The Firs Primary School
May 2015
PROGRESSION THROUGH CALCULATIONS FOR
MULTIPLICATION
MENTAL CALCULATIONS
(ongoing)
Doubling and halving
Applying the knowledge of doubles and halves to known facts.
e.g. 8 x 4 is double 4 x 4
Using multiplication facts
Tables should be taught everyday from Y2 onwards, either as part of the
mental oral starter or other times as appropriate within the day.
Year 2
2 times table
3 times table
4 times table
5 times table
10 times table
Year 3
2 times table
3 times table
4 times table
5 times table
8 times table
9 time table
10 times table
Year 4
Derive and recall all multiplication facts up to 12 x 12
Years 5 & 6 Derive and recall quickly all multiplication facts up to 12 x 12.
Using rounding
Year 6 to use rounding strategy to help complete money problems, e.g.
4 x £9.99= 4 x 10
= £40 – (4 x 1p)
= £39.96
Using and applying division facts
Children should be able to utilise their tables knowledge to derive other facts.
e.g. If I know 3 x 7 = 21, what else do I know?
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The Firs Primary School
May 2015
30 x 7 = 210, 300 x 7 = 2100, 3000 x 7 = 21 000, 0.3 x 7 = 2.1 etc
Use closely related facts already known
13 x 11 = (13 x 10) + (13 x 1)
= 130 + 13
= 143
Multiplying by 10 or 100
Knowing that the effect of multiplying by 10 is a shift in the digits one place to
the left.
Knowing that the effect of multiplying by 100 is a shift in the digits two places
to the left.
Partitioning
23 x 4 = (20 x 4) + (3 x 4)
= 80 + 12
= 102
Use of factors
8 x 12 = 8 x 4 x 3
MANY MENTAL CALCULATION STRATEGIES WILL CONTINUE TO BE
USED. THEY ARE NOT REPLACED BY WRITTEN METHODS.
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The Firs Primary School
May 2015
YR and Y1 (Stage 1)
Children will experience equal groups of objects/ beads and will count in 2s and
10s and begin to count in 5s. They will work on practical problem solving
activities involving equal sets or groups between different numbers.
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The Firs Primary School
May 2015
Y2 (Stage 2)
Children will develop their understanding of multiplication and use jottings to
support calculation:
Repeated addition

3 times 5
is
5 + 5 + 5 = 15
or 3 lots of 5 or 5 x 3
Repeated addition can be shown easily on a number line:
5x3=5+5+5
5
0
1
2
5
3
4
5
6
7
5
8
9
10 11 12 13 14 15
and on a bead bar:
5x3=5+5+5
5
5
5
Commutativity

Children should know that 3 x 5 has the same answer as 5 x 3. This can also be
shown on the number line.
5
0
1
2
3
5
3
4
5
3
6
7
5
8
3
9
10 11 12 13 14 15
3
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3
The Firs Primary School
May 2015

Arrays
Children should be able to model a multiplication calculation using an array. This
knowledge will support with the development of the grid method.
5 x 3 = 15
3 x 5 = 15
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The Firs Primary School
May 2015
Y3 (Low Stage 3)
Children will continue to use:

Repeated addition
4 times 6
is
6 + 6 + 6 + 6 = 24
or 4 lots of 6 or 6 x 4
Children should use number lines or bead bars to support their understanding.
6
0
6
6

6
6
12
6
6
18
24
6
6
Arrays
Children should be able to model a multiplication calculation using an array. This
knowledge will support with the development of the grid method.
9 x 4 = 36
9 x 4 = 36
Children will also develop an understanding of

Scaling
e.g. Find a ribbon that is 4 times as long as the blue ribbon
5 cm
20 cm
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The Firs Primary School
May 2015

Using symbols to stand for unknown numbers to complete equations
using inverse operations
 x 5 = 20

