 8 8 kg
26 ×5
− 24
24 4 . 4 4 0 kg
−2 4
0 Divide 4.44 kg by 5 to
check the answer. Find the

mass of metal rod C.

5 × 0.888 kg = 4.44 kg
The mass of the longest metal rod is 4.44 kg.

156 €€Vary the questions by changing the original mass of the metal rod to enhance 5.1.1 (i)
pupils’ understanding.

3 A weighing scale is used to observe the length of
spring stretch when a weight is placed on it. The
maximum length of spring stretch for this scale is
6 cm. When a weight of 500 g is hung on the scale,
the length of spring stretches 3 cm.

a State the length of spring stretch if a weight of
750 g is hung on the scale.

b What is the maximum weight, in kg, that can be
hung on the scale?

Solution

Weight Stretch length
500 g 3 cm
750 g
maximum 6 cm

a Step 1 750 g = 500 g + 250 g
Find the length of spring
500 g 3 cm stretch for 250 g first.

÷2 ÷2 750 g Step 2
3 cm + 1.5 cm = 4.5 cm
250 g 1.5 cm

1 . 5 cm
2 3 . 0 cm

−2
10

−1 0
0

The length of spring stretch is 4.5 cm if a weight of 750 g is hung on the scale.

b 3 cm 500 g 2 × 500 g = 1 000 g
= 1 kg
×2 ×2
6 cm 1 000 g

The maximum weight that can be hung on the scale is 1 kg.

5.1.1 (i) €€Guide pupils to compare two measurement units using proportions. 157
€€Discuss ways to check the answers.

LENGTH AND VOLUME OF LIQUID 23 km college
12 km 9 km
1 My brother rides his motorcycle from home
to his college every day. He uses 3 of petrol 16 km
for every 100 km. The distance from home to
college is shown in the picture. Calculate the
total volume of petrol, in m , that he uses for
a round trip.

Solution home

Given • 3 of petrol is used for every 100 km. km
• Distance from home to college:

12 km + 23 km + 16 km + 9 km =

Asked for The total volume of petrol used for a round trip.

Solve

The distance to college: 12 km + 23 km + 16 km + 9 km = 60 km
The distance of the round trip: 60 km + 60 km = 120 km

Step 1 Step 2

100 km 3 100 km + 20 km = 120 km

÷5 ÷5 3 + 0.6 = 3.6
20 km = 3.6 × 1 000 m
0.6 = 3 600 m
Check

100 km 3

120 km 3 . 6
5 1 8 . 0
6
120 × 3 −1 5
100 = 158 30

5 = 3.6 −3 0
0

The total volume of petrol used for a round trip is 3 600 m .

€€Train pupils to check their answers using suitable methods. 5.1.1 (ii)
158

2 Zarif’s mother made fresh mango juice. 110 mm
She poured into glass P until it was full and 40 mm
the remainder into glass Q. The level of each
volume of juice in both glasses are labelled PQ
as shown in the picture. The volume of juice
in glass Q is 150 m . Find the volume of
mango juice in glass P.

Solution Calculate the
volume of juice
Understand • The level of juice in glass P is 110 mm. for 10 mm. Then
the problem • The level of juice in glass Q is 40 mm. use the proportion
to figure out the
• The volume of juice in glass Q is 150 m . volume of juice for
• How much is the volume of juice in glass P?
110 mm.
Plan the strategy

Level of juice Volume of juice
40 mm 150 m

40 mm ÷ 4 = 10 mm 150 m ÷ 4 = m

11 × 10 mm = 110 mm 11 × m = m

Solve

Step 1 3 7.5 m
4 1 5 0.0 m
40 mm 150 m Check
÷4 ÷4 −12
30 11 × 37.5 m
10 mm 37.5 m = (10 + 1) × 37.5 m
−28 = (10 × 37.5 m ) + (1 × 37.5 m )
20
3 7.5 m 3 7.5 m
−2 0 × 10 ×1
0
3 7 5.0 m 3 7.5 m
Step 2 3 7.5 m
× 11
10 mm 37.5 m 11

× 11 × 11 11 3 7 5 . 0 m
+ 3 7 . 5 m
37 5
4 1 2 . 5 m
110 mm 412.5 m +375 0
4 1 2.5 m

The volume of mango juice in glass P is 412.5 m .

5.1.1 (ii) €€Guide pupils to solve problems step by step using tables or determining 159
patterns.

MASS AND VOLUME OF LIQUID Chocolate Milk Recipe

1 My sister is preparing chocolate (one glass)
milk by referring to the recipe
shown in the picture. What is the 120 m of fresh milk
mass of chocolate pieces that she 100 g of ice cubes
needs if 0.96 of fresh milk is 10 g of sugar
used? 55 g of chocolate pieces
Whipped cream (optional)

Solution

Understand the problem Plan the strategy

• 120 m of fresh milk needs 55 g 120 m

of chocolate pieces. 55 g 0.96
• How many grams of chocolate ?g

pieces needed if 0.96 of fresh milk

is used?

