Complete the table. Score Number Number
of hits sentence
1
5 1 6 6×1=6
10 53
10 0
LET’S EXPLORE
Method
Find another two numbers that when multiplied will give
the same answer.
9 1×9 12 4 × 3
3 × 6 18 6 × 4 24
T EACHENRO’TSES • In the HOTs activity, explain that the scores represent the members 2.3.1 93
AB 70 and the number of hits represents the groups. 2.3.2
• Ask pupils to remember the times tables in order to get answers in
the Let’s Explore activity.
• In groups, carry out a scrapbook project of times tables of 0 to 10.
LET’S EXPLORE Get It, Win It!
Materials/Resources Participants
bottle caps (with question 2 pupils
and answer), pouch
3×3 2×7 6×8 9 14 48
Questions Answers
Method
1 Take one question and ask
your friend to answer it.
Check the answer.
2 Your friend keeps the bottle
cap if the answer is correct.
Take turns.
3 The player who collects the
most bottle caps wins.
94 EACHENRO’TSES • Prepare the bottle caps. Write questions and matching answers on 2.3.1
T stickers. Attach the questions to the outside and matching answers 2.3.2
to the inside. Place them all in the pouch.
• Ask pupils to determine their turns before they start playing.
• Emphasise the values of cooperation and honesty in the game.
DIVISION I put two muffins
on each plate.
1 These I now have
5 plates.
muffins are
baked.
10 when divided
into groups of
two gives 5.
0 2 4 6 8 10
10 divided by 2 is 5.
10 divided by 2 is equal to 5. This is the
number
sentence.
10 ÷ 2 = 5
Total number Number of Number of 10 ÷ 2 = 5
of objects objects in groups
each group
EACHENRO’TSES • Guide pupils to understand the concept of division as a collection 2.4.1
AB 71 of objects to represent groups and members using concrete materials.
T 95
• Introduce terms and symbols related to division.
2 6 satay are shared equally among 3 pupils.
How many satay does each pupil get?
6 shared among three
and each gets 2.
6 divided by 3 is 2.
6 divided by 3 is equal to 2.
6÷3 =2
Total number Number of Number of
objects in
of objects groups each group
Can 2 pupils share
6 satay equally? Discuss.
96 EACHENRO’TSES • Guide pupils to understand the division concept as sharing equally 2.4.1
to represent groups and members using concrete materials.
T
• Surf http://www.snappymaths.com/division/earlydiv/interactive/
AB 72 sharing/sharingframe.htm
3 There are 8 pieces I give 4 pieces
of jelly altogether. of jelly to
Wendy.
8 1 time I give another
– 4 1 time 4 pieces to
Selvi.
4
– 4
0
04 8 2
48
–4 –4
8÷4= 2 –8
0
12 pieces of jelly are arranged
in groups of six. How many 12
4
groups do we get? 4
4
– 0 1 time
1 time
–
T EACHENRO’TSES • Guide pupils to understand the concept of division as repeated 2.4.1
AB 73 subtraction using counters and base blocks.
97
• Surf http://www.homeschoolmath.net/teaching/md/division-
multiplication.php
4 There are
18 pens.
Each packet
contains 6
pens.
18 pens
How many do we get when 18 is divided by 6?
0 6 12 18 18 ÷ 6 = 3
What multiplied
by 6 will give 18?
00:9
18 pens Scan
me
9:00
0 6 12 18
18 ÷ 3 = 6 3 × 6 = 18
Complete
× 3 = 18 this.
98 EACHENRO’TSES • Guide pupils to relate division with multiplication through simulation 2.4.1
activities using objects.
T
• Emphasise that division is an inverse of multiplication.
AB 74 • Surf http://www.mathinenglish.com/worksheetview.
php?id=3532&stid=70038
BUILD UP DIVISION TABLES
1
16 ÷ 2 = 8
× 2 = 16
16 lollipops
0 2 4 6 8 10 12 14 16 18
4 ÷ 2 = 2 10 ÷ 2 = 5 14 ÷ 2 = 18 ÷ = 9
2
16 ÷ 4 = 4
× 4 = 16
16 lollipops
0 4 8 12 16 20 24 28 32 36
8 ÷ 4 = 2 20 ÷ 4 = 5 28 ÷ 4 = 32 ÷ = 8
T EACHENRO’TSES • Guide pupils to construct 2 and 4 division tables using picture cards 2.4.1
and number lines.
