Mathematics Year 3

4 1 – 1 = 11 5 1 – 1 =
2 4 4 8
22
1 – 1 = 2 – 1 1111 1 – 1 = 2 – 1
2 4 4 4 4 8 8 8
4444
= 1 11111111 = 1
4 8
88888888

On the

1 1 1 fraction 1 1 1
2 4 4 4 8 8
– = chart, – =

1 = 2
2 4

and

1 = 2 .
4 8

6 5 – 1 = 5
6 3 6

5 – 1 = 5 – 1 ×2 Simplify the
6 3 6 3×2 answer.

= 5 – 2
6 6

= 3 ÷ 3
6 ÷ 3

= 1
2

5 – 1 = 1
6 3 2

Can you subtract 1 from 1 ?
2 6
Discuss.
Saiz sebenar
TEACHNOETRE’SS • Emphasise that to subtract a fraction, the denominator must be of equal value. 3.1.6 (ii)
94 • Use 2, 4, 6, 8 and 10 times tables to help pupils determine the equivalent 3.1.6 (iii)
3.1.6 (v)
fractions.

7 7 – 1 = 8 2 – 5 =
10 2 3 9

7 – 1 = 7 – 1 × 5 2 – 5 = 2 × 2 – 5
10 2 10 2 × 5 3 9 3 × 2 9

= 7– 5 = – 5
10 10 9

= 2 ÷ 2 =
10 ÷ 2

= 1 2 – 5 =
5 3 9

7 – 1 = 1
10 2 5

9 9 – = 3 10 – 2 = 2
10 10 5 5

9 – 6 = 3 4 – 2 = 2
10 10 10 5 5 5

9– 6=3 4 – 2 = 2
10 10 10 5 5 5

LET’S TRY

Solve these.

a 7 – 5 = b 5 – 1 = c 2 – 2 =
8 8 6 6 3 9

d 1 – 3 = e 4 – = 1 f –7=1
2 10 5 5 10 10

Saiz sebenar

AB TEACHNOETRE’SS • Guide pupils to multiply correctly to find the equivalent fractions. 3.1.6
62 • Guide pupils to subtract fractions of the same denominator involving
an unknown. 95

RECOGNISE FRACTIONS OF HUNDREDTHS
AND DECIMALS

1 How beautiful! The kitchen There are 100 tiles,
16 of them are blue.
tiles are so colourful.

a 16 of 100 is sixteen hundredths.
Sixteen hundredths is written as 16 .
100

16 in decimal is 0.16. It is read as
100 zero point one six.

fraction of 16 0.16 decimal
hundredths 100

decimal point

b 4 of 100 tiles are pink. 4
4 of 100 is 4 . 100
100

4 in decimal is 0.04. 0.040.04
100

ones tenths hundredths zero point
four zero four
Saiz sebenar 00 4 hundredths

96 AB63 TEACHNOETRE’SS • Ask pupils to state the fractions and the decimals of the white and the green 3.1.4
tiles in the diagram above. 3.2.1

• Guide pupils to read out decimal numbers correctly according to their place
value using word cards and number cards.

21 Zero point zero eight. I coloured
23 of 100
I coloured 8 of 100 squares.
squares.

31 This is our zero point
seven two
decimal project.

Correct the
incorrect.

zero point sixty

41 44 of 100 What are the decimal

squares are
red. and hundredths fraction
of the white squares?

44 = 0.44
100

Saiz sebenar

TEACHNOETRE’SS • Provide sufficient paper or hundred square grids for colouring activities 3.2.2 97
to represent various decimal numbers. 3.4.1

5 Write the fractions and decimals of the coloured parts.

0.45 = 45 58 = 0.58 10 = 1.0
100 100 100

What is incorrect? Correct it.

How many squares
should be coloured?

