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PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION
Year 1
knowing & using number facts
Count on or back in ones, twos, fives and tens and use this knowledge to
derive the multiples of 2, 5 and 10 to the tenth multiple.
Multiplication is related to doubling and counting groups of the same size.
2x3=6
Looking at columns
2+2+2
3 groups of 2
Looking at rows
3+3
Counting using a variety of practical resources
Counting in 2s e.g. counting socks, shoes, animal’s legs…
Counting in 5s e.g. counting fingers, fingers in gloves, toes…
Counting in 10s e.g. fingers, toes…
2
5
4
10
6
15
8
20
Using pictures to help
There are 3 sweets in one bag.
How many sweets are there in 5 bags?
Arrays and repeated addition
Brighter children may move onto looking how multiplication can be represented as an
array of dots.
4 x 2 or 4 + 4
2 x 4 or 2 + 2 + 2 + 2
Year 2
x = signs and missing numbers
solve missing numbers by understanding that multiplication can be
done in any order.
=2x7
7x2=
7 x = 14
14 = x 7
x 2 = 14
14 = 2 x
x ∇ = 14
14 = x ∇
Arrays and repeated addition
Introduce all children to arrays.
4 x 2 or 4 + 4
2 x 4 or 2 + 2 + 2 + 2
Count on in multiples on a numberline.
2x4=8
4x2=8
0
1
2
3
4
5
6
7
8
To know doubles of 2 digit numbers by partitioning
Double 15
10
+
5
20
+ 10 = 30
More able year 2’s may be introduced to a simple grid method
•
X
10
5
2
20
10
= 30
Derive and recall multiplication facts for the 2, 5 and 10 timestables and the related division facts; recognise multiples of 2, 5
and 10.
Year 3
•
Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10
times-tables and the corresponding division facts; recognise
multiples of 2, 5 or 10 up to 1000.
Multiply one-digit and two-digit numbers by 10 or 100, and describe
the effect.
•
Continue to use repeated addition
3x4=12
0
3
6
9
12
Doubling multiples of 5 up to 50
35 x 2 = 70
30
5
60
10=70
Partition
X
30
5
2
60
10
=70
Year 4
• Multiply and divide numbers to 1000 by 10 and then 100 (wholenumber answers), understanding the effect; relate to scaling up or
down.
•
Derive and recall multiplication facts up to 10 x 10, the
corresponding division facts and multiples of numbers to 10 up to
the tenth multiple.
Partitioning
Continue to use partitioning
Partition
47 x 6 = 282
47 x 6 = (40 x 6) + (7 x 6) = 282
Grid method
• Children approximate answers first.
23 x 7 is approximately 20 x 10 = 200
x
7
•
x
30
8
20
140
3
21
= 161
Moving onto using the grid method for 2 and 3 digit numbers.
72x38=
70
2100
560
2
60
16
= 2160
= 576
2736
Year 5
•
Refine and use efficient written methods to multiply and divide
HTU U, TU TU, U.t U and HTU U
•
Recall quickly multiplication facts up to 10 x 10 and use them
to multiply pairs of multiples of 10 and 100; derive quickly
corresponding division facts
Grid method
372 x 24 is approximately 400 x 20 = 8000
x
20
4
300
70 2
6000 1400 40
1200
280 8
=7440
=1488
=8928
More able will also also use grid method with decimals.
Some children may move onto the following method.This mehod is
used at the high school.
This method can also be used with decimals.
(Step 1) Multiply 301 x 1.2
3
0
1
1
2
Fill the numbers around the outside of the box
(S te p 2 ) M u ltip ly 3 0 1 x 1 .2
3
0
0
1
0
0
3
0
0
0
1
1
0
6
0
2
2
M u ltip ly th e o u ts id e n u m b e rs a n d e n te r in th e
b o xe s
(Step 3 ) Multiply 301 x 1.2
3
0
0
1
0
3
0
0
0
0
6
3
1
0
0
6
1
2
1
2
2
We then add the diagonal numbers
(Step 4 ) Multiply 301 x 1.2
3
0
0
0
3
0
0
0
6
3
6
1
0
1
0
0
1
2
2
3612 Now add the decimal point one place
Answer = 361.2
1
2