SK Year 5 Mathematics DLP

THINK - PAIR - SHARE


Tools/Materials question cards, A4 paper, pen
SAMPLE QUESTION CARDS

Print 1 350 pieces of cards in The price for 4 kg of
10 minutes. biscuits is RM58.
Calculate the number of cards What is the price for 2 kg
printed in 12 minutes. of biscuits?

Task

1 Answer the question received in the A4 paper.
2 Choose a friend and present your answers.
3 Correct each other’s answer.
4 Present the work in front of the class.







1 The following is a cocoa jelly recipe for one mixture.



• 3 tablespoons of
• 1 packet/10 g of jelly powder cocoa powder
• 400 m of evaporated milk • 1 piece of

• 800 m of water pandan leaf

3
• cup of granulated sugar • a pinch of salt
4


a Calculate the volume of evaporated milk needed when using 20 g
of jelly powder.

b What is the volume of evaporated milk for three mixtures?
c What is the mass of jelly powder for 1 200 m of water?


2 The picture shows the price for 1 kg of granulated sugar.
a State the price for 2 kg of granulated sugar.
1 kg
Sugar b What is the mass of granulated sugar that
1 kg can be bought with RM8.55?
RM2.85



243
• Carry out group activities involving daily life situations such as
7.3.1
cooking based on simple recipes using the correct proportions.

y
SOLVE THE PROBLEMS entrance
6 B
1 The Cartesian plane shows
the duty positions for four 5

school prefects. Jessica is
on duty at entrance A. The 4
distance of Resma’s duty
position from Jessica is 3
canteen
4 units horizontally and bicycle
3 units vertically. What is the 2 parking
spot
coordinate of Resma’s duty
position? 1
entrance

A x
O 1 2 3 4 5


Understand the problem

• Jessica is on duty at entrance A.
• The distance of Resma’s duty position from Jessica is 4 units
horizontally and 3 units vertically.
• Find the coordinate of Resma’s duty position.

Plan the strategy On the Cartesian plane, mark the distance of 4 units
horizontally and 3 units vertically from entrance A.
Solve
y
Check
6

5 Coordinate of Coordinate of
Resma’s duty Jessica’s duty
4
position is (5, 3) position is (1, 0)
Resma’s duty
3
position (5, 3) Calculate the horizontal distance:
2 5 units – 1 unit = 4 units

1 Calculate the vertical distance:
x 3 units – 0 unit = 3 units
O 1 2 3 4 5
Jessica’s duty The coordinate of Resma’s
position (1, 0) duty position is (5, 3).


244
7.4.1 • Guide pupils to solve problems by drawing a Cartesian plane.

2 Initially, the mass of package R and the mass of package T was 1 kg
and 4 kg respectively. Herma put in a honeydew of the mass of 2 kg
inside package R. Calculate the ratio of the current mass of package R
to the current total mass of package R and T.


Solution
Summarise the
information in
Package R T
a table.
Initial mass 1 kg 4 kg
The mass of a honeydew put inside 2 kg none
the package

Current mass ? 4 kg


Find the ratio of the current mass of package R
to the current total mass of package R and T.

Mass of a Draw
Initial mass honeydew diagrams

1 kg 2 kg to represent
the current
the current mass of package R mass.
3 kg


the current mass of package T
4 kg



the ratio of the current mass of package R to the current total mass
of package R and T



:
3 7

The ratio of the current mass of package R to the current total mass
:
of package R and T is 3 7.


What is the ratio of the current total mass of package
R and T to the mass of package T?


245
• Guide pupils to use representations to state the ratios between
7.4.1
two quantities.

3 Every day, Encik Lau drives his car 36 km from home to the office.
He uses 3 of petrol for a one-way journey. What is the distance
travelled, in km, with 40 of petrol?



Solution



Given 3 petrol 36 km


Asked for 40 petrol ? km

36 km ÷ 3 = 12 km (distance for 1 petrol)
Find the distance
travelled with 1
of petrol.

36 km
















40 × 12 km = 480 km (distance for 40 petrol)
Let’s check
the answer.
1 2 km
40 4 8 0 km 12 km 1
−4 0
8 0 distance for 3 3 × 12 km = 36 km
− 8 0
0


The distance travelled with 40 of petrol is 480 km.




How many days can Encik Lau use the
40 of petrol for his two-way journey?



246
7.4.1 • Guide pupils to solve problems using the unitary method.

1 The Cartesian plane shows the location of several places in
an office building.

y
canteen
5
T
Q
4
meeting
room
3


P clocking in
2 machine
main S
door R
1
reception

x
O 1 2 3 4 5


a State the horizontal distance and the vertical distance from S to Q.

b What is the distance travelled by Lucy from R to the canteen?
c Puan Edith works at R. The distance of Encik Ragu’s workplace
from Puan Edith’s is 3 units horizontally and 1 unit vertically.
What is Encik Ragu’s coordinate?

2 The volume of water left in bottle J and bottle K is 0.5 and 3
respectively. Hazel poured 1.5 of water in bottle J. State the ratio
of the current total volume of water in bottle J and K to the current
volume of water in bottle J.

3 Adira used 2 cups of brown sugar and 5 cups of flour to make a type
of biscuit. How many cups of brown sugar is needed for 15 cups
of flour?
4 A printer can print 400 posters in 1 hour 20 minutes. How much time,
in minutes, is needed to print 700 similar posters?





247
7.4.1

y
6
F
1 The Cartesian plane shows points E, F and G. 5
G
a State the distance of: 4
i point E from the origin.
3
ii point F from the origin. E
2
iii point G from the origin.
b State the distance from point E to F. 1
c State the distance from point F to G. x
O 1 2 3 4 5 6

2 State the horizontal distance and vertical distance:
a from (3, 7) to (5, 8). b from (6, 2) to (2, 3).

3 The table shows Kaswini’s expenditure at the school canteen
for four days.

Day Monday Tuesday Wednesday Thursday
Money RM5 RM3 RM4 RM1

a State the ratio of expenditure on Monday to the expenditure
on Tuesday.
b State the ratio of expenditure on Wednesday to the total
expenditure from Monday to Thursday.
c State the ratio of the total expenditure from Monday to Thursday
to the expenditure on Tuesday.

4 The following are the ingredients used to make a syrup mixture.


150 m of syrup concentrate
1.25 of water
1 kg of granulated sugar


Calculate:
a the volume of syrup concentrate when 2 kg of granulated sugar
is used.
b the mass of granulated sugar needed for 450 m of syrup
concentrate.
c the volume of water needed for 225 m of syrup concentrate
to get the same taste.