MMIINNDD 0.9
CCHHAALLLLEENNGGEE

LET’S TRY

1 Match the correct word cards to the numeral cards, and read
them out.

zero point 9 sixty-seven 0.05
one eight 100 hundredths

nine 0.18 zero point 67
hundredths zero five 100

2 Colour the decimal parts and fractions on hundred square grids.

a 3 = 0.03 b 24 = 0.24 c 0.65 = 65
100 100 100
Saiz sebenar
TEACHNOETRE’SS • Provide sufficient hundred square grids to pupils to represent decimals 3.1.4
98 AB64 and fractions of hundredths. 3.2.1
• Surf http://www.visnos.com/demos/percentage-fraction-decimals-grid 3.2.2
3.4.1

COMPARE DECIMALS

1 Which mass The red squares
are more.
is heavier,
0.45 kg 0.2 kg

or 0.2 kg?

ones tenths hundredths 0.45 is larger than 0.2

0 45 0.45 kg is more
0 20 than 0.2 kg.

Compare the tenths digits.
4 is larger than 2.

2 Which is smaller, 0.03 or 0.07?
value becoming larger

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
value becoming smaller

0.03 comes before 0.07

0.03 is smaller than 0.07

LET’S TRY

Which decimal is larger? Explain.

a 0.1 0.11 b 0.52 0.25 c 0.08 0.8

Saiz sebenar

AB65 TEACHNOETRE’SS • Surf www.superteacherworksheets.com/place-value/orfering-cards-set 3.2.3
• Use common objects in daily life for the activity of comparing decimals.
99
BA 2

ADDITION OF DECIMALS

1 What is the total height of this shelf?
0.3 m 0.3 m + 0.5 m =
m

0.5 m Method 1 Colour 3 of
0.3 + 0.5 = 0.8 the 10 parts.

Colour
another
5 parts.

Arrange the Method 2
digits. Make
sure that the ones tenths
decimal point
is aligned. 0 3
+0 5
Add the tenths
0 8

0.3 m + 0.5 m= 0.8 m
The total height of the shelf is 0.8 m.

2 Add both volumes.
0.25 ℓ + 0.4 ℓ = ℓ
0.25 ℓ 0.4 ℓ
Method 1 0.4 = 0.40 Method 2

Add the blue and 025
the red squares. +0 4 0

065

0.25 0.40 0.25 ℓ + 0.4 ℓ = 0.65 ℓ

Saiz sebenar The total volume is 0.65 ℓ.

TEACHNOETRE’SS • Emphasise that when pupils write decimal numbers, the decimal points 3.2.4
must be aligned before adding any numbers.
100

3 Add 0.45 and 0.36. + 0.10 + 0.10 + 0.06 0.36
0.45 + 0.36 =
0.60 0.70 0.80 0.90
+ 0.10
0.81
Method 1
0.40 0.50

0.45

Method 2 1

045
+0 3 6

081

0.45 + 0.36 = 0.81

4 0.09 m + m = 0.87 m Subtract 0.09 from 0.87.

0.09 m ? 7 17

0.87 m 0.87
– 0.09

0.78

0.09 m + 0.78 m = 0.87 m

LET’S TRY b 0.74 c 0.58
+0.16 +.
Solve these.
a 0 . 2 kg 0.90

+ 0 . 6 9 kg

kg

d 0.03 + 0.5 = e 0.8 + = 0.99

Saiz sebenar

AB66 TEACHNOETRE’SS • Remind pupils that addition of decimal numbers is the same as addition of 3.2.4
whole numbers.
101
• Provide questions on addition of decimal numbers involving an unknown
for reinforcement.

SUBTRACTION OF DECIMALS

1 0.7 m

0.2 m

What is the length of the wooden
plank after it is cut?

0.7 m – 0.2 m = m

Method 1 Method 2 Use a number line.

ones tenths 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 7 – 0.1 – 0.1
–0 2

0 5

Subtract the tenths
7 tenths – 2 tenths = 5 tenths

0.7 m – 0.2 m = 0.5 m
The remaining part of the wooden plank is 0.5 m.

