St Stephens Community Academy
Calculation Policy for Mathematics
The following calculations policy has been devised to meet the requirements of
the National Curriculum 2014 for the teaching and learning of mathematics, and
also to give pupils a consistent and smooth progression of learning in calculation
across the school. Please note that early learning in number and calculation in YF
follows the ‘Development Matters EYFS document and this calculation policy is
designed to build on progression from the content and methods established in
the Early Years Foundation Stage.
Age stage expectations
The calculation policy is organised according to age stage expectations as set
out in the National Curriculum 2014, however it is vital that pupils are taught
according to the stage that they are currently working at, working at a lower
stage until they are secure enough to move on. Children must consolidate their
learning with mathematical challenges in various contexts before moving on to
the next stage.
Providing a context for calculation
It is important that any calculation is given a real life context or problem
solving approach 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. This must be a priority within calculation
lessons.
Choosing a method:
Children need to be taught and encouraged to use the following processes in
deciding what approach they will take at solving a calculation, to ensure they
select the most appropriate method for the numbers involved.
Can I do it in my head
using a mental strategy?
Could I use some
jottings to help me?
Should I use a written
method to work it out?
To work out a
tricky calculation
Approximate
Calculate
Check it!
Overview of Key Stage 1
Children in Years 1 and 2 will be given a really solid foundation in the basic
building blocks of mental and written arithmetic. Through being taught place
value, they will develop an understanding of how numbers work, so that they are
confident in 2-digit numbers and beginning to read and say numbers above 100.
A focus on number bonds, first via practical hands-on experiences and
subsequently using memorisation techniques, enables a good grounding in these
crucial facts, and ensures that all children leave Y2 knowing the pairs of
numbers which make all the numbers up to 10 and 20. Their knowledge of
number facts enables them to add several single-digit numbers, to use related
facts up to 100 and to add/subtract a single digit number to/from a 2-digit
number.
Another important conceptual tool is their ability to add/subtract 1 or 10, and
to understand which digit changes and why. This understanding is extended to
enable children to add and subtract multiples of ten to and from any 2-digit
number. The most important application of this knowledge is their ability to add
or subtract any pair of 2-digit numbers by counting on or back in tens and ones.
Children may extend this to adding by partitioning numbers into tens and ones.
Children will be taught to count in 2s, 3s, 5s and 10s, and will have related this
skill to repeated addition. They will have met and begun to learn the associated
2x, 3x, 5x and 10x tables. Engaging in a practical way with the concept of
repeated addition and the use of arrays enables children to develop a
preliminary understanding of multiplication, and asking them to consider how
many groups of a given number make a total, will introduce them to the idea of
division. They will also be taught to double and halve numbers, and will thus
experience scaling up or down as a further aspect of multiplication and division.
Fractions will be introduced as numbers and as operators, specifically in relation
to halves, quarters and thirds.
Overview of Lower KS2
In the lower juniors, children build on the concrete and conceptual
understandings they have gained in KS1 to develop a real mathematical
understanding of the four operations, in particular developing arithmetical
competence in relation to larger numbers. In addition and subtraction, they are
taught to use place value and number facts to add and subtract numbers
mentally and will develop a range of strategies to enable them to discard the
‘counting in ones’ or fingers-based methods of KS1. In particular, they will learn
to add and subtract multiples and near multiples of 10, 100 and 1000, and will
become fluent in complementary addition as an accurate means of achieving fast
and accurate answers to 3-digit subtractions. Standard written methods for
adding larger numbers are taught, learned and consolidated, and written column
subtraction is also introduced.
This key stage is also the period during which all the multiplication and division
facts are thoroughly memorised, including all facts up to the 12 x 12 table.
Efficient written methods for multiplying or dividing a 2-digit or 3-digit number
by a single-digit number are taught, as are mental strategies for multiplication
