PROGRESSION THROUGH CALCULATIONS
FOR MULTIPLICATION Revised for Curriculum 2014
MENTAL CALCULATIONS (ongoing)
These are a selection of mental calculation strategies:
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
5 times table
10 times table
Year 3
2 times table
3 times table
4 times table
5 times table
8 times table
10 times table
Year 4
Derive and recall all multiplication facts up to 12 x 12
X and
÷ by 10 and understand its effect
Years 5 & 6 Derive and recall quickly all multiplication facts up to 12 x 12.
X and ÷ by 10, 100 and 1000 and understand its effects
Establish whether a number up to 100 is prime
Recall prime numbers up to 19
Page 1 of 10
Using and applying multiplication and 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?
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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YR
Children will experience equal groups of objects 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. For example: pairing socks, grouping objects.
How many
socks? How
many pairs of
socks?
How many pairs of
gloves? How many
fingers?
Y1
Children will continue to work with practical examples.
For example:
There are 3 sweets in one bag.
How many sweets are there in 5
bags?
For example:
Looking at columns
2+2+2
3 groups of 2
Looking at rows
3+3
2 groups of 3
Counting using a variety of practical resources:
Counting in 2s e.g. counting socks, shoes, animal legs…
Counting in 5s e.g. counting fingers, fingers in gloves, toes…
Counting in 10s e.g. counting fingers, toes…
Beginning to link the bead frame and bead string to show equal grouping (see Year 2)
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Y2
Children will develop their understanding of multiplication and use jottings to support
calculation:

Know 2, 5, 10 x tables

Recognise odd and even numbers

Understand multiplication as repeated addition

Continue to use a variety of resources such as number sticks, cubes and small
objects.

Children should be able to model a multiplication calculation using an array.

They should use x = symbols to record simple mental calculation facts
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 string or 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

Arrays
Children should be able to model a multiplication calculation using an array. This
knowledge will be supported with the development of the grid method.
5 x 3 = 15
3 x 5 = 15
Y3



Reinforce work on arrays as Year 2, extending to 2-digit x 1-digit multiplication such
as 16 x 5
Know 2, 3, 4, 5, 8, 10 x tables
Children will continue to use Repeated addition
4 times 8
is
8 + 8 + 8 + 8 = 32
or 4 lots of 8 or 8 x 4
Children should use number lines or bead bars to support their understanding.
8
0
8
8
8
16
8
24
32
 Arrays
Children should be able to model a multiplication calculation using an array. This knowledge
will be supported with the development of the grid method.
8 x 4 = 32
8 x 4 = 32
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Partitioning (linking to arrays)

I can split 14 into 10 and 4
10 x 5 = 50 and 4 x 5 = 20
That equals 70 altogether.
14 x 5 = (10 x 5) + (4 x 5)
= 50 + 20
= 70
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4
10
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50
20
5
50
4
20
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
Using symbols to stand for unknown numbers to complete equations using inverse
operations
 x 5 = 20
3 x  = 18
 x  = 32
Y4







Know 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 x tables up to 12 x 12
Use place value and known and derived facts to multiply mentally, including by 0 and 1
Multiply together 3 numbers
Children will continue to use arrays where appropriate leading into the grid method.
Multiply two-digit and three-digit numbers by a one-digit number using a formal
written layout, such as the grid method and then short multiplication.
Recognise and use factor pairs and commutativity in mental calculations
Solve problems involving multiplying and adding, including using the distributive law to
multiply 2-diit numbers by 1-digit, and scaling problems.
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x
10
4
(6 x 10) + (6 x 4)
6

24
60
60
+
24
84
Grid method
TU x U
(Grid method – multiplication by a single digit)
For example:
23 x 8
Children will approximate first
23 x 8 is approximately 25 x 8 = 200
x
8
20
160
3
24
I’ll split 23 into 20 and 3
8 x 20 = 160 and 8 x 3 = 24
That equals 184 altogether.
160
+ 24
184
 Short multiplication
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Children should be shown how the grid method leads onto this method and that the
children are actually doing the same maths in both.
Y5

Grid method
Extend grid multiplication to three/four digit by one/two digit numbers and show that
short and long division can be a more effective method, particularly when dealing with
large numbers.
HTU x U
(Short multiplication – multiplication by a single digit)
346 x 9
Children will approximate first
346 x 9 is approximately 350 x 10 = 3500
x
9
300 40 6
2700 360 54
I can partition a
3 digit number
into hundreds,
tens and units.
2700
+ 360
+
54
31 1 4
1 1
TU x TU
(Grid method – extending grid method)
72 x 38
Children will approximate first
72 x 38 is approximately 70 x 40 = 2800
x
70
2
30 2100 60
8
560 16
2100
+ 560
+
60
+
16
2736
1
Page 8 of 10
Using similar methods, they will be able to multiply decimals with one decimal place by a
single digit number, approximating first. They should know that the decimal points line up
under each other.
e.g. 4.9 x 3
Children will approximate first
4.9 x 3 is approximately 5 x 3 = 15
x
3
4
12
0.9
2.7
+
12
2.7
14.7
Long multiplication
Y6
 Multiply multi-digit numbers up to four digits by a 2-digit whole number using long
division.
 Children will approximate first
372 x 24 is approximately 400 x 25 = 10000
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Long multiplication
 Multiply one-digit numbers with up to two decimal places bt whole numbers,
approximating first. They should know that the decimal points line up under each
other. The Short multiplication method can be used when any calculation involves
multiplying by a single integer.
TU.th
4.92 x 3
Children will approximate first
4.92 x 3 is approximately 5 x 3 = 15
4.92
3X
12.76
**********************
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.
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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