7.1.1
248 7.2.1
7.3.1

5 Solve the problems below.
a The Cartesian plane shows the positions of the uniformed units at
a camping site.
y
Symbol Uniformed Unit
4
Scouts
3 Malaysian Red Crescent
Society (MRCS)
2 PERGERAKAN PUTERI ISLAM MALAYSIA PERGERAKAN PUTERI ISLAM MALAYSIA Puteri Islam

1 Girl Guides

School Youth Cadet
x
O 1 2 3 4 Corps (SYCS)

i One member of the Girl Guides who is at (4, 2) wishes to go
back to her society’s camp. What are the horizontal distance
and vertical distance that she has to go through?
ii Haris from SYCS society moved 4 units horizontally and
3 units vertically to meet a friend. What is the name of
Haris’s friend’s uniformed unit society? State the coordinate of
Haris’s friend.

b Neyla bought 2 m of blue ribbon. She also bought a red ribbon.
The length of red ribbon is 1 m more than the length of blue
ribbon. State the ratio of the length of blue ribbon to the length of

red ribbon.

c The table shows the distance and travel duration of an
Electric Train Service (ETS) from Ipoh to Kuala Lumpur.

Distance 175 km

Duration 2 hours 40 minutes

What is the distance travelled by the ETS in 32 minutes?


d The cost of a pair of trousers is 3 times the cost of a shirt. State the
ratio of the cost of a shirt to the total cost of the shirt and a pair
of trousers.




249
7.4.1

LUCKY LETTERS


two dice (a-f and g-l), 12 question cards
Tools/Materials
(scan QR Code), a Cartesian plane,
players’ answer cards, score sheet
k b
Participants 4 pupils in a group and a referee h l f a

y
Cartesian Plane example of question cards
6
h l State the letter on the
point situated 4 units
5
b g horizontally and 3 units
a c vertically from point g. e
4

k i j
3 Mass of a Mass of a
packet of packet of
d ciku langsat
2 f
2 kg 3 kg
1 State the ratio of the mass of
a packet of ciku to the total
e x mass of a packet of ciku and
O 1 2 3 4 5 langsat. c

example of players’ answer card example of the score sheet
Player’s name : Linda Round/ 1 2 3 Total
Letter The distance of Correct/ Answer of Correct/ player marks
a letter from the Incorrect question Incorrect Linda 5 10 5 20
origin card Sukri 10 10 5 25
1 unit horizontally Wong 5 10 5 20
c  5 : 2 
4 units vertically Kugan 5 5 5 15
3 units
e  Point d 
horizontally
How to play
1 The first player throws one of the dice. Write the distance of the letter that
appears on the dice from the origin. 5 marks are given for the correct answer.

2 The referee gives a question that matches the letter.
3 The first player answers the question. 5 marks are given for the correct answer.
4 Take turns to play until all question cards are answered.
5 The player who scores the highest marks wins the game.


• Scan QR code to print question cards from (a) until (l).
250 7.1.1, 7.2.1, • Determine players’ turn. Every question card that has been
7.3.1, 7.4.1
answered correctly cannot be used again. Questions can be
modified according to pupils’ ability.

8 8 DATA HANDLING
D
ANDLING
A
T
A H


INTERPRETING PIE CHARTS




1 SURVEY BY THE MATHEMATICS CLUB


WAYS OF SK BUDI PUPILS
title GO TO SCHOOL

Car sector
14% of the 12%
pupils in Bicycle Bus
our school 22% 52%
walk to
school. Walking Most of the
14% pupils come to
school by bus.
data in
percentage
Yes, more than
half of them take
the bus.








a % of the pupils go to school by bicycle.
b The difference in percentage between pupils who go to
school by car and by bicycle is %.


Discuss other information that you
can get from the pie chart above.




The pie chart shows the distribution of data in the form of
a circle. The total percentage of the pie chart should be 100%.



• Gather a few pie charts from magazines, books, or newspapers. 251
8.1.1 • Ask pupils to interpret the information from the pie charts in groups
and present the outcome of each group.

2 Leisure Activities Among of 80 pupils
of Year 6 a Find the percentage of
Monopoly.
10%
% 35% 100% − (10% + 35%
+ 22.5% + 17.5%)
17.5%
22.5% = 100% − 85%

= 15%

The percentage of
Key: Scrabble Chess Draughts Monopoly is 15%.
Monopoly Sudoku

b Calculate the number of pupils for the activity with
the highest percentage.


The game with the highest 35% of the pupils
percentage is Scrabble. play Scrabble.
7
35 4
35% of 80 pupils = × 80 pupils
100
5
1
= 28 pupils


The number of pupils for the activity with
the highest percentage is 28.





c How many pupils play Sudoku?

The percentage of Sudoku is 10%.
10
10% of 80 pupils = × 80 pupils
100
= 8 pupils
The number of pupils who play Sudoku is 8.




Is the difference between the number of pupils who play
Draughts and Chess more than 5? Discuss.


• Vary questions like finding the number of pupils for Draughts,
252 the difference between the number of pupils who play Sudoku and
8.1.1 Scrabble, and the total number of pupils for Draughts and Sudoku.
• Emphasise on daily time management so that the time to study is
more than the time to play.

3 Types of Favourite Books Calculate the percentage of comic fans.
Among Year 5 Dedikasi Pupils
6 out of 30 pupils love to read comics.
6
The fraction for comic fans is 30 .
Comic 2

6 6
The percentage of comic fans = × 100%
Fiction 30
1
15 = 20%
Non-Fiction
9 The percentage of comic fans is 20%.





Is the percentage of fiction and
non-fiction book fans 80%? Prove it.







1 Favourite Sports of Study the pie chart on the left and answer
200 Pupils the following questions.
a What is the most favourite sport?
Badminton b What is the percentage of table tennis

Table 15% players?
tennis
c Calculate the number of hockey
Hockey Football players.
20% 60%
d Calculate the difference between

table tennis players and badminton
players.

Favourite Colours
2 Answer the following questions based on the
pie chart of favourite colours as shown. 4
a What is the percentage of red colour fans? 10
5
b Calculate the difference in percentage
between the blue and white colour fans. 5
c Is the percentage of black colour fans 8
12.5%? Prove it. 8




253
• Encourage pupils to create their own questions based on
8.1.1
the pie chart and ask their friends to answer the questions.

MODE, RANGE, MEDIAN, AND MEAN



1 Frequency, mode, and range of data


smallest Donation Amount Number of
donation value or (RM) Donors
minimum value RM10 1

mode RM12 4 highest
RM15 3 frequency
biggest donation
value or RM20 2
maximum value RM25 1


Range is the difference The frequency of RM12
between the maximum donation is 4. RM12 is the
value and minimum value. mode because it has the
highest frequency. What is
the range of the data?






Sir, the range of the data
is RM15. RM25 minus
RM10 is equal to RM15.






Frequency is the number of a particular value in a set of data.
Mode is the value which appears most often in a set of data.
Range is the difference between the maximum value and minimum
value in a set of data.










14 13 13 15 12 13 10 15

What is the number in so that the set of data has the mode of 12?
State the range of the data.

254 • Explain the meaning of frequency, mode, and range based on set
8.2.1
of data available in newspapers, magazines, and the Internet.

