DOVEDALE PRIMARY SCHOOL CALCULATION POLICY
This policy focuses on the four operations of addition,
subtraction, multiplication and division and includes a list
of the key mental maths skills that support written
methods.
The bar Model must be taught as a specific skill to solve problems!
ADDITION:
There are some key basic skills that children need to help
with addition, which include:

counting

estimating

recalling all addition pairs to 10, 20 and
100 (7 + 3 = 10, 17 + 3 = 20, 70 + 30 =
100)

knowing number facts to 10 (6 + 2 = 8)

adding mentally a series of one-digit
numbers (5 + 8 + 4)

adding multiples of 10 (60 + 70) or of 100
(600 + 700) using the related addition fact,
6 + 7, and their knowledge of place value

partitioning
two-digit and
three-digit
numbers into multiples of 100, 10 and 1 in
different ways (432 into 400 + 30 + 2 and
also into 300 + 120 + 12)

understanding and using addition and
subtraction as inverse operations
Using and applying is a key theme and one of the aims of
National Curriculum and before children move onto the
next stage in written calculation it is important that their
skills are broadened through their use and application in a
range of contexts, these include:
 using inverse
 missing box questions
 using units of measure including money and time
 word problems
 open ended investigations
To Develop Conceptual Understanding
Y1 – Using Numicon/practical apparatus (include money):
1. Count all objects
2. Count on…
3. Use of a number track to count on
Y2 – Using Numicon/practical apparatus if required (include money
and some measures):
1.
2.
3.
4.
5.
Use of a number line to count on
Count in tens, then bridge
Round, add and adjust
Partition and recombine using base ten
Jottings to solve problems
Y3 - Using Numicon/practical apparatus if required (include money
and measures):
1. Use of a number line (pupils must be taught to use efficient jumps)
2. Round, add and adjust e.g. 243 + 198 - + 200, then -2
3. Place value counters to support e.g. 264 + 158 use 100s, 10s, 1s in a place
value grid
4. Jottings to solve problems
Y4 – Use of place value counters/base ten to support if required
(include money and measures):
1. Formal written methods with up to 4 digits – with place value counters
alongside the calculations
2. Formal written methods – pupils must be able to explain each step
demonstrating a secure understanding of place value
3. Formal written methods to solve problems
Y5 – Use of place value counters/base ten to support if required
(include money, measures and decimals with a different numbers
of decimal places):
1. Formal written methods with more than 4 digits – with place value counters
alongside the calculations
2. Formal written methods – pupils must be able to explain each step
demonstrating a secure understanding of place value
3. Formal written methods to solve multi-step problems
Y6 - Use of place value counters/base ten to support if required
(include money, measures and decimals with a different numbers
of decimal places):
1. Formal written methods with more than 4 digits in multi-step problems– with
place value counters alongside the calculations
2. Formal written methods to solve complex multi-step problems – pupils must
be able to explain each step demonstrating a secure understanding of place
value
Please refer to the stages below for examples.
Stage 1: Practical (combining) and adding on (increasing)
Prior to recording addition steps on a number line, children will w
practically with equipment where they are combining sets of objects.
they become more confident, this practical addition of sets of objects will
mirrored on a number line so that the two are being done together a
children are adding on. This will prepare them for the abstract concept
adding numbers rather than objects
 Combining two or more sets of objects up to 10
 Add using a numberline up to 10 and beginning to record
 Add by counting on up to 10 without a numberline
Stage 2: Number tracks, number lines and 100 squares
Steps in addition can be recorded on a number line. The steps often brid
through a multiple of 10. Steps can be recorded from left to right on
number line or in a vertical movement (down) and horizontal movem
(right) on a 100 square
With practise, children will need to record fewer jumps
2: Number tracks and numbed number lines
PLACE VALUE MUST BE FULLY SECURE (KNOWLEDGE
OF DIGIT VALUES IN 2-DIGIT NUMBERS) BEFORE
CHILDREN ARE INTRODUCED TO STAGE 3
Stage 3: Partitioning
 Partition both numbers into tens and units or hundreds, tens and unit
 Partitioning up to 50 – no bridging
+10
35
45
This
builds
on
children’s mental maths
skills of partitioning
and recombining
 Partitioning up to 100 – with bridging
 Counting on from the largest number (in known multiples)
48 + 20 (+10, +10) = 68
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57
58
59
60
61 62 63 64 65 66 67
68
69
70
71 72 72 74 75 76 77
78
79
80
68 + 5 = 73
4
As soon as children are secure in partitioning to add and recombine then