Solve

Method 1 Method 2

0.96 = 0.96 × 1 000 m 912600  mm = 8
= 960 m

120 m 55 g 960 m of fresh milk can make
8 glasses.
8
960 × 55 g
960 m 120 = 440 g 1 glass 55 g of chocolate pieces

4 1 8 glasses g of chocolate

55 g pieces

×8 8 × 55 g of chocolate pieces
= 440 g of chocolate pieces
440 g

Check 440 g ÷ 55 g = 8 Does she use 80 g of sugar
and 800 g of ice cubes?
8 × 120 m = 960 m Discuss.
= (960 ÷ 1 000)
= 0.96

440 g of chocolate pieces is needed if 0.96 of fresh milk is used.

€€Get pupils to work in groups on a different recipe which involves mass and 5.1.1 (iii)
160 volume of liquid. Give suitable questions for each group to solve.

2 A block of 250 g butter gives you 271.74 m Nastaultral
of melted butter. My sister is melting
5 blocks of butter and adding it to 2 000 m Butter
of evaporated milk to make cream soup.
Calculate the volume of the cream soup mixture. Fresh

250 g

Solution

Given • A block of 250 g butter gives 271.74 m of melted butter.
Asked for • 5 blocks of the same butter are melted and added to 2 000 m
Solve
of evaporated milk.
Calculate the volume of the mixture of melted butter and
evaporated milk.

5 × 271.74 m + 2 000 m =

Step 1 Step 2

1 piece 271.74 m 1 358.7 m + 2 000 m =  m
5 pieces  m
1 3 5 8 . 7 m
3 32 + 2 0 0 0 . 0 m

2 7 1 . 7 4 m 3 3 5 8 . 7 m
×5
1 358.7 m + 2 000 m = 3 358.7 m
1 3 5 8 . 7 0 m

Check 3 3 5 8 . 7 m 2 7 1 . 7 4 m
− 2 0 0 0 . 0 m 5 1 3 5 8 . 7 0 m
1 3 5 8 . 7 m
−1 0
35 Does 4 blocks of
butter give more
−3 5 than 1 of melted
08 butter? Prove it.

−5
37

−3 5
20

− 20
0

5 × 271.74 m + 2 000 m = 3 358.7 m

The volume of the cream soup mixture is 3 358.7 m .

5.1.1 (iii) €€Guide pupils to construct correct number sentences to solve the problems. 116611

3 ORGANIC FERTILISER PROJECT
Ingredients
• 1 kg of waste materials (fruit peels, vegetable waste, dried leaves, grass)
• 150 g of black soil
• 1 of water
Method
1 Combine all the waste materials, black soil, and water.
2 Mix and loosen the mixture a few times.

3 Let it decompose for three months.

Our teacher, Mr Peter Unggah asked our group to produce organic fertiliser
as shown above. What is the mass of black soil and volume of water
needed for 2.5 kg of waste materials?

Solution

• 150 g of black soil and 1 of water needed for 1 kg of waste materials.
• Find the mass of black soil, in g, and litres of water for 2.5 kg of waste materials.

Solve using 1 kg of waste materials 1 of water
proportion. 2.5 kg of waste materials 2.5 of water

1 kg or 1 000 g of waste materials need 150 g of black soil.
2.5 kg of waste materials = 2 500 g of waste materials

1 000 g of waste materials 150 g of black soil 2

2 500 g of waste materials 2 500 g × 150 g 2 5 g
1 000 g x 1 5
1 2 5
= 25 g ×15 + 2 5 0
= 375 g
3 7 5 g
Check Waste materials Black soil Water
1 . 0 kg 1 .0
1 . 0 kg 1 1 .0
+0.5
+ 0 . 5 kg 150 g
150 g 2.5
2 . 5 kg + 75 g

375 g

375 g of black soil and 2.5 of water are needed for 2.5 kg
of waste materials.

€€Create a project which involves mass, volume of liquid, and length. Ask each 5.1.1 (iii)
162 group to present their project.

LET’S DO IT 20 cm

Solve these problems.
a A water bottle with the measurement shown is fully filled with

1 200 m of drinking water. After drinking, the level
of water dropped to 8 cm. How much water was drunk?

b Our family went to visit Pahang National Park.
The distance from our house to Pahang National Park is 270 km.
My father’s car consumes 9.4 of petrol for every 100 km.
Calculate the volume of petrol for a round trip.

c Puan Selvi wants to make jelly. Based on the recipe, 2 of water
is used to dissolve 250 g of sugar and 20 g of jelly powder.
Calculate the mass of jelly powder needed by Puan Selvi if she
uses 5 of water.

