Barwell Infant School
KS1 Calculation Policy
Barwell Infant School Calculation Policy
The following calculation policy has been devised to meet requirements of the National Curriculum 2014
for the teaching and learning of mathematics, and is also designed to give pupils a consistent and
smooth progression of learning in calculations across the school.
Age stage expectations
The calculation policy is organised according to age-related 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; being moved onto the next level as soon as they are ready, or working at a lower
stage until they are secure enough to move on.
Providing a context for calculation
It is important that any type of 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.
Choosing a calculation method
Children need to be taught and encouraged to use the following processes in deciding what approach
they will take to a calculation, to ensure they select the most appropriate method for the numbers
involved:
Can I do it in my head?
Can I draw some jottings to help me?
Do I need to get some equipment to help me?
Remember:
Estimate
Calculate
Check it mate!
Barwell Calculation Policy – Addition
Mental Strategies
Key Questions
Generalisations
Vocab
Notes & Guidance (NC 2014)
Statutory Requirements (NC 2014)
Year 1

Read, write and interpret mathematical statements
involving addition (+) and equals (=) signs

Represent and use number bonds within 20

Add one-digit and two-digit numbers to 20, including 0

Solve one-step problems that involve addition, using
concrete objects and pictorial representations, and missing
number problems such as 10 = 6 + 
Year 2

Solve problems with addition:

using objects and pictorial representations, including
those involving numbers, quantities and measures

applying their increasing knowledge of mental and
written methods

Recall and use addition facts to 20 fluently, and derive and
use related facts up to 100

Add numbers using concrete objects, pictorial
representations, and mentally, including:

a two-digit number and ones

a two-digit number and tens

two two-digit numbers

adding three one-digit numbers

show that addition can be done in any order (commutative)

Recognise the inverse relationship between addition and
subtraction and use this to check calculations and solve
missing number problems

Pupils memorise and reason with number bonds to 10 and
20 in several forms (for example, 9 + 7 = 16 and 16 = 7 + 9).

Pupils extend their understanding of the language of
addition to include sum and difference.

They should realise the effect of adding 0.
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Pupils combine and increase numbers, counting forwards.
Pupils practise addition to 20 to become increasingly fluent
in deriving facts (i.e. 3 + 7 = 10 to calculate 30 + 70 = 100).

They discuss and solve problems in familiar practical
contexts, including using quantities.

They check their calculations, including by adding to check
subtraction and adding numbers in a different order to
check addition.

Recording addition in columns supports place value and
prepares for formal written methods with larger numbers.
addition, add, forwards, put together, more than, total,
altogether, distance between, difference between, equals, same
as, most, pattern, odd, even, digit, counting on.
addition, add, more, plus, make, sum, total, altogether, equals, ,
is the same as, tens, ones, partition, near multiple of 10,
tens boundary, more than, one more, two more… ten more…

True or false - Addition makes numbers bigger?

Noticing what happens when you count in tens.

True or false - You can add numbers in any order and still
get the same answer?

odd+odd=even, even+even=even and odd+even=odd.

When introduced to the equals sign, children should see it
as signifying equality NOT as introducing the answer.

Show that addition of two numbers can be done in any
order (commutative).
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How many altogether?
How many more to make…?
I add …more. What is the total?
How many more is… than…?
How much more is…?
What number is one more/two more/ten more…
What can you see here?
What is the same/different?
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How many altogether?
How many more to make…?
How many more is… than…?
Is this true or false?
If I know that 17 + 2 = 19, what else do I know?
(e.g. 2 + 17 = 19; 19 – 17 = 2; 19 – 2 = 17; 190 – 20 = 170).
What do you notice?
What patterns can you see?

