Multiplication
Here are some words your child might use or come
across when multiplying.
Methods we use for multiplying!
Drawing pictures
Counting in 2s
Counting in 5s
Counting in 10s
Questions to practise e.g.
There are five sweets in one bag. How many sweets are there in 3
bags?
Repeated Addition
5 x 3 is the same as 5+5+5
This can be shown on a number line:
5 x 3 = 15
+5
+5
+5
____________________________________________________________
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Multiplying in Any Order
e.g. Understanding 3 x 4 is the same as 4 x 3
We can show this works by using a number line.
Example 1:
5 x 3 = 15 is the same as 3 x 5 = 15
+5
+5
+5
____________________________________________________________
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
+3
+3
+3
+3
Example 2:
2 x 6 = 12 is the same as 6 x 2 = 12
+2
+2
+2
+2
+2
+2
_________________________________________________
0
1
2
3
4
5
6
7
8
9 10 11 12
+6
+6
+3
Arrays
(When objects are arranged in rows and columns)
Any multiplication can be drawn as an array:
Example 1:
Example 2:
5 x 3 = 15
6 x 2 = 12
2 x 6 = 12
3 x 5 = 15
Learning Times Tables
It is vital that as children begin to understand the steps
above that they start to learn their times tables.
If they do not learn these by heart it will make it very
difficult for the children to complete the methods we will
move onto next.
This means being able to:
Recite e.g:
1 x 2 = 2
2 x 2 = 4
3 x 2 = 6
4 x 2 = 6
5 x 2 = 10
6 x 2 = 12
7 x 2 = 14
8 x 2 = 16
9 x 2 = 18
10 x 2 = 20
11 x 2 = 22
12 x 2 = 24
Quick recall e.g:
5 x 2 = ?
AND
11 x 2 = ?
Partitioning
(Multiplying the tens and units of the start number separately)
As a number sentence:
14 x 5 = 70
This can be shown as an array:
14 x 5 = (10 x 5) + (4 x 5)
= 50 + 20
= 70
10
5
Grid Method for TU X U
(Continues Partitioning)
Example 1:
23 x 8 =
Step 1: (partition the start
number and multiply each part)
X
20
3
8
160
24
Step 2: (add the two answers)
Example 2:
58 x 7 = 406
Step 1: (partition the start
number and multiply each part)
X
50
8
7
350
56
Step 2: (add the two answers)
4
Grid Method for HTU X U
357 x 6 = 2142
X
300
50
7
6
1800
300
42
Grid Method for TU X TU
72 x 38 = 2736
X
70
2
30
2100
60
8
560
16
Grid Method for ThHTU X U
4356 x 8 = 34848
X
4000
300
50
6
8
32000
2400
400
48
Short Multiplication TU X U
(used for multiplying by 1 digit numbers)
14 x 8 = 112
(For ALL Short Multiplication work from right to
left)
This is how children will set
this method out. (The
pictures below shows the
steps of what is happening.)
Step 1:
Step 2:
Step 3:
Start with the units
column e.g.
4 x 8 = 32
The 3 tens in 32 are
carried to the next
column.
Move to the next column
(right to left) e.g.
1x8=8
However, we already have
3 in this column from step
1 so we need to add
these together i.e.
8 + 3 = 11
More examples of Short Multiplication
(used for multiplying by 1 digit numbers)
Example 1:
Example 2:
Example 3:
Short Multiplication involving decimals
(used for multiplying by 1 digit numbers)
Example 1:
35.6 x 8 = 284.8
Step 1:
Calculate as if there are no
decimal places i.e.
Example 2:
29.43 x 3 = 88.29
Step 1:
Calculate as if there are no
decimal places i.e.
Step 2:
Put the decimal places into the
answer e.g.
In this question there was one
decimal place in 35.6 so we need
to put 1 decimal place into the
answer i.e. 2848 becomes 284.8
Step 2:
Put the decimal places into the
answer e.g.
In this question there were two
decimal places in 29.43 so we need
to put 2 decimal places into the
answer i.e. 8829 becomes 88.29
Long Multiplication
(used for multiplying by numbers with more than 1 digit)
Example 1:
72 x 38 = 2736
(For ALL Long Multiplication work from right to
left)
This is how children will set
this method out. (The
pictures below shows the
steps of what is happening.)
Step 1:
Start with the units
column e.g. 72 x 8 = 576
Follow the same process
as for short
multiplication. (Do not
worry about the 3 in the
tens column at this
stage.)
Example 2:
Step 2:
Move to the next column
(right to left) e.g.
72 x 3 = 216
We put a 0 in the units
column because it is
actually 72 x 30 which is
ten times bigger than
72 x 3.
Example 3:
Step 3:
We then add the two
answers together.
Example 4:
It is very important that children remember that when they add their working out
together they do not add any of the small digits used for carrying in their
multiplication. However, they must include any digits involved in carrying for
addition.
Here the small digits used for carrying in addition have been coloured red to show
this.
Long Multiplication involving Decimals
(used for multiplying by numbers with more than 1 digit)
Example 1:
3.57 x 24 = 85.68
Step 1:
Calculate as if there are no
decimal places i.e.
Example 2:
1 decimal place in 6.8 so 1
decimal place in the
answer - 29620.8
Step 2:
Put the decimal places into the
answer e.g.
In this question there were two
decimal places in 3.57 so we need
to put 2 decimal places into the
answer i.e. 8568 becomes 85.68
Example 3:
Example 4:
2 decimal places in 9.43
AND 1 decimal place in
25.3 which is 3 decimal
places altogether.
2 decimal places in 243.56
AND 3 decimal places in
7.253
which is 5 decimal places
altogether.
So we need 3 decimal
places in the answer 238.579
So we need 5 decimal
places in the answer 1766.54068