LET’S PRACTISE

Solve these problems.

a 5 kg of rice is fully filled in a container. The level of rice in the container is 20 cm.

After a few days, the level of rice in the container is reduced to 4 cm.

Calculate the mass, in g, of rice left.

b The picture shows two metals, R and Q of the

Metal R same type with different length and mass.
80 cm i Find the mass of metal Q.

Metal Q 10.2 kg ii Calculate the difference in mass of
metal R and metal Q.
0.6 m
p kg

c A water tank can store 1 000 of water. The level of water in the tank is 1.5 m when full.
Calculate the level of water, in cm, when the remaining volume of water is 350 .

d ANCHOVIES FRITTER RECIPE i Based on the given recipe, how
250 g of wheat flour much volume of water and mass of
3 g of fine salt anchovies are needed if 800 g
180 m of water of wheat flour is used?
50 g of anchovies (cleaned)
Cooking oil for frying ii Find out the mass of wheat flour and
the volume of water needed for 100 g
of anchovies.

5.1.1 (i), (ii), (iii) €€Carry out activity to solve problems such as Gallery Walk. 116633
€€Guide pupils to solve problems step by step using Polya method.

LET'S EXPLORE TEST AND REVIEW

Tools/Materials Wooden sticks (20 cm), rubber bands (10 rings), transparent plastics, rulers,
Participants hooks, 3 containers filled with pebbles or sand (300 g, 500 g, and 1 000 g),
10 marbles, measuring cylinders, weighing scales, water bottles,
1 of water, and tables.
TABLE
OF TASK
4 pupils in a group.

Task

STATION 1 MASS AND VOLUME OF LIQUID SCAN ME

1 Fill the measuring cylinder with 200 m STATION 1
of water. Marble Volume of
mass water (m )
2 Weigh the mass of a marble and record it.
3 Put in the marbles one at a time carefully into (g)
0 200
the measuring cylinder.
4 Record the total mass of marbles and the

volume of water after putting each marble.
5 Make conclusion about the mass of marbles

and the volume of water.

STATION 2 VOLUME OF LIQUID AND LENGTH

1 Measure 300 m of water and fill it in a bottle. STATION 2
Volume Level of
2 Measure the level of water in the bottle and of water water (cm)
record it.
(m )
3 Pour in another 100 m of water, measure 300
the level of water and record it. 400
500
4 Repeat step 3 for 2 times. 600
5 Make conclusion about the volume of water

and the level of water.

STATION 3 MASS AND LENGTH

1 Tie rubber bands together in fives. STATION 3

2 Insert the rubber bands through the wooden Weight Length of
(g) stretched
stick and hold. Measure the length of rubber bands

rubber bands. (cm)
3 Place a hook on the rubber bands and hang
300
300 g of pebbles or sand as shown in the picture.
4 Measure the length of stretched rubber bands. 500

5 Repeat steps 3 and 4 for the following weight 1 000

of pebbles or sand:

a 500 g b 1 000 g

6 Make a conclusion about the mass of weight

and the length of stretched rubber bands.

€€Prepare all the materials and apparatus needed for this activity in all 5.1.1 (i), (ii), (iii)
164 three stations. Scan the QR code to get the tables.

€€Guide pupils to make correct conclusion for each task.

6 SPACE An angle is
formed when
LET’S FORM ANGLES two lines meet.

Teacher, how do we
form an angle?

Measure the value of an angle
from a straight line using a

protractor and mark the value.
Then, draw a line to form the angle.

50° ANGLE

1 Draw a straight line.
Mark two points as A and B.

2 Place the protractor’s baseline exactly on AB.
Ensure that the centre of the protractor is

exactly on point A.
Read the inner scale from 0° to 50°.
Mark and label it as C.

3 Remove the protractor.
Join points A and C.
Label the angle as 50° between

straight lines AC and AB.

6.1.2 €€Ask pupils to form other acute angles such as 20°, 45°, and 78°. 165
€€Select a few pupils to present their works respectively.

90° ANGLE 2 F Place the baseline
1 Draw a straight line E and the centre
D of the protractor
of 6 cm long. exactly on point
Mark two points. E. Read the outer
Label it as D and E. scale from 0° to
90°. Mark and
DE label it as F.

You are given a ruler and 3 Remove the protractor. F
a pencil. Explain how you
90°
can form a 90° angle.
E
Draw a straight line from E

to F. Label the angle as 90°

between straight lines EF D

and ED.

108° ANGLE Q R
1 Draw a straight line PQ.

P

2 Place the baseline and the Q
centre of the protractor R What is the type
exactly on point Q. Read
the outer scale from 0° to of angle for 50°,
108°. Mark and label as R. P 90°, and 108°?

3 Remove the protractor. 108°
Draw a straight line from Q

Q to R. Label the angle as
108° between straight lines
QR and QP.

