Stoke Minster CE (A) Primary School
Multiplication Policy
Mental and written calculation methods should be taught alongside each other throughout the entirety of this progression. When teaching children to calculate, emphasis
should be placed on choosing and using the method that is most efficient.
Multiplication- YEAR 4 (Stage 4)
Expectations
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recall multiplication and division facts for
multiplication tables up to 12 × 12
use place value, known and derived facts to
multiply and divide mentally, including:
multiplying by 0 and 1; dividing by 1;
multiplying together three numbers
recognise and use factor pairs and
commutativity in mental calculations
multiply two-digit and three-digit numbers
by a one-digit number using formal written
layout
solve problems involving multiplying and
adding, including using the distributive law to
multiply two digit numbers by one digit,
integer scaling problems and harder
correspondence problems such as n objects
are connected to m objects.
Vocabulary: : odd, even, count in twos, threes, fives, count in tens (forwards from/backwards from)
How many times? Lots of, groups of, once, twice, three times, five times , repeated addition, array, row, column, double, halve,
product, multiples of four, eight, fifty and one hundred , scale up, multiplication facts (up to 12x12), inverse, derive
Guidance & Written Methods for Multiplication
Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency.
Pupils practise mental methods and extend this to three-digit numbers to derive facts, (for example 600 ÷ 3 = 200
can be derived from 2 x 3 = 6).
Pupils practise to become fluent in the formal written method of short multiplication and short division with exact
answers (see Mathematics Appendix 1).
Pupils write statements about the equality of expressions (for example, use the distributive law 39 × 7 = 30 × 7 + 9
× 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)). They combine their knowledge of number facts and rules of
arithmetic to solve mental and written calculations for example, 2 x 6 x 5 = 10 x 6 = 60.
Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder
numbers. This should include correspondence questions such as the numbers of choices of a meal on a menu, or
three cakes shared equally between 10 children.
Written Methods – Steps (Also refer to Y3 policy)
Steps:
1. The grid method
Revise use of this method to multiple TU x U and check understanding using Dienes apparatus.
Move to multiplying HTU x U and TU x TU using the grid method.
Three digit by one digit products using the grid method (HTU x U)
153 x 4 Estimate 150 x 4 (double and double again) =600
X
100
50
3
4
400
200
12
400 + 200 + 12 = 612
Check with estimate of 600. The answer is reasonable
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Year 4 multiplication continued . . .
Related calculations and estimates
To utilize further methods, children need to
a) know their multiplication facts up to 12 x 12
b) be able to identify and use related calculations
and place value effectively
e.g. for 47 X 6 they must be able to calculate 40 X 6.
They need to recognise the ‘root’ calculation
4 x 6 = 24
and understand that as 40 is ten times greater than 4,
the product will also be ten times greater.
40 x 6 = 240
or for 234 x 3 they must be able to recognise the
‘root’ calculation
2x3=6
and understand that as 200 is a hundred times greater
than 2, the product will be also be a hundred times
greater.
200 x 3 = 600
Two-digit by two-digit products using the grid method (TU x TU)
Children first make an estimate by rounding each number to the nearest ten.
Having calculated the sections of the grid, children will decide whether to add the rows or columns first as
they become more confident with recognising efficient calculations.
They will choose jottings, informal or formal written methods depending upon which is most appropriate.
Children should be expected to complete this for TU X TU but not for larger numbers.
Adding the rows or adding the columns
This should be decided by the child depending on the numbers that are produced through the calculation.
a) 53 x 18 Estimate 50 x 20 = 1000
X
50
3
10
500
30
8
400
24
Adding the columns is the most efficient calculation: 500 + 400 = 900
30 + 24 = 54
Add 900 and 54 954
Check with estimate of 1000. The answer is reasonable.
b) 38 x 17
Estimate 40 x 20 = 800
X
30
8
10
300
80
7
210
56
Adding the rows is easier:
300 + 80 = 380
210 + 56 = 266
380 + 200 = 580
580 + 60 = 640
640 + 6 = 646
As both 38 and 17 were rounded up, the higher estimation of 800 is expected and makes this answer
reasonable.
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Year 4 multiplication continued . . .
2.
Progression from the grid method to the formal written layout of expanded short method of
multiplication
• The first step is to represent the method of recording in a column format, but showing the working.
Draw attention to the links with the grid method above.
• Children should describe what they do by referring to the actual values of the digits in the columns. For example,
the first step in 38 × 7 is ‘thirty multiplied by seven’, not ‘three times seven’, although the relationship 3 × 7 should
be stressed.
TU x U
38 X 7 is approximately 40 X 7 = 280
Children should be expected to multiply the units first which enables them to move towards the compact method.
38
X 7
56 (8 x 7)
210 (30 x 7)
266
Check with estimate of 280. The answer is reasonable.
HTU x U (including money)
X
6
£6.00
£36.00
£6.32 X 6 is approximately £6 X 6 = £36
£ 0.30
£1.80
£ 0.02
£ 0 .12
x
£6.32
6
.12
(2p x 6)
1.80 (30p x 6)
36.00 (£6.00 x 6)
£37.92
Check with estimate of £36. As an original factor was rounded down by 32p the answer is reasonable.
The children can use the expanded column method and check with the grid method until confident.
When children have developed a secure understanding, use just the expanded column method, then progress to
compact short multiplication (see Y5).
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