Multiplication
and Division
M O DE LS
Multiplication – groups and arrays
When we put objects into rows and columns like this we call it
an array. Arrays can make it easier to work out how many objects
there are in a group. We can
5
use skip counting to help.
2 rows
5
2 rows of 5 is 10
1 How many dots are in the arrays?
a
b
rows of
is
c
rows of
is
rows of
is
d
row of
is
2 How many dots are there?
Did you count every dot or did you use
a different strategy? Explain how you did it.
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Multiplication – repeated addition
One way to describe multiplication is
repeated addition. Look at this array.
5
There are 3 rows. There are 5 dots
in each row. We can think of this as:
5
3 rows
5
5 + 5 + 5 = 15
1 How many dots are in the array?
a
b
rows of
is
rows of
is
+
=
+
=
rows of
is
c
d
rows of
+
+
is
+
=
+
+
+
=
2 How many dogs are
here? Record using
repeated addition.
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Multiplication – the × symbol
We know that …
+ means add or join
− means subtract
= means the same as
What does × mean? It means ‘of’.
2 × 5
We have 2 rows
of
5
Row 1
5 butterflies
Row 2
5 butterflies
2 rows of 5 is 10 altogether. We write this as 2 × 5 = 10
1 How many dots are in the array? Write the number facts.
a
b
3
rows of
×
4
is
rows of
is
=
×
=
c
d
rows of
is
rows of
is
×
=
×
=
2 Colour the right
number of squares
to match the facts.
2 rows of 5 is 10
2 × 5 = 10
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Division – relating multiplication and division
We can use the same arrays to make multiplication and division
facts. This array shows:
3 rows of 4 is 12
12 counters divided into 3 rows is 4
3 × 4 = 12
12 ÷ 3 = 4
AND
1 Use the arrays to finish the number statements and facts.
a 2 rows of 5 is
×
10 divided into 2 rows is
=
÷
b 4 rows of 2 is
c
=
divided into
×
=
×
=
÷
=
÷
d
rows is
=
×
=
÷
=
2 Now you can only see part of the arrays. Can you still finish the facts?
4
a
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×
=
÷
=
b
×
÷
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5
=
=
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Introducing multiplication – 5 times table
1
11
21
31
41
51
61
71
81
91
Here is a skip counting pattern
on a hundred grid. It shows
a counting pattern of 5.
1
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9 10
19 20
29 30
39 40
49 50
59 60
69 70
79 80
89 90
99 100
Finish each pattern by counting in 5s:
+5
a
20
+5
+5
+5
+5
25
+5
b
45
2
2
12
22
32
42
52
62
72
82
92
50
Show × 5 multiplication facts on each number line.
a Finish labelling this number line and then show 5 jumps starting from 0:
0
5
20
This is the same as
30
40
× 5 =
b Finish labelling this number line and then show 7 jumps starting from 0:
0
5
10
This is the same as
35
45
× 5 =
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Multiplication facts – 2 times table
Counting in 2s, will help you know many times table facts.
1
Complete each pattern by counting in 2s:
a
2
4
b
32
34
c
2
12
18
14
18
26
Show how many dots there are in
each array by counting in 2s. Then
write the times table fact below:
c 3 twos
× 2 =
a 6 twos
× 2 =
d 5 twos
× 2 =
8
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b 8 twos
× 2 =
e 4 twos
× 2 =
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f 9 twos
× 2 =
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Multiplication facts – 4 times table
Practise your 4 times table.
1
Write the multiplication fact for each array:
a 3 fours
b 4 fours
× 4 =
d 6 fours
× 4 =
e 7 fours
× 4 =
2
× 4 =
f 9 fours
× 4 =
How many cupcakes are there on:
a 4 plates?
× 4 =
c 7 plates?
× 4 =
10
× 4 =
c 5 fours
D
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b 3 plates?
× 4 =
d 9 plates?
× 4 =
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e 2 plates?
× 4 =
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Multiplication facts – 3 times table
4
Label the number line so it goes up in 3s:
0
5
3
Write two turnaround facts for each array. The first one has been done for you.
a
d
4
×
3
= 12
3
×
4
= 12
×
=
×
=
b
e
×
=
×
=
×
=
×
=
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c
f
×
=
×
=
×
=
×
=
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Multiplication facts – square numbers
A square number is a number multiplied by itself.
These arrays show the first 3 square numbers.
1
1 × 1 = 1
2 × 2 = 4
3 × 3 = 9
1 squared = 1
2 squared = 4
3 squared = 9
Here is another way to show square numbers. Look at the array shown on each
grid and write the square number multiplication:
a
b
×
=
4 squared =
2
c
×
=
×
6 squared =
=
7 squared =
On this grid, shade the largest square number you can:
×
=
squared =
3
Answer these:
a 81 =
18
D
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squared
b 25 =
squared
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c 64 =
squared
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Division – linking multiplication and division facts
Knowing multiplication facts will help with division facts.
6 × 4 = 24
6 rows of 4 is 24.
24 ÷ 4 = 6
1
24 divided into 4 shares is 6.
Describe each of these arrays using one multiplication and one division fact:
× 4 = 12
a
b
× 5 = 30
12 ÷ 4 =
30 ÷ 5 =
× 4 = 16
c
16 ÷ 4 =
2
This time, you are given part of the array. Complete the array and then write one
multiplication and one division fact that matches:
a
b
c
30
D
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×
=
÷
=
×
=
÷
=
×
=
÷
=
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Mental multiplication strategies – doubling and halving
We can change the factors of a multiplication question to make it easier. Look
at 16 × 3. If we halve the larger factor and double the smaller factor, we make
an array on the grid that is the same size. Both arrays have the same amount of
squares. Count the squares, are they equal to 8 × 6?
16
×
Halve
8
1
3
Double
×
6
=
Make these problems easier by using doubling and halving. Shade an array for each:
a
18
×
Halve
3
Double
×
b
14
×
Halve
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=
4
Double
×
20
48
=
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Division – division is repeated subtraction
Division can also be thought of as repeated subtraction.
Look at 30 ÷ 5 = ? This question is asking how many groups of 5 there are in 30.
Jump in 5s along the number line and then count the jumps.
6
−5
5
−5
0
1
4
−5
5
10
3
−5
2
−5
15
So, 30 ÷ 5 = 6
1
−5
20
25
30
Show these division facts as repeated subtraction. First label the number lines and
then show the jumps.
a 36 ÷ 6 =
0
36
b 21 ÷ 3 =
0
2
21
Write a division fact to match these number lines. Show the jumps.
a
÷
0
b
4
÷
0
24
=
8
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16
20
24
28
=
8
E
12
16
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Division – linking multiplication and division facts
Knowing multiplication facts will help with division facts. This is because they
are opposites. Look at how we can describe this array:
1
6 groups of 4 is 24.
4 × 6 = 24
4 groups of 6 is 24.
24 ÷ 4 = 6
24 divided into 4 shares is 6.
24 ÷ 6 = 4
24 divided into 6 shares is 4.
Describe each of these arrays using two multiplication and two division facts:
a
c
2
6 × 4 = 24
×
=
×
b
×
=
=
×
=
÷
=
÷
=
÷
=
÷
=
×
=
×
=
×
=
×
=
÷
=
÷
=
÷
=
÷
=
d
Draw an array of 6 rows of 3 then describe it with multiplication and division facts.
×
=
×
=
÷
=
÷
=
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This is also called
a fact family.
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