Children should experience regular counting on from
different numbers in 1s and in multiples of 2, 5 and 10.
Children should memorise and reason with number bonds
to 20, experiencing the = sign in different positions.
They should see addition and subtraction as related
operations; e.g. 7 + 3 = 10 is related to 10 – 3 = 7.
Children should have opportunities to explore partitioning
numbers in different ways; e.g. 7 = 6 + 1, 7 = 5 + 2, 7 = 4 + 3
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Children should experience regular counting on from
different numbers in steps of 2, 3, 5 and 10
Number lines should continue to be an important image to
support mathematical thinking; e.g. adjusting.
They should continue to see addition as both combining
groups and counting on.
As well as number lines, 100 squares should be used to
explore patterns in calculations, encouraging children to
think about ‘What do you notice?’
Barwell Calculation Policy – Addition
Year 1
Year 2
+ and = signs
Adding 9 or 11 (adjusting)
Children need to understand the concept of equality
(things being exactly the same) before using the = sign.
Calculations should be written either side of the equals sign
so that the sign is not just interpreted as ‘the answer’.
Adding 9 or 11 should be done by adding 10 and adjusting by 1;
e.g.
+ 10
15 + 9 =
15
15 + 10 - 1 = 24
24
25
-1
Counting and combining sets of objects
Partitioning in different ways and recombining
Combining two sets of objects (aggregation)
3+4=7
e.g. 47 + 25 = 72
Which will progress onto adding on to a set (augmentation)
Which will progress into exchanging:
Numicon should also be used at this stage
+
Understanding counting on with a number track
As well as continuing to practise counting on orally from a given
number, children use number tracks to count on; i.e.
Methods
3+4=7
0
1
2
3
4
5
6
7
8
9
Understanding counting on with a number line
3+4=7
10
Partitioning without equipment
Children should use partitioning to support adding two two-digit
numbers
43 + 26  40 + 20 = 60
3+6=9
60 + 9 = 69
Partitioning using a number line
Continue to use number lines to develop understanding of
counting on, including counting on in tens and ones.
As children become familiar with marked number lines, they
should move on to working on and drawing blank number lines.
Partitioning and place value
Use Dienes, Numicon and bundles of straws to model
partitioning teen numbers into tens and ones; i.e.
23 + 12 = 23 + 10
= 33 + 2
= 35
+ 10
+2
23
33
35
14 = 10 + 4
Partitioning and bridging through 10 on a number line
As addition often bridges through a multiple of 10, children
should be able to partition numbers to support this; e.g.
+5
+2
8+7=
8 + 2 + 5 = 15
8
10
15
Missing numbers
Missing number problems
Missing numbers need to be placed in all possible positions:
3+4=
=3+4
3+=7
7=+4
Missing numbers calculations become increasingly difficult; e.g.
14 + 5 = 10 + 
32 +  +  = 100
35 = 1 +  + 5
Barwell Calculation Policy – Subtraction
Read, write and interpret mathematical statements
involving subtraction (–) and equals (=) signs

Solve problems with subtraction:

Using objects and pictorial representations, including
those involving numbers, quantities and measures

Applying their increasing knowledge of mental and
written methods

Represent and use number bonds and related subtraction
facts within 20

Subtract one-digit and two-digit numbers to 20, including 0


Solve one-step problems that involve subtraction, using
concrete objects and pictorial representations, and missing
number problems such as 7 = – 9.
Recall and use subtraction facts to 20 fluently, and derive
and use related facts up to 100

Subtract numbers using concrete objects, pictorial
representations, and mentally, including:

a two-digit number and ones

a two-digit number and tens

two two-digit numbers

Show that subtraction cannot can be done in any order

Recognise the inverse relationship between addition and
subtraction and use this to check calculations and solve
missing number problems.

subtraction, subtract, take away, distance between, difference
between, more than, minus, less than, equals = same as, most,
least, pattern, odd, even, digit,
subtraction, subtract, take away, difference, difference between,
minus, tens, ones, partition, near multiple of 10, tens boundary
less than, one less, two less… ten less… one hundred less

True or false? Subtraction makes numbers smaller.

Noticing what happens when you count back in tens.

When introduced to the equals sign, children should see it
as signifying equality. They should become used to seeing it
in different positions.

odd – odd = even, even – even = even, odd – even = odd

Show that subtraction cannot be done in any order.

Recognise the inverse relationship between addition and
subtraction, and use this to check calculations and missing
number problems.
How many are left/left over? How many have gone?
How many fewer is… than…?
If I know that 9 – 2 = 7, what else do I know?
(e.g. 9 – 7 = 2 so 90 – 20 = 70 etc.)
What do you notice?
What patterns can you see?
Key Questions
Generalisations
Notes & Guidance (NC 2014)

Year 2
Vocab
Statutory Requirements (NC 2014)
Year 1
Pupils memorise and reason with number bonds to 10 and
20 in several forms (e.g. 16 – 7 = 9 and 7 = 16 – 9).

Pupils extend their understanding of the language of
subtraction to include difference.

They should realise the effect of subtracting 0.


They discuss and solve problems in familiar practical
contexts, including using quantities.
Pupils practise subtraction to 20 to become increasingly
fluent in deriving facts (i.e. 10 – 7 = 3 and 100 – 70 = 30)

They check their calculations, including by adding to check
subtraction.