2 This is the time recorded for Year 5
male participants from the Kenari
House in a cross-country run.



Time Recorded in a
Cross-Country Run Time Recorded in a
Name Time Cross-Country Run
Zariq 26 minutes The pictograph
Peter Tan 23 minutes 23 minutes represents the
Hakimi 25 minutes 25 minutes data of the time
Fazil 25 minutes recorded on the
Harvinder 26 minutes 26 minutes left. We are going
to determine
Cheng 28 minutes the median and
Amer 26 minutes 28 minutes mean for this
Ikhwan 29 minutes data.
Jason 26 minutes 29 minutes
represents 1 person


a Arrange the data in ascending order.
23, 25, 25, 26, 26, 26, 26, 28, 29

The fifth data is located in the middle of the data.
So, the median is 26 minutes.


23 + 25 + 25 + 26 + 26 + 26 + 26 + 28 + 29 Total time
b Mean =
1 + 2 + 4 + 1 + 1 Total number of participants

(1 × 23) + (2 × 25) + (4 × 26) + (1 × 28) + (1 × 29)
=
9
(23 + 50 + 104 + 28 + 29)
= Median is the value of the data
9 in the middle of a set of data
234 that has been arranged in
= ascending or descending order.
9
= 26 Mean is the result obtained by
dividing the total value of a set of
The mean is 26 minutes. data by the number of the data.
Mean is also known as average.

What is the mode and
range of the data above?


• Explain the meaning of median and mean. 255
8.2.1 • Guide pupils to determine the mode, range, median, and mean
from a different set of data.

3 The bar chart shows Daily Pocket Money Identify
daily pocket money the existing
for 10 pupils. 4 information.
Determine the: Number of pupils 3

a mode. 2
1
b range. 0

c median. RM4 RM5 RM6 RM7
Value of money
d mean.

minimum highest maximum
value frequency value


a RM5 has the highest frequency, which is 4. The mode is RM5.



b Range = maximum value – minimum value
= RM7 – RM4
= RM3
The range is RM3.



c Arrange the data in descending order.
RM7, RM7, RM7, RM6, RM5, RM5, RM5, RM5, RM4, RM4 Calculate the
average of both
two data in the middle data in the middle
RM5 + RM5 to obtain the
Median = median.
2
RM10
= the total value of money
2 d Mean =
= RM5 the number of pupils
= (2 × 4) + (4 × 5) + (1 × 6) + (3 × 7)
The median is RM5.
2 + 4 + 1 + 3
= 8 + 20 + 6 + 21
If 2 other 10
pupils bring 55
RM7, does the = 10
mode change?
Discuss. = 5.5
The mean is RM5.50.

256 • Guide pupils to obtain important information from the bar chart
8.2.1
before finding the range, mode, median, and mean.

Recycled Materials
4 The pie chart shows the mass of Gathered
recycled materials gathered by 16 kg
10 pupils. 10%
State the: 10 kg
20%
a mode. 14 kg
b median. 40% 12 kg
30%
c mean.





a Mass 10 kg 12 kg 14 kg 16 kg
Percentage 20% 30% 40% 10%

20 30 40 10
Number of × 10 × 10 × 10 × 10
pupils 100 100 100 100
= 2 = 3 = 4 = 1
The number of pupils that gathered 14 kg of recycled
materials is the most.

The mode is 14 kg.


b Arrange the data in ascending order.
10, 10, 12, 12, 12, 14, 14, 14, 14, 16

12 kg + 14 kg
Median =
2
= 13 kg

The median is 13 kg.

Total mass 2 other pupils
c Mean = managed to gather
Total of pupils
10 kg of recycled
= (2 × 10) + (3 × 12) + (4 × 14) + (1 × 16) materials. Is the
2 + 3 + 4 + 1 median of the current
= 20 + 36 + 56 + 16 data equal to 12 kg?
Discuss.
10
128
=
10
= 12.8
The mean is 12.8 kg.

257
• Guide pupils to obtain important information from the pie chart
8.2.1
before calculating the range, mode, median, and mean.

1 Class Quiz 1 Quiz 2 Based on the table on the left, what
is the range of the marks of:
Alpha 78 92
a quiz 1?
Beta 82 90
b quiz 2?
Sigma 86 91
Theta 80 88

2 The pictograph shows the time taken Exercise Duration
by a few pupils to exercise in a day. 45 minutes
Determine the: 60 minutes

a range. 75 minutes

b mode. represents 2 pupils

c median.


3 5 Score of 10 Archers The bar chart shows the score of 10
Number of archers 4 a State the: ii median.
archers.


3
mode.
i
2
b Calculate the mean.
1
0
1 2 3 4
Score



4 The pie chart shows the Number of Beyblades
number of Beyblades owned 1 Beyblade
by 10 pupils. Calculate the: 10%

a range.
4 Beyblades 2 Beyblades
b mode.
40% 20%
c mean.
3 Beyblades
30%








• Conduct the ‟Try These” activity in groups. Ask each group to
258 discuss and solve the problems.
8.2.1
• Ask each group to present their calculations and guide the group
that faces problem.

SOLVE THE PROBLEMS
Height in metre

1 The note shows the height of 10 pupils. 1.25, 1.25, 1.25, 1.30,
Find the range, mode, and median of 1.15, 1.30, 1.25, 1.25,
their heights. 1.30, 1.25




Understand the problem Plan the strategy


• There are 10 data of Arrange the data in ascending order.
the pupils’ height.
• Find the range, mode, minimum • Identify the maximum
and median. height range, mode, height

and median.

Solve

1.15, 1.25, 1.25, 1.25, 1.25, 1.25, 1.25, 1.30, 1.30, 1.30



minimum height two data in the middle maximum height


Range = maximum height – minimum height

= 1.30 m – 1.15 m

= 0.15 m
The range is 0.15 m.

The highest frequency is 1.25 m which is 6 pupils.

The mode is 1.25 m.

The median is located at the fifth and the sixth data.
1.25 m + 1.25 m Calculate the
Median = mean of the data.
2
2.5 m
=
2
= 1.25 m
The median is 1.25 m.



• Form a group of 10 pupils and collect the data of the pupils’ height. 259
Then, find the range, mode, median, and mean of the data.
8.3.1
• Conduct a Gallery Walk and discuss the steps of calculation made.

2 There are 10 participants in a Science Science Quiz Marks
quiz. The marks of each participant are 5
shown in the bar chart. Determine the: 4

a range. Number of participants 3
2
b mode. 1

c mean. 0 100 95 Marks
90 85 80




Understand the problem Plan the strategy

• The marks of the 10 participants. • Identify the:

Marks 100 95 90 85 80  maximum mark.
 minimum mark.
Number of 1 4 2 2 1
participants  highest frequency.
• Arrange the data.

• Find the range, mode, and mean. • Calculate the total marks of
the 10 participants.
Solve


a The maximum mark is 100. b The mark of 95 has
The minimum mark is 80. the highest frequency,
Range = 100 – 80 which is 4.
= 20 The mode is 95 mark.