99
• Discuss the relation between 2 and 4 division tables by counting back
in twos and fours.
3 How many groups
do we get when
the fruits are
divided into threes?
15 ÷ 3 = 5
0 3 6 9 12 15 3 1 5
15 ÷ 3 = 5 –15
0
0 3 6 9 12 15 18 21 24 27
6÷3=2 9÷3=3 12 ÷ 3 = 4
18 ÷ 3 = 6 21 ÷ 3 = 27 ÷ = 9
4
0 5 10 10 ÷ 5 = 2
0 5 10 15 20 25 30 35 40 45
15 ÷ 5 = 3 20 ÷ 5 = 4 30 ÷ 5 =
EACHENRO’TSES • Guide pupils to build 3 and 5 division tables using base blocks and 2.4.1
picture cards.
100 T
• Guide pupils to understand the relation between number lines and
number sentences.
5
54 54 is divided by 6
54 ÷ 6 = 9 9 × 6 = 54
0 6 12 18 24 30 36 42 48 54
6÷6=1 12 ÷ 6 = 2 18 ÷ 6 = 3
24 ÷ 6 = 30 ÷ = 5 36 ÷ = 6
6
Put 49 marbles in
sevens into the holes.
We get 7 holes.
49 ÷ 7 = 7
0 7 14 21 28 35 42 49 56 63
7 ÷ 7 = 1 14 ÷ 7 = 2 21 ÷ 7 = 42 ÷ = 6
EACHENRO’TSES • Guide pupils to divide using objects such as batu seremban and 2.4.1
checkers in groups of 6 and 7.
T 101
• Surf http://www.mathinenglish.com/worksheetview.php?id=860&stid
=70005
7 There are
24 chicken wings
altogether. Each
skewer holds 8
chicken wings.
24 ÷ 8 = 3
0 8 16 24 32 40 48 56 64 72
8 ÷ 8 = 1 16 ÷ 8 = 2 48 ÷ 8 = 72 ÷ = 9
8 27 are grouped in
nines. How many
groups will there be?
1 There are
2 3 groups.
3
27 ÷ 9 = 3
0 9 18 27 36 45 54 63 72 81
18 ÷ 9 = 2 45 ÷ 9 = 5 54 ÷ 9 = 63 ÷ = 7
EACHENRO’TSES • Guide pupils to divide any number by 8 and 9 through repeated 2.4.1
AB 75-79 subtraction.
102 T
• Ask pupils to build division table cards of 8 and 9.
LET’S ANSWER b
Complete these.
a
10 ÷ 5 = 18 ÷ 6 =
c d
0 4 8 12 16 0 9 18 27 36 45
–4 –4 –4 –4 –9 –9 –9 –9 –9
16 ÷ = 45 ÷ =
e 40 ÷ 5 = f 72 ÷ =9
9× = 72
× 5 = 40
g 24 ÷ 6 = h 21 5÷4
÷÷÷ ÷ 9
÷2= 3÷0 7
=== 6 2.4.1
÷ =2
103
T EACHENRO’TSES • Provide more practices in worksheets or question cards.
• Provide a variety of activities such as cross number puzzles to
strengthen pupils’ understanding.
DIVISION INVOLVING 1, 10 AND 0
1 I put fish in ones There are 3 bowls.
into the bowls.
0 1 23 3÷1= 3 Any number
–1 –1 –1 Check divided by 1 equals
3÷1= 3 the number itself.
3 ×1=3
2
30 eggs Each tray is filled with 10 eggs.
There are 3 trays.
30 ÷ 10 =
Method 1 tens ones Group in tens.
We get 3 groups.
Method 2 10 20 30
0
– 10 – 10 – 10
30 ÷ 10 = 3
104 T EACHENRO’TSES • Guide pupils to divide the numbers by 1 through simulation. 2.4.1
2.4.2
• Emphasise that when a number is divided by 1, the answer is the
number itself.