2 Subtract 0.28 ℓ from 0.54 ℓ.

0.54 ℓ – 0.28 ℓ = ℓ

4 14

0.54
– 0.28

0.26

Saiz sebenar 0.54 ℓ – 0.28 ℓ = 0.26 ℓ

TEACHNOETRE’SS • Emphasise that to subtract decimal numbers, the decimal points must be 3.2.5
aligned.
102
• Remind pupils that subtraction of decimal numbers is the same as

subtraction of whole numbers.

3 Calculate the difference between 0.13 kg and 0.6 kg.

0.6 kg – 0.13 kg = kg

0.6 = 0.60 5 10 We cannot subtract
3 hundredths from
0.60
– 0. 13 0 hundredths.
Therefore, regroup
0.47 from the tenths to

the hundredths.

0.6 kg – 0.13 kg = 0.47 kg
The difference between 0.13 kg and 0.6 kg is 0.47 kg.

4 0.95 – = 0.52 Check the answer.
0.43 + 0.52 = 0.95
0.95
– 0.52

0. 43

0.95 – 0.43 = 0.52

LET’S TRY b 0.7 c 0.59
– 0.34 –.
Solve these.
0. 43
a 0.39m
– 0.28m
m

d 0.82 mℓ – 0.63 m ℓ = m ℓ e 0.93 – = 0.4

Saiz sebenar

AB67 TEACHNOETRE’SS • Encourage pupils to check their answers using addition. 3.2.5 103
• Surf http://www.k5learning.com/free-math-worksheets/third-grade-3/

fractions-and-decimals

RECOGNISE PERCENTAGES

1 Did you know?

Did you

know?

More than sixty Jellyfish has more
percent of our water in its body.
body is water! Ninety-five percent.

2a 26 of 100 is 26 .

26 in 100 is written as 26%.
100 percentage

We read it as twenty-six percent.

This is the percentage symbol.

b 74 of 100 is 74 .
100
74 in percentage is written as .
100
We read it as .

88 91 Say your test
100 100 marks in percentages.

Maylee Danial
3 Aman
Saiz sebenar3 Aman
• Ask pupils to provide examples of percentage in daily life.
104 AB TEACHNOETRE’SS • Surf https://www.teachervision.com/graph-chart-0/blank-100-grid 3.1.4
68 to print hundred square grids for pupils to practise stating percentages 3.3.1
3.3.2
based on the number of coloured squares. 3.4.2

3 Write the percentages and fractions of hundredths.

Sixty-four 15% is 15 .
percent. 100

64 = 64% 15% = 15
100 100

4 35%
forty-seven
percent

Write the percentages above.

5 42% pupils of I coloured 42
42% 3 Alpha are
girls. State the squares green. 42 in decimal
percentage in 100
42% is equal
decimal.
to 42 . is 0.42.
100

0.42

42% = 0.42

Saiz sebenar

6A9B-70 TEACHNOETRE’SS • Provide sufficient hundred square grids to represent various fractions 3.3.3 105
of hundredths and percentages. 3.3.4
• Surf https://www.extendoffice.com/documents/excel/2419-excel-grid- 3.4.2
3.4.3
paper-template.html

6 8% =

8% = 8 ones tenths hundredths
100
8 008
100 is 8 hundredths.

8 hundredths in decimal is 0.08.

8% = 0.08

7 0.69 = MMIINNDD Which decimals
0.65 0.66 0.67 0.68 0.69 CCHHAALLLLEENNGGEE have equal
percentage
65 66 67 68 69 values? Explain.
100 100 100 100 100
0.4 0.04 0.40
0.69 = 69%

LET’S TRY

1 Say and write the percentages in words.

a 6% b 27% c 30% d 54%

2 Write the fractions a b c
of hundredths and b 3% c 19%

percentages of the

coloured parts.