The range is 20.

c The total marks

= (1 × 100) + (4 × 95) + (2 × 90) + (2 × 85) + (1 × 80)
= 100 + 380 + 180 + 170 + 80
= 910

910
Mean =
10
What is the median
= 91 for the data above?

The mean is 91.


260 • Guide pupils to understand the questions by looking for important
8.3.1
information from the bar chart.

3 The pie chart shows the number of Jelly Flavours in a
four jelly flavours in a container. Container
Mango
a What is the percentage of Kiwi 13
kiwi flavour? 20
Grape
b Calculate the mean of each Strawberry 25
jelly flavour. 22







Solution Kiwi Mango Grape Strawberry
20 13 25 22

100%
? %

Total up 20, 13, 25 and 22 to calculate the total number of jellies.

There are 4 jelly flavours.




a Number of kiwi flavour = 20 b Mean = total number of jellies
number of flavours
Total number of jellies
80
= 20 + 13 + 25 + 22 = 4

= 80 = 20
The percentage of kiwi flavour
1
20 25
= × 100%
80
4
1
= 25%







The percentage of kiwi flavour is 25%.

The mean of each flavour is 20.




261
• Vary questions using the above information such as finding the
8.3.1
percentage of other jellies and find the mode.

Solve the following problems.

a The table shows Syira’s savings in 10 days.

Savings RM0.50 RM1 RM1.50
Number of days 2 5 3

Find the range, mode, median, and mean.

b Ben collected data of his friends’ mass. Mass of a Group of Pupils
He presented the data as shown in
the pictograph. Determine the range, 28 kg
mode, median, and mean of his 30 kg
friends’ mass. 32 kg

represents 1 pupil



c The bar chart indicates the marks Environmental Quiz Marks
of Mr Shanker’s pupils for an
Environmental Quiz. 4
i What is the range of their marks? 3

ii Is the median of the marks for the Number of pupils 2
quiz equal to 62? Prove it. 1
iii Calculate the mean of the marks for 0 60 62 68 70
the quiz. Marks



d The pie chart shows the duration of Total Number of Hours
studying, in hours, for 10 pupils in of Studying in a Week
a week. 1 hour
10%
i Determine the mode, median, 7 hours
and mean. 5 hours 30%
20%
ii State the ratio of the number of
6 hours
pupils who study for 7 hours to 40%
the total number of pupils.






262
8.3.1

1 The pie chart shows the favourite food
of 10 pupils.
Favourite Food
a Calculate the number of pupils who
like chicken rice. Biryani rice
Chicken rice
b Find the difference between the 40% 30%
number of pupils who like Fried rice
Biryani rice and chicken rice. 30%

c What is the fraction of pupils who
like fried rice from the total number
of pupils?
2 The following is the volume of water brought by 9 pupils.

,
Wanie 800 m Pauline 750 m , Imah 500 m , Airis 750 m , Prema 500 m ,
Noni 800 m , Jenny 750 m , Anita 500 m , Kogila 500 m

State the: a range. b mode. c median. d mean.

3 The pictograph shows the Jogathon
donation by a few donors. Jogathon Donation
a How many people donated RM4? RM4
b Find the range, mode, median, RM5
and mean.
RM6

c Calculate the percentage of donors who
donated RM4 from the total number of represents 2 people
donors.

4 The bar chart indicates the monthly Monthly Savings
savings of 10 pupils of 5 Gemilang.
a Determine the range, mode, 5
median, and mean. Number of pupils 4

b State the fraction of pupils who 3
saved RM15 from the total number 2
of pupils. 1
0
RM10 RM15 RM20 RM25
Amount of savings




8.1.1, 263
8.2.1, 8.3.1

PAIR WORK ACTIVITY



Tools/Materials dice, A4 papers, pens


Task


1 Throw the dice 10 times.

2 Jot down the number on the dice for each throw on the A4 paper.
For example: 2, 3, 3, 4, 4, 1, 6, 3, 5, 1

3 Construct a table. Number on the dice 1 2 3 4 5 6
For example:
Frequency 2 1 3 2 1 1




4 Find the range, mode, median, and mean.

GROUP ACTIVITY



Tools/ Materials task cards, body mass weighing scale, measuring tape,
papers, pens, MS Excel/MS Word software
Steps
1 The group leader votes for a task as shown below.



Task 1 Task 3

Collect the Collect the data
data of the Task 2 of the body Task 4
height (cm) of Collect the data mass (kg) of 10 Collect the data
10 friends. of daily pocket friends. of the number
money of 10 of siblings of 10
friends. friends.

2 Each group will record the data using suitable software such as MS Excel
or MS Word.
3 Find the range, mode, median, and mean by showing the calculation
in detail.

4 Present the outcome through Gallery Walk.

• Pupils are encouraged to construct a bar chart or pie chart to represent the
264 8.2.1, recorded data using MS Excel or MS Word software.
8.3.1 • The task questions can be varied based on the skills learned such as
interpreting the pie chart and problem-solving involving data management.

A Choose the correct answer.
3
1 Which of the following statements is 9 2 m = cm
false? A 4 B C D
1 2.75 27.5 275 2 750
A hour = 15 minutes 1
4 10 5 km + 0.7 km + 130 m = m
1 5
B day = 12 hours A 6 030 B 6 080
2
1 C 6 330 D 6 580
C year = 3 months 7
4 11 16 m – 850 cm – 3.5 m = cm
1 10
D decade = 10 years A 452 470 722 785
C
D
B
2
2 Which is the correct match? 12 Which of these unit conversions
is true?
A 0.2 hour 3 months A 4.5 kg = 450 g
B 0.25 day 6 minutes B 1.03 kg = 1 030 g
C 0.85 kg = 85 g
C 0.5 year 2 years D 14.2 kg = 1 420 g

1
D 0.1 decade 6 hours 13 4 kg = g

4
D
B
C
3 What is the difference between 5 days A 414 425 4 140 4 250
4
10 hours and 2 days 15 hours? 14 4 kg ÷ 100 = g
A 2 days 5 hours B 2 days 19 hours A 5 B C D
C 3 days 5 hours D 3 days 19 hours 0.48 4.8 48 480
1
1 15 8.5 + 3 + 90 m =
4 8 hours + 3 hours 37 minutes = 2
2 A 12.09 B 12.9
B
A 11 hours 49 minutes 12 hours 7 minutes C 13.09 D 13.9
C 11 hours 57 minutes 12 hours 17 minutes
D
16 Based on the regular pentagon
5 1 century 59 years − 0.12 century = diagram, what is the
A 39 years B 47 years value of angle x?
B
C 147 years D 171 years A 95° 103° x
D
6 What is the duration, in days, from C 108° 110°
7 February until 15 May 2020? 17 3 cm Calculate the perimeter,
A 97 days B 99 days in cm, of the composite
C 10 days D 103 days shape of the two
7 1.5 cm = mm regular hexagons.
A 30 cm B 33 cm
A 0.015 B 0.15 C 15 D 150
C 36 cm D 39 cm
8 180 m = km
265
A 18 B 1.8 C 0.18 D 0.018

18 The diagram shows a 23 The table shows the volume
composite shape of a square of grape juice in three jugs R,
and a right-angled triangle. S, and T.