P

€€Ask the pupils to do the activity in pairs to form other obtuse angles such as 6.1.2
166 100° and 165° angles and get them to check their work among themselves.

TRY IT OUT

TAolaotls//BMaahatenrials Geogebra software

Participants In pairs

Steps
Form angle ABC
1 Launch Geogebra software.

Click Geometry.
2 Click Point on Object.
3 Plot three points.
4 Click Segment. Click point A and join

with point B. Click point B and join
with point C.
5 Click Angle. Next, click points C, B,
and A. The value of angle ABC will
appear on the diagram.
6 Click Move. Click and hold, move point
A or B or C. See the changes in the
value of angle ABC.

FORM ANGLE
TUTORIAL

SCAN ME

LET’S DO IT

Using a ruler and a protractor, form the angles below.

a 10° b 25° c 40° d 68° e 87°
j 174°
f 95° g 130° h 115° i 142°

€€Guide pupils to carry out the Try It Out activity in groups so that they can explore 167
6.1.2 various angle values up to 180°.

€€Scan the QR code to watch how to form angle ABC.

DRAW AND MEASURE INTERIOR ANGLES
OF REGULAR POLYGONS

This shape is drawn 11 AUGUST 2022
on a dotted grid
paper. What is the We measure the sides, teacher.
method to prove All sides must have equal length.
that this is an
We can measure the
equilateral triangle? angles too. Every angle

must be 60°.

Excellent answers!
We will learn to draw
regular polygons and
measure the interior

angles.

Think of other suitable Square grid paper
materials that can be used to
draw regular polygons and Dotted grid paper
measure each of the angles.

Equilateral triangle grid paper

Protractor cm
inches

Ruler

€€Discuss various materials and suitable methods to draw shapes of regular 6.1.1
168 polygons including the ones that have been learned such as tracing the

surfaces of 3D objects.

EQUILATERAL TRIANGLE EQUILATERAL Let’s use this equilateral
TRIANGLE triangle grid paper to draw
Method 1 GRID PAPER
1 SCAN ME an equilateral triangle.

C
2

A 4 units B 4 units

• Mark point A. A 4 units B
• Count 4 units on the triangle
• Count 4 units on the triangle
grid to the right and mark as grid from point A upwards.
point B.
• Join points A and B. • Mark as point C. Join point A
• Label it as 4 units. with point C.
3 C
• Label it as 4 units.

4 units 4 units
4 units
4
C

A 4 units B 4 units 60°

• Join point B with point C. 60° 60°
• Label it as 4 units.

A 4 units B

• Place the centre of the protractor on point A.
• Ensure that the baseline of the protractor

overlaps line AB.
• Read the value of the angle on line AC and

label it.
• Repeat to measure angles B and C.

6.1.1 €€Scan the QR code to print the materials. Ask pupils to draw equilateral triangles 169

with length of sides of 4 units, 5 units, and 7 units in their mathematics exercise

books and measure the angles.

€€Remind pupils to measure the angles correctly as learned in Year 5.

Method 2 1 A
Draw a straight
I can draw an cm
equilateral triangle line of 4 cm long. inches
using a blank paper
Mark as point A.
and a ruler.

2 Mark the centre of the line at 2 cm.
Draw a perpendicular line.

A

cm A cm
inches inches

3 cm B
inches A
Measure 4 cm from
point A until it touches
the perpendicular line
and mark it as point B.

4 B

Label C and join A
points B and C. C
Measure angles A,

B, and C.

€€Remind pupils about perpendicular lines. 6.1.1
170

SQUARE

Let’s draw a square. It must
have four points of equal
distance.

1

D C

A Mark points A, B, C,
and D at a distance of
5 units between one
another.
B

2D C
A
Join all the points.
Make sure that all sides
are of equal length.

B

Explain other

3 methods to draw
DC squares as well
as to measure the

Measure the angles.

interior angles of

each angle. Label

90° the angles.

AB

€€Ask pupils to draw squares. Encourage pupils to draw in various ways 171
6.1.1 such as using a blank paper and a ruler.

REGULAR PENTAGON

Let’s draw a regular pentagon. Each angle of the pentagon is 108°.

1 A 5 cm B

cm Draw a straight line of 5 cm
inches long. Label it as A and B at
each end of the line.
2 Measure angle A, 108°.
Draw a long straight line. cm
inches

A 5 cm B

A 5 cm B
3 Measure angle B, 108°.

Draw a long straight line.

cm
inches
A 5 cm B
cmA 5 cm B C
inches4E 5 cm Measure 5 cm from B along the
straight line drawn and label it as C.
A 5 cm B Measure 5 cm from A along the
straight line drawn and label it as E.

172 6.1.1

5 C cm
E 5 cm inches

E C
5 cm
A 5 cm B 5 cm B
A

Measure angle C, 108°. Draw a long straight line.