3a 40 ÷ 10 = 4
0 10 20 30 40
10 20 30 40 50 60 70
b
0
10 ÷ 10 = 1 20 ÷ 10 = 2 50 ÷ 10 =
60 ÷ = 6 70 ÷ =
4a There are no
biscuits left
to share with So we do
not get
Rajan. any biscuit.
0÷2= 0
b 0÷4= 0 c 0 ÷ 9 = ?
Check Check
0 ×4=0 ? × 9 = ?
0 divided
by any number
equals 0.
T EACHENRO’TSES • Guide pupils to divide any number by 10 through simulation using 2.4.1
AB 80 objects and picture cards.
2.4.2 105
• Emphasise that when 0 is divided by a number, the answer is 0.
Any number cannot be divided by 0.
5 Division tables
1 2 345
1÷1=1 2÷2=1 3 ÷ 3 = 1 4 ÷ 4 = 1 5 ÷ 5 = 1
2÷1=2 4÷2=2 6 ÷ 3 = 2 8 ÷ 4 = 2 10 ÷ 5 = 2
3÷1=3 6÷2=3 9 ÷ 3 = 3 12 ÷ 4 = 3 15 ÷ 5 = 3
4÷1=4 8÷2=4 12 ÷ 3 = 4 16 ÷ 4 = 4 20 ÷ 5 = 4
5÷1=5 10 ÷ 2 = 5 15 ÷ 3 = 5 20 ÷ 4 = 5 25 ÷ 5 = 5
6÷1=6 12 ÷ 2 = 6 18 ÷ 3 = 6 24 ÷ 4 = 6 30 ÷ 5 = 6
7÷1=7 14 ÷ 2 = 7 21 ÷ 3 = 7 28 ÷ 4 = 7 35 ÷ 5 = 7
8÷1=8 16 ÷ 2 = 8 24 ÷ 3 = 8 32 ÷ 4 = 8 40 ÷ 5 = 8
9÷1=9 18 ÷ 2 = 9 27 ÷ 3 = 9 36 ÷ 4 = 9 45 ÷ 5 = 9
6 divided by 3.
2
10 divided by 5.
EACHENRO’TSES • Guide pupils to build division tables of 1 to 10. 2.4.1
• The animal pictures can be related to the learning of Science in topics
106 T
such as tame and wild animals.
• Surf http://www.teachingideas.co.uk/sites/default/files/
divisontablesjd.pdf
6 7 8 9 10
6 ÷ 6 = 1 7 ÷ 7 = 1 8 ÷ 8 = 1 9 ÷ 9 = 1 10 ÷ 10 = 1
12 ÷ 6 = 2 14 ÷ 7 = 2 16 ÷ 8 = 2 18 ÷ 9 = 2 20 ÷ 10 = 2
18 ÷ 6 = 3 21 ÷ 7 = 3 24 ÷ 8 = 3 27 ÷ 9 = 3 30 ÷ 10 = 3
24 ÷ 6 = 4 28 ÷ 7 = 4 32 ÷ 8 = 4 36 ÷ 9 = 4 40 ÷ 10 = 4
30 ÷ 6 = 5 35 ÷ 7 = 5 40 ÷ 8 = 5 45 ÷ 9 = 5 50 ÷ 10 = 5
36 ÷ 6 = 6 42 ÷ 7 = 6 48 ÷ 8 = 6 54 ÷ 9 = 6 60 ÷ 10 = 6
42 ÷ 6 = 7 49 ÷ 7 = 7 56 ÷ 8 = 7 63 ÷ 9 = 7 70 ÷ 10 = 7
48 ÷ 6 = 8 56 ÷ 7 = 8 64 ÷ 8 = 8 72 ÷ 9 = 8 80 ÷ 10 = 8
54 ÷ 6 = 9 63 ÷ 7 = 9 72 ÷ 8 = 9 81 ÷ 9 = 9 90 ÷ 10 = 9
36 ÷ 4 = 9
LET’S ANSWER
Write three number sentences for the answers in .
a b c
6÷1= 6
30 ÷ 5 = 6
68 9
T EACHENRO’TSES • Conduct a quiz answering division tables spontaneously. 2.4.1
• Provide more practices in worksheets or question cards.