or division with large but friendly numbers, e.g. when dividing by 5 or multiplying
by 20. Children will develop their understanding of fractions, learning to reduce
a fraction to its simplest form as well as finding non-unit fractions of amounts
and quantities. The concept of a decimal number is introduced and children
consolidate a firm understanding of one-place decimals, multiplying and dividing
whole numbers by 10 and 100.
Overview of Upper KS2
Children move on from dealing mainly with whole numbers to performing
arithmetic operations with both decimals and fractions. They will consolidate
their use of written procedures in adding and subtracting whole numbers with
up to 6 digits and also decimal numbers with up to two decimal places. Mental
strategies for adding and subtracting increasingly large numbers will also be
taught. These will draw upon children’s robust understanding of place value and
knowledge of number facts. Efficient and flexible strategies for mental
multiplication and division are taught and practised, so that children can
perform appropriate calculations even when the numbers are large, such as
40,000 x 6 or 40,000 ÷ 8. In addition, it is in Y5 and Y6 that children extend
their knowledge and confidence in using written algorithms for multiplication
and division. Fractions and decimals are also added, subtracted, divided and
multiplied, within the bounds of children’s understanding of these more
complicated numbers, and they will also calculate simple percentages and ratios.
Negative numbers will be added and subtracted.
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 taught through real life
experiences and word problems.
 Children should be encouraged to consider
if a mental calculation would be
appropriate before using written methods.
 Children should be encouraged to
approximate their answers before
calculating.
 Children should be encouraged to check
their answers after calculation using an
appropriate strategy.
NB: Pupils should be moved onto the next stage
when ready, even if this is in the next Year
group.
Year 1
Key vocabulary: add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line
Key skills for addition at Y1:
Read and write numbers to 100 in numerals, incl. 1—20 in words
Recall bonds to 5,6,7,8,9, 10 and 20, and addition facts within 20
Count to and across 100
Count in multiples of 1 2, 5 and 10
Count on in ones from a given 2-digit number
Add two single-digit numbers
Add three single-digit numbers spotting doubles or pairs to 10
Count on in tens from any given 2-digit number
Add 10 to any given 2-digit number
Use number facts to add single-digit numbers to two-digit numbers e.g. use 4
+ 3 to work out 24 + 3, 34 + 3…
Add by putting the larger number first
Solve simple 1-step problems involving addition, using objects, number lines and
pictorial representations.
Children are encouraged to develop a mental picture of the number system in
their heads to use for calculation. They develop ways of recording calculations
using pictures, etc.
They use numberlines and practical resources to support calculation and
teachers demonstrate the use of the numberline.
3+2=5
+1
+1
___________________________________________
0
1
2
3
4
5
6
7
8
9
Children then begin to use numbered lines to support their own calculations
using a numbered line to count on in ones from a 2-digit number.
18 + 5 = 13
+1 +1 +1 +1
+1
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Bead strings or bead bars can be used to illustrate addition including bridging
through ten by counting on 2 then counting on 3.
 Children should have access to a wide range of counting equipment,
everyday object, number tracks and number lines, numicon, and be shown
numbers in different context.
 Read and write the addition(+) and equals (=) signs within number
sentences
 Interpret addition number sentences and solve them: 8+3=
15+4
4+3+1 =
+
=6
This builds on from prior learning of adding by combining two sets of object into
one group (5 cubes and 3 cubes) in the EYFS.
Year 2
Key vocabulary: add, more, plus, and, make, altogether, total, equal to, equals, double,
most, count on, number line, sum, tens, units, partition, addition, column, tens boundary
Calculation skills for addition at Y2:
Add a 2-digit number and ones, using number facts and bridging 10 (e.g. 27 + 6)
Add a 2-digit number and tens (e.g. 23 + 40)
Add pairs of 2-digit numbers (e.g. 35 + 47)
Add three single-digit numbers (e.g. 5 + 9 + 7)
12, 20 and bonds of tens to 100 (30 + 70 etc.)
-digit numbers (tens and ones)
Show that adding can be done in any order (the commutative law).
ng concrete objects, pictorial representations, involving numbers,
quantities and measures, and applying mental and written methods.
Children will begin to use ‘empty number lines’ themselves starting with the
larger number and counting on.