5 cm Jug Volume
4 cm
R 9 680 m
1
3 cm S 5
2
Calculate the area, in cm , of the 4
diagram above. T 4.5
2
B
2
2
D
A 31 cm 28 cm 24 cm 22 cm 2 What is the total volume of grape
C
1
19 2 hours = juice in jugs R, S, and T?
4 A B
A 125 minutes B 135 minutes 19.43 19.53
C 145 minutes D 160 minutes C 20.43 D 20.53
20 Which of the following statements 24 The picture shows a straight road.
is true?
1
A century = 5 years
2
1
B century = 25 years
5
1
C century = 30 years
4 5 lamp posts were installed in one
1
D century = 10 years line with equal distance between
10 one and another. The distance
21 The duration taken by Zaleha to between the first and the fifth
answer examination questions 3
lamp post is 3 km. Calculate the
Section Duration 5
A 1.2 hours distance, in m, between the first
and the second lamp post.
B 0.7 hour
A 720 m B 760 m
Calculate the difference in the C 900 m D 950 m
duration taken, in minutes, to answer
Section A and Section B. 25 The diagram shows a composite
B
A 20 minutes 30 minutes shape of cuboid M and cube N.
D
C 40 minutes 50 minutes
4 cm
22 The volume of water in the M N
pail shown is the same as
the total volume of water R S
in 20 glasses of equal size. The volume of the composite shape
3
4 Calculate the volume of above is 224 cm . Calculate the
4 length, in cm, of RS.
5 water in each glass.
D
C
B
A 220 m B 230 m A 10 cm 12 cm 14 cm 16 cm
266
C 240 m D 250 m

26 Rohaida’s age is 5.2 decades. Zira’s 30 The diagram shows a pencil

age is 13 years older than Rohaida. case made by Kavi for the
What is Zira’s age? Mathematics project.
A 38 years B 39 years 12 cm

C 65 years D 67 years 8 cm
1 10 cm
27 Puan Norlia bought 3 kg of flour.

2
She used 1.7 kg of flour to make
doughnuts and 580 g to fry chicken. 8 cm 8 cm
What is the mass, in g, of flour left? 8 cm

A 1 022 g B 1 032 g What is the volume, in cm , of the
3
C 1 220 g D 1 320 g pencil case?
3
28 The table shows the volume of juice A 512 cm B 960 cm 3
3
in two containers, X and Y. C 1 024 cm D 1 472 cm
3

Container Volume of mango juice 31 Puan Chin bought two rolls of
3 green and yellow curtains.
X 6
4 The total length of the curtains
Y 2.35 more than container X 1
is 29 m. The length of the
4
What is the volume of mango juice, green curtain is twice the length
in , in container Y? of the yellow curtain. Calculate
A 13.5 9.1 11.45 15.85 the length, in cm, of the yellow
C
B
D
29 The Cartesian plane shows the location curtain.
of two cities, M and N. A 325 cm B 650 cm
y C 975 cm D 980 cm
N
4 32 The bar chart shows the Science

3 marks of 10 pupils in Class 5
2 Hang Tuah.
M Science Marks
1
x 4
O 1 2 3 4 5 3
Calculate the horizontal distance and Number of pupils 2
vertical distance from city M to city N. 1

Horizontal Vertical 0 40 50 60 70 80
distance distance Marks
A 4 units 3 units Which of the following statements
B 3 units 4 units is true about the bar chart above?
C 4 units 2 units A The range is 10.
D 2 units 4 units B The mode is 4.
C The mean is 58.
D The median is 70.
267

B Answer the following questions. b Measure angle y using a
protractor.
1 The picture shows a number of blue
and red balloons.
y



State the value of y.

6 The diagram shows a
State the ratio of: composite shape of a square
a the number of red balloons to the PQRS and a rectangle TUVW.
number of blue balloons. S 15 cm R
b the number of blue balloons to
the total number of red and blue
balloons.
W V
2 Solve these.
1 5 cm
a 8 years + 2 years 7 months
6 P T U Q
= years months 4 cm
a Calculate the perimeter, in cm,
4
b 5.3 decades − 3 decades of the blue region.
5
2
= decades years b Calculate the area, in cm , of
the blue region.
c 0.32 century − 14 years = years
7 The incomplete pictograph shows
a
3 Calculate the product of 3.2 m by 85. the sale of ice creams for four
State the answer in cm. days.
4
b 9 km ÷ 100 = m
5 Monday
a
4 The picture shows the Tuesday
volume of cooking oil in a
bottle. State the volume of Wednesday
the cooking oil in m . Thursday

2
b 6 ÷ 10 = m 3 represents 50 ice creams
5 3 The number of ice creams sold on
4
a
5 Name the polygon based on the Wednesday is 125% of the number
following characteristics:
of ice creams sold on Monday.
7 corners 7 straight sides of equal a Find the difference in the number
length 7 symmetrical axes of ice creams sold between
7 obtuse angles 14 diagonals Tuesday and Thursday.
b Calculate the sale of ice creams
on Wednesday.
268

8 The picture shows a dialogue 10 The picture shows the mass of three
between two pupils. types of fish.

Good morning. When
did your unit’s camping
start? We have been
1
here for 3 days.
4 4
4 kg 4.65 kg 4 080 g
5
a Calculate the total mass, in kg, of
the three types of fish.
b Calculate the difference of mass
between the heaviest fish and the
We started camping on Monday at lightest fish.
10:00 a.m.. Our camping will end on
Wednesday at 12:00 p.m.. 11 Puan Kalsom is 47 years old.
1 7 years later, Naqiu’s age will be
a Convert 3 days to hours.
4 1
b What is the duration of the 3 of Puan Kalsom’s age. What is

School Youth Cadet Corps’ Naqiu’s age now?
camping? 12 The diagram shows the travelling
9 The table shows the number of time by a postman from R to V.
green, yellow, and red marbles S
in a box. The number of blue 1 hour 10 minutes 55 minutes
marbles is not shown. 2 3 U
Colour Number of marbles R T 4 hour
V
Green 108
Yellow 72 He starts from R at 8:20 in the
Red 30 morning. What time will he reach V?
Blue
13 The incomplete table shows the
Complete the pie chart to mass of bags D, E and F.
represent the percentages of
yellow, red, and blue marbles. Bag D E F
1
Mass 3 kg 5.08 kg
5

Green The mass of bag F is 590 g less than
36% the mass of bag D. Calculate:
a the mass, in kg, of bag F.
b the mean mass, in kg, of one bag.

269

14 The Cartesian plane shows the location 16 The table shows the number of
of schools K, L and M. pupils in Class 6 Intan and 6 Emas.
y Number of pupils
Class
6 Boy Girl
6 Emas 14 16
5 6 Intan 12 13
L
4 a Calculate the percentage of boys
M in Class 6 Intan.
3 3
K b of the total pupils in Class 6
2 5 1
Intan and of the total pupils
3
1 in Class 6 Emas participated in a
x camping activity. Complete the
O 1 2 3 4 5 pictograph below to represent

a Tick  for the school that has the number of pupils in Class 6
the same horizontal distance and Intan and Class 6 Emas who
vertical distance from the origin. participated in the camping
activity.