Recording subtraction in columns supports place value and
prepares for formal written methods with larger numbers.
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How many are left/left over?
What number is one less, two less, ten less…
How many fewer is… than…?
How much less is…?
What can you see here?
Is this true or false?
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Children should experience regular counting back from
different numbers in 1s and in multiples of 2, 5 and 10.
Children should memorise and reason with number bonds
to 20, experiencing the = sign in different positions.
They should see addition and subtraction as related
operations, e.g. 7 + 3 = 10 is related to 10 – 3 = 7.
Children should begin to understand subtraction as both
taking away and finding the difference between numbers,
and should find small differences by counting on.
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Mental Strategies
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They should count regularly back in steps of 2, 3, 5 and 10.
Counting back in tens from any number should lead to
subtracting multiples of 10.
They should practise subtraction to 20 to become more
fluent, and use the facts that they know to derive others.
Children should learn to check their calculations, including
by adding.
They should continue to see subtraction as both take away
and finding the difference between numbers, and should
find a small difference by counting on.
Barwell Calculation Policy – Subtraction
Year 1
Year 2
Subtraction as ‘taking away’
Subtracting 9 or 11 (adjusting)
Children will continue to relate subtraction to ‘taking away’,
using objects to count ‘How many are left?’ after some have
been taken away.
Subtracting 9 or 11 should be done by subtracting 10 and then
adjusting by 1; e.g.
+1
35 - 9 =
7–4=3
25
24
35 - 10 + 1 = 24
35
- 10
Partitioning and ‘taking away’
Numicon should also be used at this stage:
e.g. 47 - 25 = 22
Understanding subtraction as counting back on a number track
NB With numbers that bridge the tens barrier, children will have
to learn to exchange a ‘ten’ for ‘ones’
As well as continuing to practise counting back orally from a
given number, children use number tracks to count back:
7-4=3
0
1
2
3
4
5
6
7
8
9
10
Partitioning using a number line
Continue to use number lines to develop understanding of
counting back, including counting back in tens and ones:
34 – 23 = 11
Understanding counting back with a number line
7-4=3
12
13 14
-1 -1
-1
24
34
Methods
11
- 10
- 10
This should then progress to more efficient methods:
It is crucial that children also understand subtraction as
meaning the difference between two numbers
14
34
11
7-4=3
-3
- 20
Finding the difference using a number line
To find the difference, children should practise counting on from
the lower number.
34 – 23 =
33
23
34
+ 10
+1
Difference:
10 + 1 = 11
Finding the difference using a number line
7-4=3
The strategies listed above should also be practised using a
hundred square
Working towards formal written methods
Recognising subtraction as the inverse of addition
47 – 25 =
tens
ones
Children should see addition and subtraction as related
operations (e.g. 7 + 3 = 10 is related to 10 – 3 = 7);
this understanding could be supported by an image like this:
-2=7
ones
7
5
20
2
Missing number problems
Missing number problems
9-=7
tens
40
- 20
2=-7
7=9-
As Year 1, plus
-=9
9=-
Barwell Calculation Policy – Multiplication

Vocab
Generalisations
Key Questions
Mental Strategies
Solve one-step problems involving multiplication by
calculating the answer using concrete objects, pictorial
representations and arrays with the support of the teacher.

Through grouping small quantities, pupils begin to
understand multiplication and doubling.

They make connections between arrays, number patterns,
and counting in twos, fives and tens.
Notes & Guidance (NC 2014)
Statutory Requirements (NC 2014)
Year 1
Year 2

Recall and use multiplication facts for the 2, 5 and 10
multiplication tables, including recognising odd and even
numbers

Calculate mathematical statements for multiplication and
write them using the multiplication (×) and equals (=) signs

Show that multiplication of two numbers can be done in
any order (commutative)

Solve problems involving multiplication using materials,
arrays, repeated addition, mental methods, and
multiplication facts, including problems in contexts.

Pupils use a variety of language to describe multiplication.