they should be able to work with larger numbers using the same method
148 + 25 = 173
Stage 4: Column (short method)
33
+22
______
55
48
+36
236
+ 148
__1______
___1_____
84
Children should be encou
estimate their answers first
384
Column addition remains efficient when used with larger whole numbers
decimals, and when adding more than two numbers, once learned,
method is quick and reliable
 Place Value headings must be in upper case for tens and units- T U
 1 digit per square, double line for answer
T U
3 3
+ 2 2
5 5
SUBTRACTION:
There are some key basic skills that children need to help
with subtraction, which include:
 counting
 estimating
 recalling all addition pairs to 10, 20 and
100 along with their inverses (7 + 3 = 10,
10 – 3 = 7, 17 + 3 = 20, 20 – 3 = 17, 70 +
30 = 100, 100 – 30 = 70)
 knowing number facts to 10 and their
inverses ( 6 + 2 = 8, 8 - 2 = 6)
 subtracting multiples of 10 (160 - 70) using
the related subtraction fact, 16 - 7, and
their knowledge of place value
 partitioning
two-digit and
three-digit
numbers into multiples f 100, 10 and 1 in
different ways (432 into 400 + 30 + 2 and
also into 300 + 120 + 12)
 understanding and using subtraction and
addition as inverse operations
Using and applying is a key theme and one of the aims of
National Curriculum and before children move onto the
next stage in written calculation it is important that their
skills are broadened through their use and application in a
range of contexts, these include:
 using inverse
 missing box questions
 using units of measure including money and time
 word problems
 open ended investigations
To Develop Conceptual Understanding
Y1 – Using practical apparatus (include money):
1. Count on, then count how many are left
2. Count back on a number track/number line
3. Find the difference between using Numicon
Y2 – Using practical apparatus if required (include money and
some measures:
1. Using a number line to subtract
2. Find the difference between by counting up on a number line/jotting of a
number line
3. Taking away and exchange using place value counters/base ten
4. Jottings to solve problems
Y3 – Using place value counters/base ten if required alongside the
calculation (include money and measures):
1. Taking away and exchange using place value counters/base ten
2. Jottings to solve problems
Y4 – Use of place value counters/base ten to support if required
(include money and measures):
1. Formal written methods with up to 4 digits – with place value counters
alongside the calculations
2. Formal written methods – pupils must be able to explain each step
demonstrating a secure understanding of place value
3. Formal written methods/jottings to solve problems
Y5 – Use of place value counters/base ten to support if required
(include money, measures and decimals with different number of
places):
1. Formal written methods with more than 4 digits – with place value counters
alongside the calculations
2. Formal written methods – pupils must be able to explain each step
demonstrating a secure understanding of place value
3. Formal written methods to solve multi-step problems
Y6 - Use of place value counters/base ten to support if required
(include money, measures and decimals with a different numbers
of decimal places):
1. Formal written methods with more than 4 digits in multi-step problems– with
place value counters alongside the calculations
2. Formal written methods to solve complex multi-step problems – pupils must
be able to explain each step demonstrating a secure understanding of place
value
Please refer to the stages below for examples.
Stage 1: Practical (taking away)
Prior to recording subtraction steps on a number line, children will wor
practically with equipment where they are ‘taking away’ a small group from
a larger set of objects. As they become more confident, this practica
subtraction will be mirrored on a number line so that the two are bein
done together. This will prepare them for the abstract concept o
subtracting numbers rather than objects
 Taking away objects from a set up to 10
 Subtract using a numberline up to 10 and beginning to record
 Subtract by counting back up to 10 without a numberline
Stage 2: Number tracks, number lines and 100 squares (Partitioning)
 Counting back (to be introduced before counting up) in multiples
 Subtract by counting back up to 20 with a numberline
 Partitioning using a numberline or 100 square
 Steps in subtraction can be recorded from right to left on a numbe
line or in a vertical movement (up) and horizontal movement (left) o
a 100 square
-30
18
74 – 27 = 47
74 – 20 = 54
54 – 7 = 47
50
20
-7
-20
47
54
74
Stage 3: Finding the Difference (Partitioning)
Counting up to find the difference when larger numbers are close togethe
particularly when carrying out money calculations that involve findin
change.
93 – 79 = 14
+10
79
89
93
Stage 4:
Column (short method)
Children should be encouraged
estimate their answers first
Column subtraction remains efficient when used with larger whol
numbers or decimals, once learned, the method is quick and reliable.

