Year 5
Multiply up to 4-digits by 1 or 2 digits
Introducing compact column multiplication from expanded multiplication.
Compare the expanded column multiplication to the compact multiplication
method.
Children need to be taught to approximate first, e.g. for 72 x 38, they will
use rounding: 72 x 38 is approximately 70 x 40 = 2800, and use the
approximation to check the reasonableness of their answer against it.
287 x 6
287
6x
4 2 (6 x 7)
4 8 0 (6 x 80) +
1 2 0 0 (6 x 200)
1
1722
287
5 4 6 x
1722
Explore with the children the values of the ‘carry digits’ of 5 and 4 and where they came
from. 6 x 7 = 42, the 40 is ‘carried’ into the tens column in the form of the 4 digit above
the answer line in the tens column place. 6 x 80 = 480, then add the ‘carried’ 40 from
the previous multiplication of the ones digit = 520. Place the digit 2 in the answer to
represent the tens value and the 500 is ‘carried’ into the hundreds column in the form of
the 5 digit above the answer line in the hundred column place. 6 x 200 = 1200, then add
the ‘carried’ 500 from the previous multiplication of the tens digit = 1700. Place the
thousand and hundred digit in the answer place value columns, giving the answer 1722.
Children need plenty of opportunities to discuss ‘What is the same?’ and ‘What is
different?’ with expanded to compact multiplication. Unpick the process and show how it
reduces the steps.
Once children are secure with the 3-digit by single-digit compact multiplication method
move to 4-digit by single digit compact method.
Introducing compact column multiplication - multiplying with 2-digits:
10
10
3
8
100
80
30
24
Grid method could be used to
introduce 2-digit multiplication,
as the relationship can be seen
in each row
18
13x
2
54
180
234
Compare the grid
method and highlight
that the bottom row of
the grid becomes the
top of the compact
method i.e. 3 x 18 –
the ‘carry’ digit of 2 is
the 20 from 3 x 8,
which is added to the 3
x 10 making the top row
of 54.
10 x 18 is the second
row.
Moving towards more complex numbers:
1234
21 26 x
7404
12340
19744
Approximate,
Calculate,
(6 x 1234)
(10 x 1234)
3652
5418 x
29216
Check it mate!
Key vocabulary groups of, lots of, times, array, altogether, multiply, count, multiplied
by, repeated addition, column, row, commutative, sets of, equal groups, _times as big as,
once, twice, three times..., partition, grid method, total, multiple, product, inverse,
square, factor, integer, decimal, expanded/compact multiplication, ‘carry‘
Key skills for multiplication at Y5:
Identify multiples and factors, using knowledge of multiplication tables to 12x12.
Solve problems where larger numbers are decomposed into their factors
Multiply and divide integers and decimals by 10, 100 and 1000
Recognise and use square and cube numbers and their notation
Solve problems involving combinations of operations, choosing and using calculations and
methods appropriately.