Rugby Free Primary School Calculations Policy
September 2016
CONTENTS
1. Introduction and Rationale
2. Aims
3. Rationale
4. Objectives
5. Planning
6. Teaching and Learning Style
7. Inclusion
8. Resources and Access
9. Cross Curricular Links
10.Health and Safety and Safeguarding
11.
Review
Rugby Free Primary School
Calculation Policy
Introduction and Rationale
This calculation policy sets out expectations for the mastery of addition, subtraction, multiplication and division as written in
the National Curriculum 2014 as well as the progression of written methods as used at Rugby Free Primary School.
It is vital that pupils are taught according to the stage at which they are currently working, being moved onto the next stage as
soon as they are ready, or working at a lower stage until they are secure enough to move on. Children should not be
discouraged from using previously taught methods in which they are secure while new concepts are becoming embedded.
Although this policy focuses largely on written calculation methods it is important to recognise that the ability to calculate
mentally lies at the heart of numeracy; in every written method there is an element of mental processing and children need to
develop the mental skills and methods to allow them to do this efficiently. However, written recording can help children to
clarify their thinking and supports and extends the development of more fluent and sophisticated strategies.
The long-term aim is for children to be able to select an efficient method that is appropriate for a given task. They should do
this by always asking themselves:

‘Can I do this in my head?' 
'Can I do this in my head using equipment or drawings?' 
'Do I need to use a written method and, if so, which one would be most efficient?' It is important that calculations are given a real life context or problem solving approach where possible to help build
children’s understanding of the purpose of calculation and to help them recognise when to use certain operations and methods
when faced with problems.
Aims




To ensure consistence and progression in our approach to calculation
To ensure that children develop efficient and reliable mental and written methods of calculation for all operations.
To ensure that children have mastery of these methods, using them accurately and appropriately with confidence and
understanding.
To ensure that all adults, including parents/carers, are able to support children in an effective and coherent manner.
Teachers – How to use this policy




Use this policy as the basis of your planning but ensure you use the previous or following years’ guidance to allow for
personalised learning.
Always use assessment for learning to identify suitable next steps in calculation for groups of children.
Always use suitable resources, models and images to support children’s understanding of calculation, as appropriate.
If, at any time, children are making significant errors, return to the previous stage in calculation/ or previous resources.
Parents/Carers – How to use this policy



When supporting your child with a particular calculation, use the policy to identify with your child the method which
they are most familiar with. Children should choose the method that they feel is most suited to the task.
Use suitable resources, models and images to support children’s understanding of calculation, as appropriate (e.g.
counters, number lines etc.)
If, at any time, your child is making significant errors, try returning to the previous stage in calculation and/or previous
resources.
Vocabulary
The following key vocabulary in the tables below should be used age appropriately. Please note:

‘Sum’ should only be used to refer to addition calculations, and not used in a more general sense, e.g. ‘lets do these
sums’ when referring to other operations like subtraction, multiplication or division.


When transferring units, tens and hundreds, etc. from one place value column to another when using the column
method for addition or subtraction, this should be referred to as ‘moving’ rather than ‘carrying’, ‘borrowing’, or
‘exchanging’.
We should not always use the term ‘equals’. It is useful to sometimes use the terminology ‘is the same as’ to clarify the
meaning of the symbol.
E.g. when reading aloud 3 + 3 = 6, you could say ‘three plus three is the same as six’.
Addition
Subtraction
Add, addition, more, plus, increase, jump forward, count on, sum,
total, altogether, get some more, tens, units, hundreds, thousands,
place value, digit, value, combine, total, score, double, near
double, how many more to make….?, equals, sign, inverse.
Subtract, take away, minus, decrease, leave, jump back, count
back, how many are left/left over? Difference between, half, halve,
how many more/fewer is….. than….?, how much more/less is….?,
equals, inverse.
Multiplication
Division
Lots of, groups of, times, product, multiply, multiplied by, multiple Divide, share, share equally, halve, one each, two each, three
of, once, twice, three times... ten times, repeated addition, array,
each…., group in pairs, threes….tens, equal groups of, divide,
double, inverse.
divided by, divided into, divisible by, remainder, factor, quotient,
inverse.
Rugby Free Primary School
Written Methods for Addition and Subtraction
Addition Pathways
Practical Methods
Concrete Addition
(using cubes, counters, etc.)
3
+
2
=
5
Use pictorial representations using images.
Written Methods
Number Sentences
Children should be able to read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs.
Represent and use number bonds and related subtraction facts within 20.
8 + 3 = 11
Number line
Counting on in 1s on a number line.
Using number facts
Partitioning to add tens and units
Expanded number sentences to understand place value.
242 +346 = 588
200 + 300 + 40 + 40 + 2 + 6 = 588
Expanded Column Addition
215 + 133 = 348
HTU
215
133 +
8 (5 + 3)
40 (10 + 30)
300 ( 200 + 100)
348
Compact Column Addition
Ensure that on the middle column, children are taught to say ’20 + 90’ as opposed to ‘2+9’ and
for hundreds column ‘200 + 100’ instead of ‘2+1’
215 + 133 = 348
HTU
215
133 +
348
226 + 193 = 419
OR
HTU
226
193 +
419
1
Compact Column Addition
Extend to numbers with any number of digits and decimals with 1 and 2 decimal places.
124.9 + 117.25 = 242.15
124.9
117.25 +
242.15
11
Subtraction Pathways
Practical Methods
Concrete Subtraction
(using cubes, counters etc.)
Teaching the children to physically take an amount away.
Using Pictorial Representations
4– 1=3
Written Methods
Number Sentences
Children should be able to read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs.
Represent and use number bonds and related subtraction facts within 20.
9 - 2=7
Number line
Counting back in 1s on a number line
Using number facts
Partitioning to subtract tens and units
Expanded Column Subtraction
48 – 7 =
40 + 8
7–
48
7–
40 + 1 = 41
Expanded Column by Moving
47 – 8 =
47
8–
40 + 7
8–
30 + 17
8–
30 + 9 = 39
Compact Column Subtraction
48
7–
41
193 – 66 = 127
Compact Column Subtraction
Extend to numbers with any number of digits and decimals with 1 and 2 decimal places.
Rugby Free Primary School
Written Methods for Multiplication and Division
Multiplication Pathways
Number Sentences
Understanding the symbol and that multiplication can be represented as repeated addition.
3x2
2+2+2=6
3 lots of 2 = 6
3x2=6
Practical Methods
Arrays
Written Methods
Number lines
Using number lines to show repeated grouping/addition.
4 x 5 = 20
Grid Methods
23 x 3 = 69
23 x 35 = 805
Expanded Multiplication
32 x 15 = 480
Column Multiplication
13 x 8 = 104
Division Pathways
Practical Methods
Sharing
Children read the number sentence 4 ÷ 2, take out 4 counters and share them between 2.
Grouping
Children read the number sentence 15 ÷ 3, take out 15 counters and group them into 3s.
Written Methods
Grouping
4÷2=2
Number line
Division as repeated subtraction
15 ÷ 5 = 3
Number lines with remainders.
18 ÷ 4 = 4 remainder 2
Chunking Method
100 ÷ 5 = 20
Compact Short Division
Children continue to use the ‘chunking’ method before they progress to short division
196 ÷ 6 = 32 r 4
Long Division
Children should be using known multiplication facts to complete long division