Column subtraction TU with exchanging Ts work alongside partitioning if required

Column subtraction HTU with exchanging Ts

Column subtraction HTU with exchanging Hs and Ts

Column subtraction of decimals to 1d.p.

Column subtraction of decimals to 2d.p.
ENSURE THAT CHILDREN NEVER USE THE
TERM
‘BORROWING’
–
THIS
IS
MATHEMATICALLY
INCORRECT.
THE
CORRECT TERMINOLOGY IS ‘EXCHANGING’
WHICH REINFORCES THE UNDERSTANDING
OF PLACE VALUE.
MULTIPLICATION:
There are some key basic skills that children need to help
with multiplication, which include:
 counting
 estimating
 understanding multiplication as repeated
addition
 recalling all multiplication facts to 12 × 12
 partitioning numbers into multiples of one
hundred, ten and one
 working out products (70 × 5, 70 × 50,
700 × 5, 700 × 50) using the related fact
7 × 5 and their knowledge of place value
 adding two or more single-digit numbers
mentally
 adding multiples of 10 (60 + 70) or of 100
(600 + 700) using the related addition fact,
6 + 7, and their knowledge of place value
 adding combinations of whole numbers
 understanding and using division and
multiplication as inverse operations
Using and applying is a key theme and one of the aims of
National Curriculum and before children move onto the
next stage in written calculation it is important that their
skills are broadened through their use and application in a
range of contexts, these include:
 using inverse
 missing box questions
 using units of measure including money and time
 word problems
 open ended investigations
To Develop Conceptual Understanding
Y1 – Using concrete objects, pictorial representations and practical
apparatus:
1. Count in 2s, 5s, 10s e.g. 2 frogs on each lily pad
2. Count in 2s, 5s, 10s with a hundred square if required
Y2 – Using Numicon, practical apparatus, pictorial representations
and arrays if required:
1. E.g. 5 frogs on each lily pad 5 X 3 = 15
2. Link to repeated addition with concrete apparatus, pictorial
representation or an array
3. Children to draw their own arrays
Y3 – Using concrete apparatus or Numicon if required:
1. Repeated addition using a number line (if required)
2. Commutativity
3. Introduce the grid method alongside concrete apparatus
4. Partitioning e.g. If I know 10 X 3 = 30, 13 X 3 = 10X3 + 3X3
Y4 – Using concrete apparatus or Numicon if required:
1. Commutativity
2. Partitioning e.g. If I know 10 X 3 = 30, 13 X 3 = 10X3 + 3X3
3. Develop the grid method
4. Introduce column method (if appropriate)
Y5 – Using concrete apparatus or Numicon if required:
1. Commutativity e.g. If I know 4 x 6, then 0.4 x 6 is ten times smaller
and 0.4 x 0.6 is ten times smaller again
2. Partitioning e.g. If I know 10 X 3 = 30, 20 X 3 = 60, so 23 x3 =
20X3 + 3X3
3. Introduce column method (or embed if covered in Y4)
4. X decimals
Y6 - Using concrete apparatus or Numicon if required:
1. As above
2. Multiplying 4-digit by a 2-digit number
Please refer to the stages below for examples – include money
and measures.
Stage 1: Practical (repeated addition)
Children will work practically with equipment grouping objects to see
multiplication as repeated addition. As they become more confident, this
practical grouping of objects will be mirrored on a number line using the