6
D

E CE C

cminches

5 cm 5 cm

A 5 cm B A 5 cm B

Measure angle E, 108°. Draw a long straight line. Label it as D at the intersection
of line EC.

7D

108°

E 108° 108° C

5 cm

108° 108°

A 5 cm B
Erase extended lines at points C, D, and E.
Label the angles and the length of the sides.

6.1.1 €€Surf the Internet to get the shapes of regular pentagon and five-pointed star. Print 173

the shapes and give them to pupils. Ask pupils to draw regular pentagon using the

given shapes and measure the angles.

REGULAR HEXAGON T 4 units S
4 units 4 units
Method 1 U R

Let’s draw a regular hexagon. 4 units 4 units
Remember, the six sides must be Q

of equal length!

1 Count 4 units for the six
sides. Mark six points and
label them as P, Q, R, S, T,
and U. Join all the points.

P 4 units
S
2
T
120°

U Measure and label
R every interior angle.

P Q Can a regular hexagon be
drawn on a square grid
Method 2 2 paper? Discuss.
Draw six equilateral 13
triangles that can
be joined to form a 64
hexagon. 5

€€Explore other methods to draw hexagon other than using the equilateral triangle 6.1.1
174 grid paper.

€€Discuss shapes of hexagon that can be found in daily life situations such as
honeycomb.

REGULAR HEPTAGON

Method 1 1

I use a heptagon 2
shape from

MS Word software
and print it out.

Click Shapes and select
Heptagon from Basic Shapes.

3 Click Shift on the keyboard
and drag the mouse
Method 2 to enlarge the size of a
1 regular heptagon.

Print out the shape.

128.5° Measure and label the
2 interior angles of the
regular heptagon.

Join the seven vertices
of the star to draw
a regular heptagon
and measure every
interior angle.

128.5°

Get a picture of a
seven-pointed star.

€€Train pupils to draw a heptagon with suitable methods to obtain a regular 175
6.1.1 heptagon shape that has an angle of 128.5°.

REGULAR OCTAGON
1 D raw a straight line of 4 cm long and

label it as A and B at each end of the
straight line.
Measure angle 135° at A and B.
Mark and draw a straight line
passing through the point.

2 M easure 4 cm from A and mark it as H.
Measure 4 cm from B and mark it as C.

3 M easure and mark 4 cm from C and H.
Label it as D and G.

4 M easure angle 135° at D and G.
Mark and draw a straight line passing

through the point.

€€Guide pupils to draw and measure lines correctly to form a correct 6.1.1
176 regular octagon.

5 M easure and mark 4 cm from D and G. Label it as E and F.

6 J oin E and F. Erase extended lines at points C, H, E, and F.
Label every angle of the regular octagon.

THINK Charles and Raymond drew a regular polygon each. The
SMART number of sides of the regular polygon drawn by Charles is
2 times the number of sides of the regular polygon drawn by
Raymond. What are the shapes of regular polygon that
might be drawn by Raymond and Charles?

LET’S DO IT

Draw and measure the interior angles of the following regular polygons using
grid papers, ruler, protractor, and other suitable materials.

a Equilateral triangle b Square

c Regular hexagon d Regular pentagon

e Regular heptagon f Regular octagon

€€Ask pupils to draw regular polygons up to eight sides based on their creativity.
6.1.1 Get them to measure and label the interior angles. 177

RECOGNISE CIRCLES

CENTRE OF A CIRCLE, DIAMETER, AND RADIUS

a Wow, these logos are beautiful,
teacher. Which logo will you
Yes, Ikram. All of
choose for our robotics team? these logos were

designed from circles.

Tomorrow, you will learn all
about circles.

b Teacher, what does a
circle have?

This red dot is the centre of the circle.

It is usually represented by the letter O.

The curved line that forms this circle is

called the circumference of a circle.

O 6.2.1
centre of
the circle

circumference
of the circle

€€Use various sizes of circle to stimulate pupils’ understanding about the centre
178 of circle and the circumference.

c Ikram, based on the notes, which one is the

diameter? Which one is the radius?

Monday 29 August 2022

The centre of a circle is circumference The diameter is a straight line that
the point located in the of the circle connects two points on the circumference
middle of the circle. O and passes through the centre of the circle.

The radius is a straight centre of The circumference of a
line that connects the the circle circle is the closed curve
centre of the circle with that forms the boundary
the circumference. of the circle.

The red line is the diameter.
The yellow line is the radius.

d circumference of
the circle
The length of the radius
from the centre of the circle

is always equal.

centre of Can you relate radius
with diameter? Explain.
diameter the circle
O

radius

€€Inform pupils that the length of all radii in a circle is equal. 179
6.2.1 €€Guide pupils to relate radius with diameter.