Pupils are introduced to the multiplication tables. They
practise to become fluent in the 2, 5 and 10 multiplication
tables and connect them to each other.
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They connect the 10x table to place value, and the 5x table
to the divisions on the clock face.
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They begin to use other multiplication tables and recall
multiplication facts perform written and mental
calculations.
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Pupils work with a range of materials and contexts in which
multiplication relates to grouping quantities, to arrays and
to repeated addition.
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They use commutativity and inverse relations to develop
multiplicative reasoning (i.e. 4 × 5 = 20 and 20 ÷ 5 = 4).
ones, groups, lots of, doubling, repeated addition, groups of,
times, columns, rows, times longer/bigger/higher etc. …times as
big/long/wide etc.
multiple, multiplication array, multiplication tables/facts,
groups of, lots of, times, columns, rows
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Understand that a quantity of counters can be arranged in
different arrays; e.g. 6 as 3+3 or 2+2+2
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Understand the commutative law of multiplication;
e.g. that 3x2 is the same as 2x3
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Understand that when counting in twos, the numbers are
always even.
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Understand that repeated addition can be shown on a
number line.
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Understand the inverse relationship between
multiplication and division.
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Use an array to explore how numbers can be organised
into groups.
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What do you notice?
What’s the same?
What’s different?
Can you convince me?
How do you know?
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Why is an even number an even number?
What do you notice?
What’s the same?
What’s different?
Can you convince me?
How do you know?

Children should experience regular counting on and back
from different numbers in 1s and multiples of 2, 5 and 10.
Children should memorise and reason with numbers in 2, 5
and 10 times tables.
Children should begin to understand multiplication as
scaling in terms of double and half. (e.g. that a tower of
cubes is double the height of the other tower).

Children should count regularly on and back in steps of 2, 3,
5 and 10.
Children should use a clock face to support understanding
of counting in 5s.
Children should use money to support counting in 2s, 5s
and 10s.
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Barwell Calculation Policy – Multiplication
Year 1
Year 2
Understanding doubling
Developing understanding
Initially, children should experience doubling practically by
combining two groups of equal quantity…
Children continue to develop their fluency in all of the methods
taught in Year 1.
Double 3 =
Using the 100 square to spot multiplication patterns
Children should use 100 squares to spot multiplication patterns
and enable them to make generalisations and predictions:
This will progress onto using standard equipment, such as
Numicon…
then jottings and, later, written calculations…
3 + 3 = 6
Multiplication as repeated addition
Using real life models to support multiplication
To introduce the notion of ‘times’, ask children to repeatedly
pick up (and add) the same amount a given number of times; i.e.
Children should be encouraged to use clock faces to support
counting in 5s
2x5=
Get 2…
Do it 5 times
and coins to support counting in 2s, 5s and 10s
3x4=
Methods
Pick up 3…
Do it 4 times
2x4=
5x3=
Jump on 5…
Do it 3 times
+5
0
+5
5
+5
10
5x4=
15
10 x 4 =
10 x 4 =
Add 10…
Do it 4 times
10+10+10+10 = 40
Multiplication arrays
Multiplication as scaling
Children should use objects to explore scaling; i.e. finding which
number is 2 or 3 times bigger, etc.
Children should experience seeing, creating and drawing arrays
to understand the commutative nature of multiplication
Using partitioning to support multiplication
Children should begin to use partitioning and jottings to multiply
by two-digit numbers; i.e.
14
5 x 14 =
10
X5
50
4
X5
20
50+20=70
(This will feed into the ‘grid method’ of multiplication in Year 3)
Barwell Calculation Policy – Division
Key Questions
Generalisations
Vocab
Notes & Guidance (NC 2014)
Statutory Requirements (NC 2014)
Year 1

Solve one-step problems involving division by calculating
the answer using concrete objects and pictorial
representations with the support of the teacher.

Recognise, find and name a half as one of two equal parts
of an object, shape or quantity.

Recognise, find and name a quarter as one of four equal
parts of an object, shape or quantity.
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Recall and use division facts for the 2, 5 and 10 tables,
including recognising odd and even numbers.

Calculate mathematical statements for division and write
them using the division (÷) and equals (=) signs.

Show that division of one number by another cannot be
done in any order.

Solve problems involving division, using materials, arrays,
repeated addition, mental methods, and multiplication and
division facts, including problems in contexts.

Recognise, find, name and write fractions 1/3, 1/4, 2/4 and
3/4 of a length, shape, set of objects or quantity.

Write simple fractions for example, 1/2 of 6 = 3 and
recognise the equivalence of 1/2 and 2/4.
Through sharing small quantities, pupils begin to
understand division and finding simple fractions of objects,
numbers and quantities.

Pupils use a variety of language to describe division.

Pupils begin to recall multiplication facts and use related
division facts to perform written and mental calculations.
They make connections between arrays, number patterns,
and counting in twos, fives and tens.