3 x  = 18
 x  = 32
Partitioning (Secure Stage 3)
38 x 5
= 30 x 5 = 150
= 8 x 5 = 40
= 190
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The Firs Primary School
May 2015
Y4
Children will continue to use arrays where appropriate leading into the grid
method of multiplication.
Partition- Grid method
14 x 6 =
x
10
4
(6 x 10) + (6 x 4)
6
60
24
60
+
24
84
(Stage 4)
Expanded column method for long multiplication
TU x U
Children will approximate first
23 x 8 is approximately 25 x 8 = 200
HTU
23
x 8
160 (20 x 8)
24 (3 x 8)
184
Pupils become more aware of place value issues with the layout of the
partitioning already under relevant place value positions with pupils describing
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The Firs Primary School
May 2015
actual values of the digits in the columns. To begin partitioning process with the
biggest number. Children who are secure with multiplication for TU x U should
have little difficulty in using the same method for HTU x U.
Short column multiplication – multiplication by a single digit
HTU
2
23
x 8
184
To emphasise place value of digits within the sum, particularly when referring to
numbers placed in columns larger than Units (i.e. 2 has a value of 20). It is
imperative that partitioning understanding is secure by this stage of pupils’
multiplication knowledge. Children who are secure with multiplication for TU x U
should have little difficulty in using the same method for HTU x U.
HTU
3 5
346
x 9
3114
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The Firs Primary School
May 2015
Y5 (Stage 4)
Partitioning method
HTU x U
Children will approximate first
346 x 9 is approximately 350 x 10 = 3500
346 x 9= (300 x 9) + (40 x 9) + (6 x 9)
= 2700 + 360 + 54
= 3114
Expanded column method for long multiplication
TU x TU
Children will approximate first
72 x 38 is approximately 70 x 40 = 2800
HTU
72
x 38
2100 (70 x 30)
560 (70 x 8)
60 (2 x 30)
16 (2 x 8)
2736
1
Children should describe what they do referring to the actual values of the
digits in the columns. For example, the step that involves 2 x 30 should be
described as ‘two multiplied by thirty’, not ‘two multiplied by three’, although
the relationship 2 x 3 should be stressed. Children who are secure with
multiplication for TU x TU should have little difficulty in using the same method
for HTU x TU.
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The Firs Primary School
May 2015
Short column multiplication
TU x TU
72 x 38
HTU
Multiplication sums to begin with unit columns (8x2 and 8x7)
with any carry overs placed above the sum. The second row of
numbers are to start with 0 in the units column as each sum
will incorporate the digit from the Tens column.
1
72
x 38
576
2160
2736
U.th x U
Using similar methods, they will be able to multiply decimals with one decimal
place by a single digit number, approximating first.
Pupils must be secure with their understanding of place value when
multiplying with decimal numbers, i.e. 0.9 x 3 = 2.7 can be completed using
knowledge of 9 x 3. Consequently the answer has moved one place value to
the right due to the movement of the 9 from the 9 x 3 sum to 0.9.
e.g. 4.9 x 3
Children can approximate first
4.9 x 3 is approximately 5 x 3 = 15
U. t
2
4.9
x 3
14.7
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The Firs Primary School
May 2015
To complete the sum in the same manner as the sum 49 x 3 would be completed
with the decimal point placed 1 digit from the right hand side due the sum
incorporating just 1 decimal number.
Y6
ThHTU x U
To reinforce long and short column multiplication methods to children.
4346 x 8
Children can approximate first
4346 x 8 is approximately 4346 x 10 = 43460
ThHTU
4346
x 8
32000 (4000 x 8)
2400 (300 x 8)
320 (40 x 8)
48 (6 x 8)
34768
ThHTU
234
4346
x 8
34768
Short column multiplication
HTU x TU
372 x 24
Children will approximate first
372 x 24 is approximately 400 x 25 = 10000
HTU
2
372
x 24
1488
7440
8928
1
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The Firs Primary School
May 2015
Any carry digits (overs) from partial products to be placed above sum under
relevant place value therefore a space is needed if place value letters are noted.
Carry digits from addition sums to be placed under the sum.
(Stage 5) Using similar methods, they will be able to multiply decimals with up
to two decimal places by a single digit number and then two digit numbers,
approximating first. They should know that the decimal points line up under
each other and is completed in accordance to previous examples’ layout.
U. th hth x U
4.92 x 3
Children will approximate first
4.92 x 3 is approximately 5 x 3 = 15
U. t h
2
4.92
x 3__
14.76
U. t h
2
This sum can be viewed and completed in the same way as
492 x 3 before adjusting the answer to suit place value.
This is done by placing the decimal point 2 units from the
left due to there being 2 decimal numbers in the question.
Again, sum to be completed as 32 x 44 before making
place value adjustments.
3.2
x 4.4
1.28
12.80
14.08
+ - + - + - + - + - + - +
By the end of year 6, children will have a range of calculation methods,
mental and written. Selection will depend upon the numbers involved.
Children should not be made to go onto the next stage if:
1) they are not ready.
2) they are not confident.
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The Firs Primary School
May 2015
Children should be encouraged to approximate their answers before
calculating.
Children should be encouraged to consider if a mental calculation would be
appropriate before using written methods.
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