First counting on in tens and ones.
34 + 23 = 57
+10
+10
+1 +1 +1
34

44
54 55 56 57
Then helping children to become more efficient by adding the units in one
jump (by using the known fact 4 + 3 = 7).
34 + 23 = 57
+10
+10
34
+10
+3
44
54
57

Followed by adding the tens in one jump and the units in one jump.
34 + 23 = 57
+20
+3
34

54
57
Bridging through ten can help children become more efficient.
37 + 15 = 52
+10
+3
37
47
+2
50
52
Add pairs of 2-digit numbers, moving to the partitioned column method when secure
adding tens and ones
2
3
+
3
4
=
2
3
5
0
0
0
+
+
+
3
4
7
=
5
7
Only provide examples that do not cross the boundaries until they are secure with the
method.
 Once children can add a multiple of ten to a 2-digit number mentally (e.g. 80+11)
they are ready for adding 2-digit numbers that DO cross the tens boundary
(e.g. 58+43).
5
8
+
4
3
=
5
0
+
8
4
9
0
0
+
+
3
1
1
=
1
0
1
To support understanding, pupils may physically make and carry out calculation with
Dienes base 10, numicon, or place value counters, then compare their practical version
to the written form, to build on understanding of it.
Year 3
Key vocabulary: add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units, partition, plus, addition,
column, tens boundary, hundreds boundary, increase, vertical, ‗carry‘,
expanded, compact
Key skills for addition at Y3:
Read and write numbers to 1000 in numerals and words.
-digit numbers mentally, incl. those exceeding 100.
Add a three-digit number and ones mentally (175 + 8)
Add a three-digit number and tens mentally (249 + 50)
Add a three-digit number and hundreds mentally (381 + 400)
Add pairs of ‘friendly’ 3-digit numbers, e.g. 320 + 450
 to add amounts of money using partitioning.
Begin

ve problems, including missing number problems, using number facts, place
value, and more complex addition.
-digit numbers (hundreds, tens, ones.)
, ie. number
bonds, adding the nearest multiple of 10, 100, 100 and adjusting, using near
doubles, partitioning and recombining
Use expanded column addition to add two or three 3-digit numbers or three 2digit numbers
Begin to use compact column addition to add numbers with three digits.
Begin to add like fractions. (E.g. 3/8 + 1/8 + 1/8)
Recognise fractions that add to 1. (E.g. ¼ + ¾ or 3/5 + 2/5)
 Continue to use mental methods first
 Add numbers with up to 3-digits
Continue to use partitioned column addition to add 3-digit and 2digit numbers
2
3
6
+
7
3
3
0
9
=
=
2
2
0
0
0
0
+
+
1
 Introduce the expanded column addition method:
H
T
U
Add the units first, in
2
3
6
preparation for the
+
7
3
compact method
9
1
0
0
2
0
0
3
0
9
3
0
+
6
7
0
+
3
0
0
+
9
Pupils need to
ensure that the
digits are lined up
in their correct
place value
position.
In order to carry out this method of addition:
 Children need to recognise the value of the hundreds, tens and units
without recording the partitioning.
 Pupils need to be able to add in columns.
Children who are very secure with this method should be moved to the compact
method of addition. They should then be introduced to ‘carrying’.
They compare the expanded method with the compact method to develop their
understanding of the process and the reduced number of steps involved.
2
+
3
1
3
7
0
6
3
9
Add ones first
Remind children it is 3 tens add 7
tens and not 3 add 7.
Year 4
Key vocabulary: add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units, partition, plus, addition, column,
tens boundary, hundreds boundary, increase, vertical, „carry‟, expanded, compact,
thousands, hundreds, digits, inverse
Key skills for addition at Y4:
Select most appropriate method: mental, jottings or written and explain why.
-digit number.
r to the nearest 10, 100 or 1000.
and why.
-step problems in context, deciding which operations and methods to use
Continue to practise a wide range of mental addition strategies, ie. number
bonds, add the nearest multiple of 10, 100, 1000 and adjust, use near doubles,
partitioning and recombining.
addition
2-step problems in contexts, deciding which operations and methods to use
and why.
Estimate and use inverse operations to check answers to a calculation.
Add like fractions, e.g. 3/5 + 4/5 = 7/5 = 1 2/5.
Be confident with fractions that add to 1 and fraction complements to 1. (E.g. 2/3 + ?
= 1)
Children will be encouraged to use mental methods first.
Informal:
 They will continue to use pencil and paper methods, e.g. number
lines, to support, record or explain calculations, achieving
consistent accuracy.
Formal Written
Add numbers up to 4-digits
Children will continue to partition as in Y3 moving to a more compact column
method.
e.g.
3517+ 396=3813
3
3
5
3
9
1
1
9
1
1
7
6
3
Add ones
first
Reinforce correct place value by
reminding them the actual value
is 5 hundreds and 3 hundreds,
not 5 and 3 for example.
 Apply this money in context e.g. money and measurement values.