LET’S DRAW CIRCLES Scan the QR code. Print the ruler and MODIFIED
Method 1 RULER
laminate it. Then, make a hole at every
Let’s draw a circle of 1 cm and at every 0.5 cm. SCAN ME
4 cm radius using the

modified ruler.

Remember! Do not
move the pencil
point at 0 cm.

1 Use two pencils. Place one 2 Move the pencil at the 4 cm hole to
pencil point at the 0 cm hole complete one round clockwise or
(centre of the circle) and anticlockwise.
another one at the 4 cm hole
(4 cm radius).

3 Mark the centre of the circle and
label it. Draw a radius and label it.

180 €€Prepare the modified ruler for each pupil. 6.2.2
€€Train pupils to draw circles with various radius measurements neatly.

Method 2

There are many
surfaces of round-shaped
objects that can be traced

to draw circles.

1 Draw a circle using the 2 Cut out the circle.
circumference of a medicine cup.

3 Fold the circle into four parts 4 Unfold it. Observe the folded
of equal size. intersection in the middle.

5 Mark the centre of the circle. diameter
O
Then, label the centre of
the circle and the diameter.

6.2.2 €€Ask pupils to bring any round-shaped containers for the circle drawing activity. 181
€€Carry out the activity in small groups.

THINK Draw another circle with a radius of one-third
SMART 12 cm of the radius shown in the circle on the left.

Label all the characteristics of the circle.

LET’S DO IT

1 Fill in the boxes based on the labels on the circle.
T

P O
O
PQ
Q OT

2 Complete the sentences below.

a The of a circle is the point located in the of the circle.

b The circumference of a is the that forms the boundary

of a .

c The is a straight line that connects the of a circle with

the circumference.

d The diameter is a that connects on the circumference

that passes through the centre of the circle.

3 Draw the circles based on the given information.

a b c

My radius is My radius is My radius is
3 cm. 5 cm. 8 cm.

4 Draw a circle based on the information below and label it.

O is the centre of the circle.
OH is the radius of the circle. The length of OH is 3.5 cm.
PT is the diameter of the circle. The length of PT is 7 cm.

€€Guide and check pupils' work to ensure that they answer correctly. 6.2.1, 6.2.2
182

SOLVE THE PROBLEMS

1 Father plans to build a table in the garden.
The surface of the table is a regular
hexagon and will be placed in
an area measuring 2 m long and 2 m wide.
What is the plan for a suitable size of
the table?

Solution

Understand the problem Plan the strategy

• The surface of the table is a • Draw a regular hexagon that

regular hexagon. does not exceed the length

• The area is measured as 2 m × 2 m. and width of 2 m.

• What is the plan for a suitable size • Must have space for chairs

of the table? around the table.

Solve Check

2m Regular hexagon table surface:

chair • it has six sides and vertices 
• all sides are of equal length 
2 m table surface • size does not exceed 2 m × 2 m 
• consider space for the chairs 

Discuss other surface shapes

of regular polygons, which are
suitable to make a table.

€€In groups, ask pupils to draw plans for other regular polygons such as 183
6.3.1 pentagon, heptagon, and octagon.

€€Ask each group to present their work.

2 Zahid’s sister wants to bake a cake. She needs a 10 cm
sheet of paper to be used as cake mould parchment
as shown in the picture. What is the method to make
the parchment?

Solution

Given • Circle-shaped cake mould.
• The cake mould radius is 10 cm.

Asked for The method to make a circle-shaped parchment.

Solve

Simulate forming a
circle. The radius of
the circle is 10 cm.

1 Fold paper into four parts. 2

• Using a modified ruler, place a
pencil at 0 cm. Place another pencil
at 10 cm.

• Move the pencil at 10 cm to form a
curved line.

3 Cut the paper using scissors 4
along the curved line.
Open the folds
to see the
result of the
parchment.

€€Vary length of radius and ask each pupil to simulate forming a circle 6.3.1
184 like the method above.

LET’S DO IT

1 Chee Cheong wants to make a circle from a piece of

plank measuring 25 cm long and 25 cm wide. The

radius of the circle is 8 cm. Help Chee Cheong to 25 cm

draw the circle. 25 cm

2 A group of pupils were asked to design an area for

resting. The area is of a regular octagon with the length of 5 m on each side.

Draw the plan of the area.

3 Anding wants to make a photo frame of six equal sides. The perimeter of the

photo frame is 120 cm. What is the length of each side of the photo frame?

4 Mr Awang wants to make a circle in the middle of a field. The radius of the

circle is 0.3 m. Explain how Mr Awang will draw the circle.

LET’S PRACTISE

1 Based on the information below, draw and label the interior angles for each
regular polygon.

a It has three sides of equal length. The length of each side is 5 cm.

b Each interior angle of a polygon is 135°. The length of each side is 3 cm.
c Each of the five sides measures 6.5 cm. All the interior angles are 108°.