Pupils work with a range of materials and contexts in which
division relates to sharing quantities.

They begin to relate these to fractions and measures
(i.e. 40 ÷ 2 = 20 so 20 is a half of 40).

They use commutativity and inverse relations to develop
multiplicative reasoning (e.g. 4 × 5 = 20 and 20 ÷ 5 = 4).
share, share equally, one each, two each…, group, groups of,
lots of, array
group in pairs, 3s … 10s etc. equal groups of, divide, ÷,
divided by, divided into, remainder

True or false? I can only halve even numbers.
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Grouping and sharing are different types of problems.
Some problems need solving by grouping and some by
sharing. Encourage children to practically work out which
they are doing.
Noticing how counting in multiples relates to the number
of groups you have counted (introducing times tables).

An understanding of the more you share between, the
fewer each person will get (e.g. would you prefer to share
these grapes between 2 people or 5 people? Why?)

Secure understanding of grouping means you count the
number of groups you have made. Whereas sharing means
you count the number of objects in each group.
How many 10s can you subtract from 60?
I think of a number and double it. My answer is 8.
What was my number?
If 12 x 2 = 24, what is 24 ÷ 2?
Questions in the context of money and measures;
e.g. How many 10p coins do I need to have 60p?
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How many groups of…?
How many in each group?
Share… equally into…
What do you notice?
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Children should experience regular counting on and back
from different numbers in 1s and multiples of 2, 5 and 10.
They should begin to recognise the number of groups
counted to support understanding of relationship between
multiplication and division.
Children should begin to understand division as both
sharing and grouping.
Children should begin to explore finding simple fractions of
objects, numbers and quantities; e.g.
“16 children went to the park at the weekend.
Half that number went swimming.
How many children went swimming?”
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Mental Strategies
Year 2
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Children should count regularly on and back in steps of 2, 3,
5 and 10.
Children who are able to count in 2s, 3s, 5s and 10s can use
this knowledge to work out other facts such as 2 × 6, 5 × 4.
Show the children how to hold out their fingers and count,
touching each finger in turn [for 2 × 6 (six twos), hold up 6
fingers]. This can then be used to support finding out ‘How
many 3s are in 18?’ as children count along fingers in 3s,
making the link between multiplication and division.
Use children’s intuition to support understanding of
fractions as an answer to a sharing problem;
i.e. 3 apples shared between 4 people = ¾
Barwell Calculation Policy – Division
Year 1
Year 2
Children must explore division through practical activities with
concrete apparatus involving BOTH sharing and grouping
with the support of the teacher
Children should continue to develop their understanding and
independent application of grouping AND sharing for division,
using practical apparatus, arrays and pictorial representations
Division as sharing
Using the inverse operation
Sharing will be the most familiar approach to division.
These activities may be in the form of questions such as,
“If 5 friends share 15 sweets, how many do they get each?”
Children should begin to see how multiplication and division are
closely related, and should start to use inverse operations to
solve and check calculations.
15  5 =
i.e. When asked “How many 3s are there in 15?” they count
jumps of three on their fingers until they reach 15 (recognising
that the number of fingers represents the number of groups
counted).
Division as grouping
Initially children use concrete apparatus to solve problems
involving grouping, before moving onto simple jottings.
These activities may be in the form of questions such as,
“If there are 15 children in the class, how many groups of 3 can
the teacher make?”
Grouping using a number line
Once children are familiar with the relationship between
multiplication and division, they can perform grouping on a
number line, counting from 0 in jumps of the specified amount.
This enables them to solve problems involving multiplication
tables which they are not yet familiar with; i.e.
Methods
32  8 =
0
8
16
24
32
Grouping using Numicon
Division and fractions
Numicon provides a very tactile/visual method for grouping; i.e.
Children should explore dividing groups and small quantities in
different ways so that they can see the equivalence of
1/2 and 2/4
18  6 =
Division using arrays
Children should also be encouraged to use and begin to create
arrays to help them solve division problems; i.e.
“How many 3s are there in 6?”
1
2
Use children’s intuition to support understanding of fractions as
an answer to a sharing problem; i.e.
Division and fractions
Children should use pictorial aids to explore finding ½ and ¼ of
shapes and numbers, recognising that ½ is the same as
dividing by 2 and that ¼ is the same as dividing by 4
There were 12 children. ¼ of them
went swimming. How many was this?
3 apples shared between 4 people =
 3 apples
 divided by
 4 people