• Surf http://www.fun4thebrain.com/Division/snowyfriend.html 2.4.2 107
ET’S HAVE FUN
L
Riddle me.
T
Could you do me a favour?
Help me to calculate
If you are clever
Divide eight by eight.
Mathematics is fun
Don’t we all agree?
We have only begun
Divide nine by three.
Play a counting game
Everyone can join too
Answer correctly is the aim
Divide ten by two.
The answer is provided 00:9
But hidden from our eyes
What number when divided
by seven equals five?
9:00 Scan
me
EACHENRO’TSES • Guide pupils to solve the riddles. 2.4.1
• Surf http://www.topmarks.co.uk/Flash.aspx?f=sharingv2
108
MORE DIVISION
1 There are 7 cards. The cards are divided equally
between 2 pupils. How many cards does each pupil
get? What is the remainder?
7÷2=
Method 1
remainder
Method 2
3 remainder
27
–6
1
7 ÷ 2 = 3 remainder 1
Each pupil gets 3 cards.
The remainder is 1 card.
T EACHENRO’TSES • Carry out more activities to strengthen pupils’ understanding and 2.4.1
mastery involving division operations with remainders.
109
• Explain that 2 is a divisor and the remainder has to be less than the
divisor.
• Surf http://www.fun4thebrain.com/Division/snowyfriend.html
2 There are 20 mangoes. Pile the mangoes in sixes.
How many piles do we have? How many mangoes
are left?
20 ÷ 6 =
20
Method 1 3 remainder
6 20
– 18 Remember the
2 6 times table.
Method 2 3 x 6 = 18.
Number of piles 1 234 20 – 18 = 2.
Number of 6 12 18 24 The remainder
is 2.
20 ÷ 6 = 3 remainder 2
There are 3 piles of mangoes.
There are 2 mangoes left.
110 EACHENRO’TSES • Guide pupils to divide numbers involving remainders using concrete 2.4.1
materials.
T
• Carry out a quiz that involves division questions using MS PowerPoint.
3 Divide 15 by 4. Method 2
15 ÷ 4 =
15
Method 1 – 4
3 remainder 11 1 time
4 15 – 4
7 1 time
– 12 – 4
3 1 time
3
15 ÷ 4 = 3 remainder 3 remainder
4 Calculate the answer when 43 is divided by 5.
43 ÷ 5 = 43 ÷ 5 =
8 7
5 43 5 43
– 35
– 40
3 remainder 8 remainder
43 ÷ 5 43 ÷ 5
= 8 remainder 3 = 7 remainder 8
Which answer is correct?
Why?
T EACHENRO’TSES • Carry out an activity of dividing two digit numbers by one digit numbers 2.4.1
through simulations or quizzes.
111
• Surf http://www.homeschoolmath.net/worksheets/grade4/PDFs/
Division_Remainders_2to5.pdf
5 47 ÷ 7 = Remember the
Method 7 times table.
6 6 x 7 = 42
7 47
– 42
5 remainder
47 ÷ 7 = 6 remainder 5
6 30 ÷ 8 =
Method 1 Method 2 3 x 8 = 24
3 remainder 30 – 24 = 6.
8 30
The remainder
– 24 is 6. 30 ÷ 8 =
6 3 remainder 6
30 ÷ 8 = 3 remainder 6
There are 20 matchsticks.
A matchstick house
needs 8 matchsticks.
How many houses can
be made? Calculate the
remainder of matchsticks.
112 EACHENRO’TSES • Guide pupils to divide using concrete materials. 2.4.1
• Surf http://www.helpingwithmath.com/printables/worksheets/division/
T
div0301division08.htm
• Surf http://www.helpingwithmath.com/printables/worksheets/division/
div0301division09.htm
7 40 ÷ 9 = Method 2
Method 1 4 x 9 = 36
40 ÷ 9 = 4 remainder 4 4 remainder
9 40
8 – 36
Discuss the remainder 4
in each answer.