School K School L School M The Number of Pupils in
Class 6 Intan and Class 6 Emas
b State the horizontal distance in the Camping Activity
and vertical distance from 6 Intan
school M to school L.
6 Emas
Horizontal distance units
represents 5 pupils
Vertical distance unit

3 17 The incomplete table shows the
15 Rita’s monthly salary is of her
4 History test marks for 10 pupils.
husband, Suresh. Their total salaries Marks 62 70 84 90

is RM6 300. Number of pupils 1 4 2
a Rita saves 20% of their total a How many pupils scored 70
salaries. What is the total salaries marks?
saved by Rita? b State the mode.
b What is Suresh’s monthly salary?
c Calculate the mean marks for
the 10 pupils. Then, state the
number of pupils who obtained
more than the mean marks.
270

a.m. An abbreviation for ante meridiem (antemeridian) meaning ‟before midday”
or morning.
amount A quantity of something, especially the total of a thing or things in the form of
number, size, value, or area.
angle The space between two intersecting lines, measured in degrees.
area The space occupied by a flat shape or the surface of an object.
ascending order Arrangement of numbers from the smallest to the largest.
axis of symmetry A line that divides a figure or polygon into two equal parts that are reflection
images of each other.
bar chart A chart that displays information or data using bars of the same width
horizontally or vertically displayed on the axes.
bonus An additional pay given to employees on top of their regular earnings.
buying on credit To purchase something with the promise that you will pay in the future.
The amount will be paid later in instalments with interest.
calendar A systematic schedule of the year that is divided into days, weeks, and months.
cash Banknotes or coins paid directly for purchasing goods and using services.
cash payments Paying for goods with money or debit cards without interest being charged.
century 100 years.
compound Addition of interest to the principal sum of a loan or deposit, and the interest
interest accumulated every year.
corner A place or angle where two sides or edges meet. Also known as vertex.
credit card A payment method that allows cardholders to pay for goods and services
without cash.
cube A three-dimensional shape with six square faces, 12 edges, and eight vertices.
cuboid A three-dimensional shape with six surfaces, some or all of which are
rectangular.
date A numbered day in a month, often given with a combination of the name of the
day, the month, and the year.
day 24 hours, from midnight to the midnight of the following day.
decade 10 years.
deposit A payable sum as a first payment on the purchase of goods and services, the
balance being payable later in instalments.
descending order Arrangement of numbers from the largest to the smallest.
dividend Distribution of profits by a corporation to its shareholders for investments in
business or shares.
duration The length of time from the start until the end of an event.
equilateral A triangle with all three sides equal in length and all angles are equal,
triangle measuring 60°.
frequency The number of occurrences of a value, subject, or an event in a given set of data.
horizontal Length measurement between two equivalent points or objects that is parallel to
distance the x-axis.
instalments A sum of money paid as one of several equal payments for something, spread
over an agreed period of time.
interior angle The interior space between two straight lines at the common endpoint.
investment Monetary account for transactions with financial assets and the investor will earn
account profits in the form of dividend and bonus for a certain period.
271

leap year The year that has 366 days including February that has 29 days and it occurs
every four years.
loan A sum of borrowed money that is expected to be paid back.
maximum value The highest value in a set of data.
mean Result of adding all numbers in the set of data and then dividing the number of
values in the set. The mean is also the average of the set of data.
median The middle value or number in a set of data listed in order from the smallest to
the largest or vice versa.
minimum value The lowest value in a set of data.
mixed numbers A whole number and a proper fraction represented together.
mode The value or number which appears most often in a set of data.
p.m. An abbreviation for post meridiem (postmeridian) meaning ‟after midday”
or afternoon. The time from midday to before midnight.
pattern A repetitive order or arrangement of numbers or objects.
perimeter The length of the outer side of a diagram, shape, or area.
pictograph A graph constructed with pictures or symbols to represent a quantity or set of
data.
pie chart A circular chart divided into sections or fractions to represent different values in a
set of data or information.
prime numbers Numbers that can be divided by 1 and by itself.
protractor An instrument to measure angles.
range The difference between the highest and the lowest values in a set of data.
rate A mathematical term that shows the relationship between two quantities or
values of the same ratio.
ratio A comparison of two or more numbers that indicates their sizes in relation to
each other.
rectangle A quadrilateral having four sides, four corners, four right angles, each measuring
90º, and the opposite sides have the same length and are parallel.
regular polygon A two-dimensional enclosed shape made by joining three or more straight lines.
right-angled A triangle with three sides and one right angle, 90º.
triangle
round off A process to determine the value of a number using the nearest place value.
savings Money or thing not spent that is put aside for future use.
savings account The account that enables money to be saved or deposited. The interest for
the balance will be received without maturity date and will be credited to the
account each month.
side One of the lines, straight or curved, which encloses a two-dimensional shape.
simple interest An amount of money earned by a depositor on the money savings in the bank
for a certain time.
square A quadrilateral with four equal straight sides, four right angles, and all angles
are 90º.
vertex The point where two lines meet to form an angle.
vertical distance Length measurement between two equivalent points or objects that is parallel to
the y-axis.
volume The amount of space taken up by a solid, liquid, or gas.