3 State in decimals. a 25%

4 State in percentages. a 0.42 b 0.07 c 0.86

5 Colour the hundred square grids.

a 9% b 71% c 40 d 13
100 100
Saiz sebenar

106 AB TEACHNOETRE’SS • Surf http://www.mathsisfun.com/converting-decimals-percents.html 3.3
71 for more exercises on the relationship between percentages and decimals 3.4.2
3.4.3
and vice versa.

FUN PROJECT

Tools/Materials MS Word software

Method 2a b FUN PROJECT
1

Launch MS Word. Click Insert Type 10 for rows and columns.
and choose Table. Then, click Select AutoFit to Contents. Click OK.
Insert Table.

3 4 FUN PROJECT

Create your
own design.

Select 40 square grids. Type fraction, decimal,
Select a colour and click. and percentage for the
coloured square grid.
Saiz sebenar

TEACHNOETRE’SS • Guide pupils to type fractions in their Fun Project. 3.1.4 107
• Carry out activities individually or in pairs. Print pupils’ work and 3.2.2
3.3.3
display them at the mathematics corner.

CREATE STORIES 1 kg + 1 kg = 5 kg
2 8 8
1

Devi’s father bakes a fruit cake. He adds

1 kg of flour to 1 kg of mixed dried
2 8
5
fruits. The total mass is 8 kg.

2 9 m– 3 m = 3 m
10 5 10

Li Yin has 9 m of ribbon. She uses
10
3
5 m to decorate a gift box. The length

of the ribbon left is m.

3 0.6 ℓ – 0.25 ℓ = 0.35 ℓ

0.6 ℓ 0.25 ℓ A bottle contains 0.6 ℓ of mineral
water. Another bottle has 0.25 ℓ
Saiz sebenar of mineral water. The difference in
volume of water for the two bottles
is ℓ.

108 TEACHNOETRE’SS • Assist pupils to create stories using appropriate terms as keywords. 3.5.1
Accept any stories that are related to logical mathematics.

4 95% 95
100
95% =

Jason gets 95%

in a Mathematics test.

Jason His marks in fraction is .

3 Aman

5 0.5 cm 0.5 cm + 0.4 cm = 0.9 cm

The length of the green ribbon
0.4 cm is 0.5 cm more than the red

ribbon. The length of the blue

ribbon is 0.4 cm more than the
green ribbon. So, the length of the
0.9 cm blue ribbon is cm more than
the red ribbon.

LET’S TRY

Create stories based on number sentences.

a 2 m+ 1 m= 7 m b 1 ℓ– 3 ℓ = 1 ℓ
3 9 9 2 10 5

c 0.7 mℓ + 0.05 mℓ = 0.75 mℓ d 0.9 kg – 0.38 kg = 0.52 kg

e 63% = 63 f 54 = 54%
100 100

AB TEACHNOETRE’SS • Provide number sentences involving addition of fractions, subtraction of Saiz sebenar
72 fractions, decimals, and percentages for creating stories.
3.5.1

109

SOLVE THE PROBLEMS

1 Danny’s sister is making spaghetti sauce.

She adds 1 kg of mushrooms and 1 kg of
4 2

minced beef. What is the mass of the mixed

ingredients?

Given 1 kg of mushrooms
4

1 kg of minced beef
2

Find mass of the mixed ingredients

Method 1 kg + 1 kg = kg
4 2

1 = 2 1
2 4 4

1
2

I draw a diagram.

It is 3 in tota3l.
44

1 + 1×2 = 1 + 2 Check.
4 2×2 4 4

= 3
4

1 kg + 1 kg = 3 kg
4 2 4

The mass of the mixed ingredients is 3 kg.
4
Saiz sebenar

110 TEACHNOETRE’SS • Prepare paper strips and a fraction chart for simulation activities. Carry 3.5.2
out group activities to solve problems. Provide questions such as the

above to reinforce pupils’ understanding.