9÷9=1
12 ÷ 4 = 3 10÷9=1remainder 1
13÷4=3 remainder 1 11÷ 9 =1remainder
14÷4=3 remainder 12÷9=1 remainder
15÷4=3 remainder 13÷9=1remainder 4
16 ÷ 4 = 4 14÷9= 1remainder
15 ÷ 9 = 1 remainder
16÷9=1remainder 7
17 ÷9=1remainder
18 ÷ 9 = 2
T EACHENRO’TSES • Guide pupils to use times tables to solve the division. 2.4.1
• Emphasise that the remainder must be less than the divisor.
• Surf http://www.homeschoolmath.net/worksheets/grade4/PDFs/ 113
Two_Digit_Division_Remainders.pdf
9 a 56 ÷ 10 = b 84 ÷ 10 =
5 8
10 5 6 10 8 4
– 50 – 80
6 remainder 4 remainder
56 ÷ 10 = 5 remainder 6 84 ÷ 10 = 8 remainder 4
c 99 ÷ 10 = 9 x 10 = 90
10 x 10 = 100
9
10 9 9
– 90
9 remainder
99 ÷ 10 = 9 remainder 9
31 ÷ 10 = 3 remainder 1
62 ÷ 10 = 6 remainder 2
75 ÷ 10 = 7 remainder 5
÷ 10 = 9 remainder 8
114 EACHENRO’TSES • Provide more questions in various forms such as number sentences, 2.4.2
vertical forms, and situations.
T
• Surf http://www.homeschoolmath.net/worksheets/grade4/PDFs/
AB 81-82 Division_Remainders_2to10.pdf
LET’S ANSWER
1 Fill in the blanks. time
a b 1 4 time
7 ÷ 3 = remainder – 6
8
– 6
14 ÷ 6 = remainder
2 Divide these.
a b c
2 15 7 32 8 42
– – –
remainder remainder remainder
d 11 ÷ 4 = e 39 ÷ 5 = f 80 ÷ 9 =
3 Complete these. 11 10 34
Number of wheels
Types of vehicles
Number of vehicles
Wheels remaining
T EACHENRO’TSES • Train pupils to complete the number sentences with remainders 2.4.1 115
involving divisions of 2 to 10. 2.4.2
• Provide more exercises for division and multiplication basic facts
so that pupils can calculate quickly.
• Surf http://www.mathinenglish.com/worksheetview.
php?id=1048&stid=70030
CREATE STORIES
1 There are 3 vases.
3 × 5 = 15 Each vase has 5 flowers.
The total number of
flowers is 15.
2 There are 18 apples. Nina’s
18 ÷ 9 = 2 mother puts 9 apples in
each basket. So, there are
2 baskets of apples.
3 22 crayons are distributed to
3 pupils. Each pupil gets
22 ÷ 3 = 7 remainder 1 7 crayons. The remainder of
the crayons is 1.
4 There are 9 tables. Each
table has 8 guests. There
9 × 8 = 72 are guests altogether.
5
Liew’s father has 83
83 ÷ 10 = 8 remainder 3 mangosteens. He ties the
mangosteens in bunches of tens.
He gets bunches. There are
mangosteens remaining.
116 EACHENRO’TSES • Ask pupils to create a story based on the number sentence. Accept 2.5.1
pupils’ stories based on mathematical logic.
T
AB 83-84
LET’S ANSWER
1 Create stories on multiplication. bicycles.
a There are
Each bicycle has
4 × 2 = 8 wheels. The total number
of wheels is .
b
There are aeroplanes.
Each aeroplane has
children. There are
children altogether.
4 × 3 = 12
2 Create stories on division. 16 balls are
ab divided into 2
baskets.
3 Create stories from the number sentences.
a b
6 × 10 = 60 28 ÷ 7 = 4
c 94 ÷ 10 = 9 remainder 4
EACHENRO’TSES • Guide pupils to create stories based on the picture related to daily 2.5.1
situations and the number sentences.
117
T
SOLVE IT
1 Arif bought 4 packets of 8 biscuits 8 biscuits
biscuits. Each packet has 8 biscuits 8 biscuits
8 biscuits. Calculate the
total number of biscuits.
Method
1 packet has 8 biscuits.
How many biscuits are there in 4 packets?