272

BRAIN TEASER PAGE 74
59.2 + 45.97 − 62.17 = 43 (accept any reasonable answers)
TRY IT AGAIN PAGE 88
UNIT 1 WHOLE NUMBERS AND OPERATIONS 5
1
5
1. a. b. 10 2 c. 75 9 d. 92
BRAIN TEASER PAGE 3 7 14 3 8 1
503 142, 520 314, 531 024 and accept any reasonable answers. 2. a. 27 b. c. 35 d. 12
8
BRAIN TEASER PAGE 9 3. a. 20 b. 45 c. 6 5 d. 3 16
2
13
29
13
Y, X, Z, W
BRAIN TEASER PAGE 16 4. Number One Two Three
110 000 decimal decimal decimal
BRAIN TEASER PAGE 18 place places places
975 300, 980 000 a. 6.2471 6.2 6.25 6.247
1 000 000 b. 21.3895 21.4 21.39 21.390
BRAIN TEASER PAGE 19 c. 79.0546 79.1 79.05 79.055
4 975 + 99 721 = 104 696 and accept any reasonable answers. 5. a. 18.119 b. 3.286 c. 310.716 d. 33.042 e. 103.353 f. 75.012
BRAIN TEASER PAGE 22 6. a. 12.388 b. 1 354.7 c. 4 541.45 d. 7.56 e. 1 009.6 f. 45 320
499 312 7. a. 6.453 b. 42.193 c. 0.507 d. 1.45 e. 5.914 f. 341.932
BRAIN TEASER PAGE 26 g. 8.47 h. 10.13 i. 6.732
k = 129 430 8. a. 10 b. 100 c. 1 000 d. 1 000
BRAIN TEASER PAGE 27 9. a. 140% b. 275% c. 470% d. 550%
k = 899 991
21
1
3
7
BRAIN TEASER PAGE 31 10. a. 1 10 b. 2 10 c. 4 100 d. 5 20
4, 128 940 11. a. 25 b. 675
BRAIN TEASER PAGE 37 12. a. 110% b. 120%
1
106 145 13. a. Yes. × 120 = 20 b. i. 1.265 ii. 1.27
6
BRAIN TEASER PAGE 42 c. The length of the rope must exceed 12.192 m (6.096 m × 2) because the rope needs
6 × (RM17 + RM19) = RM216 to go up and down, and to be tied as well. The suggested length of the rope is 13 m.
BRAIN TEASER PAGE 44
(60 – 17) × 3 = 129 UNIT 3 MONEY
TRY IT AGAIN PAGE 60
1. a. one hundred twenty-five thousand and ninety-eight BRAIN TEASER PAGE 95
b. six hundred forty thousand two hundred and three 1 000 × RM792.05 = RM792 050 and accept any reasonable answers.
BRAIN TEASER PAGE 98
c. nine hundred thousand and seventy-one 1 000, RM701 090, RM701 090 ÷ 100 and accept any reasonable answers.
d. 206 081 TRY IT AGAIN PAGE 115
e. 415 007
2. Place Value Digit Value 1. a. RM123 223.45 b. RM112 740.50 c. RM672 310.90 d. RM54 002.90
2. a. RM236 199.30
b. RM397 843.95
a. ones 2 3. a. RM308 937 and RM225 430 b. RM7 084
b. hundreds 700
c. tens 0 4. a. RM492 156 b. RM808 038 c. RM859 597.50
d. thousands 3 000 d. RM901 895.40 e. RM638 250 f. RM730 400
e. ten thousands 80 000 5. a. RM19 341 b. RM52 174 c. RM1 923.40
f. hundred thousands 900 000 d. RM3 124.50 e. RM5 648.49 f. RM467.37
3. a. 90, 2 6. a. 100 b. RM329.45 c. 100 d. RM74 800
b. 500 780 7. a. RM22 011 b. RM45 860.90 c. RM675 321.15 d. RM793 032.95
c. 8 hundred thousands, 6 hundreds, 0 tens 8. a. RM48 982.80 b. RM5 659.65 c. RM695 407.15 d. RM3 831.40
d. 732 005 9. Across: Down:
4. 17, 41, 53, 73, 89 1. compound 3. simple 1. credit 6. cash
5. a. is more than 2. debt 4. savings 5. investment
b. is less than 10. .
c. is less than Cash payment Buying on credit
d. is more than No debt In debt
6. a. 309 050, 309 120, 309 415, 309 827 / 309 827, 309 415, 309 120, 309 050 No interest Interest being charged
b. 901 328, 904 825, 907 995, 910 650 / 910 650, 907 995, 904 825, 901 328 Pay for the exact amount Pay extra than the original amount
7. a. 620 199 or 620 200 and 620 202 until 620 209 Payment by cash or debit card Payment by credit card
b. 850 124 until 870 999 and 871 001 until 899 999 *Accept any other reasonable answers.
8 a. about 60 000 11. a. i. RM94 829 ii. RM175
b. approximately 30 000 g or 30 kg b. i. RM291.50 ii. Yes, the balance of his salary each month is RM1 529.30
9 a. 505 132, 505 136; ascending order in fours after paying for the instalment of education loan.
b. 198 680, 198 380, 198 280; descending order in hundreds c. RM1 062
c. 503 409, 703 409; ascending order in one hundred thousands d. Insufficient amount of money. Encik Mesut’s money shorts of RM800.
d. 849 007, 839 007, 819 007; descending order in ten thousands SELF-TEST PAGE 119
10. a i. 420 000, 400 000 ii. 280 000, 300 000 Section A
iii. 640 000, 600 000 iv. 1 000 000, 1 000 000 1. D 2. B 3. B 4. B 5. D 6. A 7. B 8. B 9. C 10. B 11. C 12. A 13. D
b. 759 609, 770 174, 803 125 and accept any other reasonable answers. 14. D 15. C 16. B 17. A 18. A 19. D 20. C 21. B 22. A 23. C 24. C 25. C 26. D
11. a. 808 069 b. 498 225 c. 492 486 d. 477 838 e. 751 428 f. 570 143 27. A 28. D 29. B 30. D 31. B 32. A 33. D 34. A 35. C
g. 102 094 Section B
12. a. 647 300 b. 500 900 c. 312 000 d. 358 944 e. 365 187 f. 694 194 1. a. hundred thousands b. 400 000 c. 393 000
g. 1 000 h. 1 680 i. 156 240 2. a. 584 279 b. 487 312
13. a. 48 200 b. 7 540 c. 802 d. 168 027 e. 20 489 f. 3 429 3. a. 2 340 b. 600
g. 2 978 remainder 90 h. 204 082 i. 20 795 remainder 3 j. 7 170 remainder 62 4. a. i. RM95 600
14. a. 170 322 b. 560 470 c. 111 491 d. 566 152 ii. RM785 000
15. a. 18 b. 9 c. 249 d. 2 e. 60 f. 480 084 b.
16. a. 122 b. 49 c. 657 d. 8 499 e. 2 079 f. 21 684 (RM16 560 + RM6 060) ÷ 3
g. 31 682 h.18 680 i. 40 j. 3 391 = RM7 540
17. a. 599 821 RM16 560 – RM6 060 ÷ 3
b. i. Pakistan ii. 474 026 iii. 284 982 = RM14 540
c. i. 531 120 ii. 6 639 (RM16 560 – RM6 060) ÷ 3 9
d. y = 12 = RM3 500
e. m = 6 5. a. Savings is money that is kept and used when needed. Investment is money used
f. 15 + (5 × 30) = 165 for a specific business entity that gives profit in the future.
g. 127 b. Simple interest is an amount of money received by anyone who saved money
h. RM750 in a bank within a period of time meanwhile compound interest is an interest
UNIT 2 FRACTIONS, DECIMALS, AND PERCENTAGES received from the savings and interest collected each year.
c. Credit is some money loaned by the financial institution. Debt is a loan needed to
BRAIN TEASER PAGE 72 be paid by someone.
Any decimal numbers between 8.450 to 8.549.
273
123