Using similar methods, children will:
add several numbers with different numbers of digits;
begin to add two three-digit sums of money, with or without adjustment
from the pence to the pounds;
know that the decimal points should line up under each other, particularly
when adding mixed amounts, e.g. £3.59 + 78p.
Year 5
Key vocabulary: add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units, partition, plus, addition,
column, tens boundary, hundreds boundary, increase, „carry‟, expanded,
compact, vertical, thousands, hundreds, digits, inverse & decimal places,
decimal point, tenths, hundredths, thousandths
Key skills for addition at Y5:
Add numbers mentally with increasingly large numbers, using and practising a
range of mental strategies ie. add the nearest multiple of 10, 100, 100 and
adjust; use near doubles, inverse, partitioning and re-combining; using number
bonds.
-step problems in contexts, deciding which operations and methods
to use and why.
the value of each digit.
100 000.
Use column addition to add two or three whole numbers with up to 5 digits
Use column addition to add any pair of two-place decimal numbers including
amounts of money.
Begin to add related fractions using equivalences. (E.g. ½ + 1/6 = 3/6 + 1/6)
Choose the most efficient method in any given situation
Informal
Pupils will continue to use pencil and paper methods, e.g. number lines, to
support, record or explain calculations when necessary.
Formal
Add numbers with more than 4-digits, including money, measures and decimals
with different numbers of decimal places.
e.g. £23.59 + 7.55 = £31.14
£ 2 3 . 5 9
+
7 . 5 5
£ 3 1 . 1 4
1 1
1
1
+
2
1
2
+
2
3
1
4
4
3
8
1
8
6
4
9
3
0
3
1
.
.
.
.
0
6
7
3
1
5
0
6
1
2
3
The decimal point should be aligned in the
same way as other place value columns, and
must be in the same column in the answer
Pupils should be taught to cross through
the digits which have been carried over
in order that they are not forgotten!
Numbers should exceed 4-digits
They should add more than two values, carefully
aligning place value
Empty decimal places can be filled with a zero
to show the place value in each column
Say ‘6 tenths and 7 tenths to reinforce place
value’.
Children should understand the place value of tenths and hundreds and use this
to align numbers with different numbers of decimal places.
Year 6
Key vocabulary: add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units, partition, plus, addition,
column, tens boundary, hundreds boundary, increase, „carry‟, expanded,
compact, vertical, thousands, hundreds, digits, inverse, decimal places, decimal
point, tenths, hundredths, thousandths
Key skills for addition at Y6:
Perform mental calculations, including with mixed operations and large
numbers, using and practising a range of mental strategies.
-step problems in context, deciding which operations and methods
to use and why.
ulations and determine, in the context
of a problem, levels of accuracy.
value of each digit.
to add mentally with larger numbers and calculations of
increasing complexity.
Use column addition to add numbers with up to 5 digits.
Use column addition to add decimal numbers with up to 3-digits
inators.
2
5
9
2
3
9
9
1
3
1
.
.
.
.
.
3
0
7
3
5
2
6
8
7
0
1
1
0
0
0
1
0 0
Adding several numbers with different numbers of
decimal places (including money and measures).
 Tenths. Hundredths and thousandths should be
properly aligned, with the decimal point lined up vertically
including the answer row.
Empty decimal places can be filled with a zero
to show the place value in each column

Children must add several numbers with more than 4-digits.
By the end of year 6, children will have a range of calculation methods,
mental and written. Selection will depend upon the numbers involved.