2 Draw a regular polygon of four sides. Each side measures 5.3 cm. Label its
interior angles.

3 Using writing utensils and a protractor, draw the following angles.

a 40° b 65° c 89° d 125° e 160° f 173°

4 A circle consists of , , , and .

5 Draw circles based on the information given.
a radius of 4 cm b radius of 4.7 cm c radius of 5.2 cm

6.1.1, 6.1.2, 6.2.1, 185
6.2.2, 6.3.1

6 Solve the following problems.
a M r Gopal is arranging bricks at his garden as a border for his regular

pentagon-shaped mini flower garden. The length of one side of the
regular pentagon’s border is 5 m. Sketch the shape.

b H alina’s father plans to build a circle-shaped swimming pool.
The radius of the swimming pool is 3 m.

i Draw the plan of the swimming pool.
ii Give a suggestion about the measurement of the pool area.

c M ei Hwa’s mother wants to buy cake boards. She received many online orders
of cakes with the size of 25 cm × 25 cm. What is the suitable measurement of the
cake board she should buy? Why?

LET'S EXPLORE 6.1.1, 6.2.2, 6.3.1

Tools/Materials A4 papers, grid papers, coloured
papers, glue, water paint, crayons,
coloured pencils, scissors, pencils,
rulers, and protractors.

Participants 4 pupils in a group.

Task

1 Design a geometrical pattern from any regular
polygons up to eight sides and a circle.

2 Use the Cut-and-Paste technique or the
colouring technique.

3 Present the work.
4 Each group chooses and proposes three

types of geometrical patterns that are most
interesting.
5 Three selected patterns will be announced
as winners.

186

7 COORDINATES, RATIO,
AND PROPORTION

DISTANCE BETWEEN TWO COORDINATES

1 The Cartesian plane shows the location of Farid’s home and nearby places.

The distance for Ny 1 cm
each grid on the
6 RESTORAN

Cartesian plane is 1 cm

1 cm. 1 cm scale 5 RESTORAN

represents 1 km of Fish pond

the actual scale. 4 RESTORAN RESTORAN

Tourist spot

3 Hotel RESTORAN
2
1 RestaurantRESTORAN

O RESTORAN

Fishing village

Farid’s house Mosque Scale
1 cm represents 1 km
1 2345
x

6

a What is the horizontal distance of the mosque from Farid’s house in km?

5 km Mosque
5 cm represents 5 km
Farid’s
house
0 1 2 3 4 5 cm of the actual distance.

The horizontal distance of the mosque from Farid’s house is 5 km .

b The actual vertical distance of the hotel from Farid’s house is 2 km .
c The horizontal distance of the fishing village from Farid’s house, in km, €

is 5 km . Meanwhile, the vertical distance is 2 km . horizontally
d The actual distance of the tourist spot from Farid’s house is

and vertically.

State, in km, the horizontal distance and vertical distance €
of the restaurant from the fishing village.

7.1.1 €€Recall the horizontal distance and vertical distance of a point from the origin € 187
on the first quadrant of the Cartesian plane.

€€Discuss the horizontal distance and vertical distance of other locations on the

Cartesian plane based on scale given.

2 The Cartesian plane shows the location of € 1 unit on the Cartesian plane
represents 100 000 units of the
residential A, B, C, D, hospital, and petrol statioHOnSP.ITAL actual distance. Thus, 1 cm on
the Cartesian plane represents
Ny HOSPITAL
100 000 cm or 1 000 m or €
1 cm 1 km of the actual distance.

6 HOSPITAL 1 cm 100 cm = 1 m
100 000 cm = 1 000 m
Residential B = 1 km

Residential D Residential A

5

HOSPITAL

4

HOSPITAL

3 4 cm

HOSPITAL

2 Petrol station

1 5 cm Hospital 7 x Scale€
34 1 : 100 000
Residential C 56

O1 2

What is the actual horizontal distance and vertical distance, €
of Residential A from Residential C?

Residential Distance from origin
Horizontal distance Vertical distance

C 100 000 cm = 1 km 100 000 cm = 1 km

A 600 000 cm = 6 km 500 000 cm = 5 km

the difference of 6 km 5 km the difference of €
horizontal distance – 1 km – 1 km vertical distance

5 km 4 km

The actual distance of Residential A from Residential C is 5 km horizontally €

and 4 km vertically . Find the horizontal distance and vertical distance,
in km, of the hospital from Residential D.

THINK By using the scale of 1 : 100 000, find the horizontal
SMART distance of P from Q on the Cartesian plane if the

actual horizontal distance of P from Q is 7 000 m.

188 €€Explain that 100 000 cm is equal to 1 km. 7.1.1
€€Explain that the scale on the Cartesian plane is used to represent the actual distance.