Number sentence 4 × 8 =
4 Multiply.
×8
3 2
0 8 16 24 32
4 × 8 = 32
The total number of biscuits is 32 .
All the biscuits are shared
equally among 6 friends. How
many biscuits does each get?
118 EACHENRO’TSES • Guide pupils to solve the problems using various strategies such as 2.5.2
drawing diagrams and repeated addition.
T
2 Umar has 12 fish. He puts
4 fish into each bowl. How
many bowls are there
altogether?
Method
Draw a picture.
12 ÷ 4 = Check with a
3 number line.
4 12
– 12
0
0 4 8 12
12 ÷ 4 = 3
There are 3 bowls.
All the fish are put equally into
2 bowls. Calculate the number
of fish in each bowl.
EACHENRO’TSES • Pose a variety of questions to strengthen pupils’ understanding. 2.5.2
• Encourage pupils to use various strategies such as simulation and trial
T 119
and error.
3 50 pupils visit the
National Museum by
van. Each van can carry
10 pupils. How many
vans are needed?
Method 5 x 10 = 50
50 ÷ 10 =
Number of 1 234 5
Number of pupils 10 20 30 40 50
Create a table.
5
10 50
– 50
0
50 ÷ 10 = 5
5 vans are needed.
The 505p u p ilvsarnidedipnearlvuaknatnh.a t can
carry 9 pupils. How many vans
are needed? Discuss.
EACHENRO’TSES • Provide a variety of questions so that pupils can achieve TP6. 2.5.2
• Provide more practices in worksheets and question cards.
120
T
AB 85-86
LET’S ANSWER
Solve the problems.
1 Jasni bought 2
sheets of stickers.
Each sheet has
9 stickers. How many
stickers are there
altogether?
2 Sara arranges 48
photos equally into 6
albums. How many
photos are there in
each album?
3 I have 1 box I have 3 similar
filled with boxes of cakes.
5 cakes. Each box has 5
cakes too.
Moli Raj
Read the conversation above. Calculate the number of
cakes Raj has.
4 Madam Ho has 96 storybooks. She puts the books
equally into 10 bags to be given to the orphans.
How many books are not in the bags?
T EACHENRO’TSES • Provide more questions according to pupils’ capability to strengthen 2.5.2
their understanding.
121
• Surf http://www.mathworksheet4kids.com/word-problems/
division/1by1.pdf
ET’S HAVE FUN
L Materials/Resources Participants
3 pupils
T paper, pencil, dice, and 1 referee
Forward and Backward markers
START 3 × 7 8×5= ×8 200 – 90 700
+ 3 0 0
9 hundreds – 5 tens There are 150 A car fits 50 ÷ 10
buns. Donate 5 people.
Divide 120 buns. There 9 cars fit Miss a
56 biscuits are buns turn.
among 8 pupils. people.
Each will get . left. 308
END + 1 4 2
Congratulations! Method
Move forward
2 boxes. 1. Throw the dice. Move the marker Congratulations!
based on the number on the dice. Move forward
× 6 = 18 2. Answer the questions. If the answer
7 × 1 tens is incorrect, miss a turn. 2 boxes.
100 + 54 3. If the marker stops at the same
spot as before, throw the dice again.
4. The first player who reaches END
is the winner.
Sorry! 12 ÷ 4 637 1 hundreds Find the
Go back to – 5 2 + 4 tens remainder of
9 divided by 2.
START.
6 multiplied
by 8
122 EACHENRO’TSES • Ask pupils to determine their turns before they start playing. 2.1, 2.2
AB 87-88 Encourage pupils to check their calculation among themselves 2.3, 2.4
to make sure the answer is correct and precise. 2.5
• Inculcate the value of cooperation and honesty while playing.
Dengan ini, SAYA BERJANJI akan menjaga buku ini
dengan baik dan bertanggungjawab atas kehilangannya,
serta mengembalikannya kepada pihak sekolah pada
tarikh yang ditetapkan.
Skim Pinjaman Buku Teks
Sekolah
Tahun Darjah Nama Penerima Tarikh
Terima
Nombor Perolehan:
Tarikh Penerimaan:
BUKU INI TIDAK BOLEH DIJUAL
BT082004