2 Eslhi ewnaenetsdtso190mamk.eHaotwabmleucclohthm. oSrheeleonnglythhoafsc25lothmdoofecslosthhebut
need to buy?

Given she has 2 m of cloth Find length of cloth
5 to buy

she needs 9 m of cloth
10

Method 9 m – 2 m=
10 5

Find an equivalent fraction for 2 .
5

2×2= 4 0 1 2 3 456 7 89
5 × 2 10 10 10 10 10 10 10 10 10 10

– 4
10

Simplify the 5 ÷ 5 = 1
10 ÷ 5 2
answer 5 .
10

Check your
answer using

addition.

9 m – 2 m= 1 m
10 5 2

Eli needs to buy 1 m of cloth.
2
Saiz sebenar

TEACHNOETRE’SS • Use fraction chart and refresh pupils’ memory on how to find equivalent 3.5.2
fractions.
111
• Encourage pupils to check their answers using reverse operation, such as
checking addition by subtraction and vice versa.

3 Haqim caught 0.9 kg of lobsters. Suresh
caught 0.55 kg of lobsters. What is the
difference between the two masses of lobsters?

Given Haqim’s lobsters is 0.9 kg Find the difference
Suresh’s lobsters is 0.55 kg between the
masses of
Method 0.9 kg – 0.55 kg = lobsters

Draw a 0.35 8 10
diagram. 0.55
0.90
– 0.55

0.35

0.9 kg – 0.55 kg = 0.35 kg
The difference in mass is 0.35 kg.

4 The length of a bracelet is 0.17 m. The length of a necklace
is 0.38 m more than the bracelet. How long is the necklace?

Method Length of bracelet 0.17 m 0.38 m more
Length of necklace

0.17 m + 0.38 m = ?

1 Check 4 15

0.1 7 0.55
+0.3 8 – 0.38

0.55 0. 1 7

0.17 m + 0.38 m = 0.55 m

Saiz sebenar The length of the necklace is 0.55 m.

112 7A3B-74 TEACHNOETRE’SS • Use simulation strategies using concrete materials so that pupils can 3.5.2
understand problems and solve them.

• Train pupils to write number sentences based on fractions and decimals
story cards.

5 There are 100 pupils in the Chess Club. 45 pupils are girls.
State the percentage of the boys.

Method First, calculate
Write the information in a table. the number of boys.

Pupil Number 9
Girl 45 010 10
Boy
100 100
Total
– 45

55

55 boys of 100 pupils is 55 .
100

55 = 55%
100

The percentage of boys is 55%.

LET’S TRY

Solve the problems.
1
a In a garden, 4 of the area is covered with flowering plants.
non-flowering plants.
3 of the area is covered with
8

What is the total area covered with plants?

b There are 2 packets of sweets with the mass of 0.17 kg and

0.08 kg. What is the difference in mass between the two

packets of sweets?

Let’s drink milk for

c A cup of milk contains 30% of strong bones and

calcium. State 30% in decimal. teeth!

Saiz sebenar

AB TEACHNOETRE’SS • Prepare various problem solving questions of fractions, decimals, and 3.5.2
74 percentages. Ask pupils to solve them in groups using methods such
as bar model to reinforce pupils’ understanding. 113

FUN TIME

MATCH AND WIN

Tools/Materials 8 fraction cards, 8 percentage cards,
8 decimal cards

Participants 3 players and a referee

Examples
of cards

Method

1 The referee distributes the cards equally
among 3 players.

2 Each player aims to collect all 3 sets
of matching cards and submit them
to the referee.
3 The referee will then record the number
of matching cards from each player.

4 The first player takes one of the remaining
cards from the second player. If the

player has 3 matching cards, submit them

to the referee.
5 The second player then takes a card from

the third player.
6 Continue playing until all matching cards

are collected.
7 The player with the most number of

matching cards wins.

Saiz sebenar

114 7A5B-76 TEACHNOETRE’SS • Ask pupils to determine their turns. The referee shuffles a deck of 24 cards 3.4.1
consisting of fractions, decimals, and percentages. 3.4.2
3.4.3
• Instil values such as cooperation, honesty, and tolerance while playing.

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