Multiplication
Developing Informal and Formal Written Methods
The children will progress through these steps at their own pace. The children will be taught
the methods that are appropriate for the level they are working on. They will progress on to
the next step when they are confident in their own ability. Some children may find advanced
steps easier to understand whilst others will prefer to use an earlier step. The children are
encouraged to use the method they are confident with and produce correct answers from.
Step 1
The children will first be introduced to multiplication through repeated addition. They will be
asked to find the answer to, for example, 2 + 2 + 2 + 2. They will be taught to do this by using
practical apparatus that they can sort into the correct groups, or by using informal jottings.
This might also be linked to stories and rhymes (e.g. Noah’s Ark).
E.g. 2 + 2 + 2 + 2 = 8
Step 2
The children will then be introduced to the multiplication sign (x) and the vocabulary
associated with multiplication e.g. lots of, groups of, times, multiply, multiplied by etc.
Children will continue to use informal jottings to find the correct answer to a multiplication
question. The first digit in the sum shows the children how many ‘groups’ they need to draw,
the second digit shows the children how many objects need to be in each group. To find the
answer, the children are required to count how many objects they have drawn altogether.
E.g. 3 x 4 = 12
Step 3
Children will then progress on to using a number line to find the answer to multiplication
questions. They will start on 0. The first number in the multiplication sum shows how many
‘jumps’ will need to be made. The second number show how large each jump needs to be
(the times tables being used).
E.g. 6 x 3
1x3
1x3
1x3
1x3
1x3
1x3
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Answer: 6 x 3 = 18
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TPPS Multiplication
Step 4
Use the ‘grid method’ to multiply a 3 digit number by a single digit number, by partitioning
the number.
e.g. 346 x 9
x
300
40
6
9
2700
360
54
Side jottings are encouraged.
For example,
3 x 9 = 27
30 x 9 = 270
300 x 9 = 2700
4 x 9 = 36
40 x 9 = 360
Now add the totals within the grid.
2700 + 360 + 54. The method chosen for this addition will be the child’s choice.
346 x 9 = 3114
Step 5
Use the grid method to multiply a 2 digit number by a 2 digit number by partitioning both
numbers. Once again, we encourage the children to use side jottings.
e.g. 72 x 38
x
70
2
30
2100
60
8
560
16
7 x 3 = 21
70 x 3= 210
70 x 30 = 2100
2x3=6
2 x 30 = 60
7 x 8 = 56
70 x 8 = 560
Add the totals within the grid: 2100 + 60 + 560 + 16 = 2736
72 x 38 = 2736
Children may also choose to use the grid method when multiplying with decimals. The same
method applies, by partitioning the decimal within the grid. Side jottings help greatly with place value
understanding. i.e. If a child knows that 2 x 3 = 6, they can use this to calculate 0.2 x 3 = 0.6.
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TPPS Multiplication
Step 6
Children use the partitioning understanding from Steps 4 and 5 to apply to the formal column
written method. Taking the same calculation from Step 5, you can see the same principles
apply but in a more efficient way as children now only write the totals once as they are
adding below the totals in one step.
Children jot down the calculation in brackets to the right of the column. Again, side jottings
would be encouraged to secure place value understanding.
It is important that children work systematically through the calculation by beginning with
multiplying the bottom right digit to the digits above, starting with the smallest (furthest right).
72
x 38
16 (8x2)
560 (8x70)
60 (30x2)
+2100 (30x70)
2736
72x38=2736
1
Further examples, showing the systematic order and steps to be taken:
1) 86 x 47
2) 13 x 1.9
3) 45.8 x 7
86
x 47
42 (7x6)
560 (7x80)
240 (40x6)
+ 3200 (40x80)
4042
13.0
x 1.9
2.7 (0.9x3)
9.0 (0.9x10)
3.0 (1x3)
+10.0 (1x10)
24.7
45.8
x 7 .
5.6 (7x0.8)
35.0 (7x5)
+ 280.0 (7x40)
320.6
1 1
1 1
1
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TPPS Multiplication
J Now try these, using your chosen method:
1) 73 x 4
2) 459 x 5
3) 47 x 24
4) 63 x 3.6
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TPPS Multiplication