€€Discuss the horizontal distance and vertical distance of two different locations on the

Cartesian plane.

3 The Cartesian plane shows the location of Khairil’s house, bus station, €
taxi station, MRT station, and airport.

Ny Taxi station

5 Airport

4

Khairil’s

3 house

2

Bus station

1 Scale 3 4 5 km
012
MRT station Refer to the scale, €
O 1 2 3 4 5x 4 units equals 4 km.

a What is the horizontal distance, in km, from Khairil’s
house to the airport?

Coordinate of Khairil’s house Coordinate of the airport
(1, 4) (5, 4)

Horizontal distance = 5 units – 1 unit
= 4 units

The horizontal distance from Khairil’s house to the airport is 4 km .

b What is the horizontal distance and vertical distance, in km, from
Khairil’s house to the bus station?

Coordinate of Khairil’s house (1, 4) Coordinate of the bus station (4, 2)

Horizontal distance Vertical distance State the horizontal distance

= 4 units – 1 unit = 4 units – 2 units and vertical distance, in km,
from the taxi station to the
= 3 units = 2 units
MRT station.

The distance from Khairil’s house to the bus station €

is 3 km horizontally and 2 km vertically .

7.1.1 €€Carry out a suitable activity to determine the horizontal distance and vertical 189

distance according to scale given. For instance, pupils’ seating arrangement €

in class.

LET’S DO IT

1 The Cartesian plane shows the location of Feng and his three friends’ houses.

Ny 1 cm a S tate, in km, the horizontal distance
of Salim’s house from Feng’s house.
5
4 b S tate, in km, the vertical distance of
3 Shalini’s house from Feng’s house.
2
c S tate the actual horizontal distance

and vertical distance of Jack’s house
from Feng’s house.
Shalini’s house 1 cm
1 cm
Jack’s house

Salim’s house

1

O Feng’s house 4 Scale
5 x 1 cm represents 1 km
1 23

2 The Cartesian plane shows the N y 1 cm
location of four islands.
5
a Find the actual horizontal distance

and vertical distance of: 4 Rajin Island
i Riang Island from Rajin Island. Seronok Island

ii Seronok Island from Baik Island. 3
b State the island which is located €

at a distance of 3 km horizontally 2 Riang Island
and 2 km vertically from Baik Island.

1

Scale Baik Island x

1 : 100 000 O 1 2 3 4 5

Ny Rest area T The Cartesian plane shows the rest area T
3 5 and town H along a highway.

4

3 State the horizontal distance and vertical
distance of rest area T from town H in km.
2
Town H
1 Scale
0 1 2 3 4 5 km
O 1 2 3 4 5x

190 €€Prepare a Cartesian plane for a student-centred activity for pupils to mark the 7.1.1
nearby areas to their respective houses and find the actual horizontal distance

and vertical distance based on the chosen scale.

RATIO BETWEEN TWO QUANTITIES

1 The picture shows pupils’ activities in the science laboratory.

Rina and I will
prepare the

experiment report.

Alright. We will TIPS Ratio is the comparison of
carry out the
experiment. size or value of an object to
the size or value of another
object in the simplest form.

What is the ratio of the number of boys to the number of girls?
Step 1

boys girls

The ratio of the number of boys to the number of girls is 2 : 2.

Step 2 girls 2 pupils represent €
boys
1 group. There is €

1 boys’ group and €
1 girls’ group.

1 group 1 group

2 : 2 written in the simplest form is 1 : 1.

The ratio of the number of boys to the number of

girls is 1 : 1 . State the ratio of 5 : 5 €
in the simplest form.

7.2.1 €€Enhance pupils’ understanding on the concept of ratio between two quantities 191
by forming groups to simplify the ratio between two quantities.

€€Emphasise how to say the correct ratio. For example, the ratio of €

one to one.

2

State the ratio of the number of mangoes to the number of mangosteens.

Method 1 Step 2 Group in twos
Step 1

There are 3 groups of mangoes.
There are 2 groups of mangosteens.

The ratio of the number of The ratio of the number of

mangoes to the number of mangoes to the number of
mangosteens is 6 : 4. mangosteens is 3 : 2.

6 and 4 can be Method 2
divided by 2 without 6:4

any remainder. ÷2 ÷2

3:2

6 : 4 written in the simplest form is 3 : 2.
The ratio of the number of mangoes to the number of mangosteens is 3 : 2 .

3 THURSDAY 15 SEPTEMBER 2022

State the ratio of 3 to 9 in the simplest form.

Adam Safiya Whose answer is
3:9 correct? Discuss.
1:4 3:9
1:3

The ratio The ratio
of 1 to 4. of 1 to 3.

€€Explain that simplifying ratio is the same as simplifying fraction. 7.2.1
192 €€Emphasise that the value of ratio does not change even though it is simplified.