1
6. a. 60% b. 37 500 c. 4 375 7. a. 6 b. 25% 8. 1.2 kg / 1 5 kg TRY IT AGAIN PAGE 232
1 1. a.
9. a. 2.05 kg / 2 20 kg b. 0.25 m 10. a. RM701 100 b. RM43 700 interior angle
UNIT 4 TIME
BRAIN TEASER PAGE 125 diagonals corner
July, August
BRAIN TEASER PAGE 127
1
12 hour = 5 minutes
BRAIN TEASER PAGE 130 octagon
1 b.
decade = 1 year
10
BRAIN TEASER PAGE 137 straight side
60.0 decades
BRAIN TEASER PAGE 139 symmetrical axes
1 decade, 10 years, 120 months
BRAIN TEASER PAGE 146
0.25
BRAIN TEASER PAGE 155
15 minutes pentagon
BRAIN TEASER PAGE 161 2. a. r = 90 ° b. r = 135 °
6.1 decades – 3.7 decades = 24 years or 6.1 decades – 2.4 decades = 37 years
BRAIN TEASER PAGE 162 3. a. 36 cm b. 28 cm
3
4. a. 17 m 2 b. 7 000 cm 2
5 5. a. 3 224 cm 3 b. 17 496 mm 3
TRY IT AGAIN PAGE 172 6. a. i. 216 cm 3 ii. 1 296 cm 3 iii. No. 1 296 cm 3 − 216 cm 3 = 1 080 cm 3
1. a. 3 days 3 hours b. 52 days c. 54 days The volume of the remaining block is 1 080 cm 3 .
2. a. 12 minutes b. 1 hour 12 minutes c. 20 hours d. 174 hours b. i. 150 m 2 ii. 50 m
e. 35 months f. 1 year 6 months g. 6 decades 9 years h. 137 years
i. 35 decades j. 24 centuries 1 decade k. 5 centuries 75 years l. 823 years UNIT 7 COORDINATES, RATIO, AND PROPORTION
11
3. a. hour b. 0.875 day c. 3 years 7 months d. 24 years BRAIN TEASER PAGE 237
12
e. 10 decades 4 years f. 39 decades g. 782 years h. 1 century 60 years a = 3 and b = 5 or 11
4. 42 minutes, 31 hours, 12 years BRAIN TEASER PAGE 240
5. a. 3 centuries 97 years b. 11 decades 9 years c. 8 centuries 5 decades a. 2 : 1 b. 1 : 7
6. a. i. 60 decades. ii. 5 centuries 99 years b. 41 months c. 3 centuries 10 years TRY IT AGAIN PAGE 248
7. a. 2 years 8 months b. 31 months c. 3 years 9 months 1. a. i. 4 units horizontal and 2 units vertical
5 ii. 2 units horizontal and 5 units vertical
8. a. i. hour ii. 35 minutes iii. 1 hour 5 minutes b. 1 hour 55 minutes iii. 6 units horizontal and 4 units vertical
6
c. i. 57 years ii. Yes. 130 years – 115 years = 15 years d. 2 days 6 hours b. 2 units horizontal and 3 units vertical
e. 14 days f. i. 10 years 6 months ii. 2023 c. 4 units horizontal and 1 unit vertical
g. 3 decades 1 year or 8 decades 5 years 2 a. 2 units horizontal and 1 unit vertical
7 b. 4 units horizontal and 1 unit vertical
h. i. P = century, Q = 12 decades, R = 90 years
10 3. a. 5 : 3 b. 4 : 13 c. 13 : 3
ii. Yes. 7 decades + 12 decades = 19 decades = 1 century 9 decades 4. a. 300 m or 0.3
b. 3 000 g or 3 kg
UNIT 5 LENGTH, MASS, AND VOLUME OF LIQUID c. 1.875 or 1 875 m
5. a. i. 3 units horizontal and 2 units vertical ii. Scout (0,3)
BRAIN TEASER PAGE 179 b. 2 : 3 c. 35 km d. 3 : 4
5
km
8
BRAIN TEASER PAGE 184 UNIT 8 DATA HANDLING
4 BRAIN TEASER PAGE 254
BRAIN TEASER PAGE 190 12, range = 5
1 , 1 or 6 , 5 TRY IT AGAIN PAGE 263
BRAIN TEASER PAGE 194 1. a. 4 b. 1 c. 3
p = 2, q = 5 10

BRAIN TEASER PAGE 198 2. a. 300 m b. 500 m c. 750 m d. 650 m
0.4 kg = 1.2 kg ÷ 3 or 0.3 kg = 1.2 kg ÷ 4 3. a. 6 b. range = RM2, mode = RM4, median = RM4, mean = RM4.60 c. 60%
BRAIN TEASER PAGE 208 4. a. range = RM15, mode = RM15, median = RM17.50, mean = RM18 b. 2
0.02 SELF-TEST PAGE 265 5
TRY IT AGAIN PAGE 213 Section A
1. a. 8 b. 325 c. 9.002 d. 17.03 e. 12.6 f. 45.009 1. D 2. B 3. B 4. B 5. C 6. B 7. C 8. C 9. C 10. A 11. B 12. B
2. a. 19.11 b. 832.1 c. 845 d. 7.055 e. 14.4 f. 46 000 g. 350 h. 7.609 13. D 14. C 15. A 16. C 17. A 18. D 19. B 20. D 21. B 22. C 23. A 24. C
3. a. 616 b. Yes. 135 cm or 1.35 m 25. C 26. C 27. C 28. B 29. A 30. D 31. C 32. C
3
1
7
9
4. a. 4.2/4 5 b. 3 900/3 10 c. 0.6/ d. 8 700 /8 10 Section B
5 1. a. 3 : 4 b. 4 : 7 2. a. 10 years 9 months b. 1 decade 5 years c. 18 years
5. a. 0.65 b. 69 900 c. 6.99 d. 4 800 e. 0.081 f. 28.75 3. a. 27 200 cm b. 98 m 4. a. 3 750 m b. 640 m 5. a. heptagon b. 120 °


6. a. 1 275 b. 11.29 c. 14.15 d. 22 228 e. 86 400 f. 8.092 6. a. 70 cm b. 205 cm 2 7. a. 50 b. 500 8. a. 78 hours b. 2 days 2 hours
7. a. 1 699 g or 1.699 kg b. 0.67 9. a. b. 90
1
8. a. i. 0.85 m ii. 3.1 m b. i. 5 600 m ii. 12.09 km c. Blue Green
4 30%
d. i. 1.25 ii. 4 chocolate cakes @ 5 carrot cakes e. i. 2.5 cm ii. 3 cm 36%
UNIT 6 SPACE Red Yellow
24%
10%
BRAIN TEASER PAGE 220 10. a. 13.53 kg b. 0.72 kg or 720 g 11. 11 years 12. 10:40 a.m.
right-angled triangle 13. a. 2.61 kg b. 3.63 kg
BRAIN TEASER PAGE 226 14. a. School K School L School M

b. Horizontal distance 4 units horizontal
Vertical distance 1 unit vertical
Any combination of cube and cuboid that consists of 59 tiny cubes. The volume of the 15. a. RM1 260 b. RM3 600
composite shapes is 59 cubic units. Accept any other reasonable answers. 16. a. 48%
b.
6 Intan
6 Emas
17. a. 3 persons b. 84 c. 78.8, 6 peoples
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RM24.00 MATHEMATICS YEAR 5
ISBN 978-983-49-2951-0




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