vocabulary ‘lots of’, ‘groups of’, ‘how many lots’, ‘how many times’ so that
the two are being done together. This will prepare them for the abstract
concept of multiplying numbers rather than objects
This image can be expressed as:
 2 multiplied by 5
 Two, five times
 5 groups of 2
 5 lots of 2
 5 jumps of 2 on a number line
Stage 2: Practical and pictorial arrays (towards grid method)
Children use arrays to demonstrate
commutativity for multiplication facts
their
understanding
Children use their knowledge
of
known
multiplication
tables
7 x 3 = 21
This 3 x 7 array
can also be seen as
3 x 5 add 3 x 2
3 x 7 = 21
Stage 3: Partitioning
 Partitioning x by 2, 3, 4 and 5
24 x 3 = 72
20 x 3 = 60
4 x 3 = 12
60 + 12 = 72
of
Stage 4: Grid method
24 x 3 = 72
24 x 32 = 768
Stage 5: Column method (short)
 To be used only for multiplying by a unit (TUxU, HTUxU, ThHTUxU)
24 x 3 = 72
241 x 3 = 723
Stage 6: Column method (long)
1241 x 3 = 3723
24 x 32 = 768
1245 x 13
In the examples given, it is also
correct to multiply starting with the
tens digit (i.e. multiplying by the
To Develop Conceptual Understanding - Division
Y1 – Using concrete objects and practical apparatus:
1. Practical sharing into groups
Y2 – Using concrete objects and practical apparatus:
1. Practical sharing into groups using the language of division
2. Link to fractions
3. Use language of division linked to X tables
4. Counting along a number line e.g. how many 2s?
Y3 – Using concrete objects and practical apparatus if required:
1. Grouping using partitioning
2. Use language of division linked to X tables
3. Counting along a number line e.g. how many 4s?
Y4 – Using concrete objects and practical apparatus if required:
1. Grouping using partitioning
2. Chunking method
3. Use language of division linked to X tables
4. Introduce the short division method (if secure)
Y5 – Using concrete objects and practical apparatus if required:
1. Consolidate chunking method
2. Introducing short division carrying and remainders (including
remainders expressed as a fraction and a decimal)
3. Solve multi-step problems
Y6 – Using concrete objects and practical apparatus if required:
1. Consolidate short division and chunking carrying and
remainders (including remainders expressed as a fraction and a
decimal)
2. Solve complex multi-step problems
Please refer to the stages below for examples – include money
and measures.
There are some key basic skills that children need to help
with division, which include:
 counting
 estimating
 understanding division as repeated
subtraction
 partitioning two-digit and three-digit
numbers into multiples of 100, 10 and 1 in
different ways (432 into 400 + 30 + 2 and
also into 300 + 120 + 12)
 recalling multiplication and division facts to
12 × 12
 recognising multiples of one-digit numbers
and dividing multiples of 10 or 100 by a
single-digit number using their knowledge
of division facts and place value
 knowing how to find a remainder working
mentally, for example, find the remainder
when 48 is divided by 5
 understanding and using division and
multiplication as inverse operations
Using and applying is a key theme and one of the aims of
National Curriculum and before children move onto the
next stage in written calculation it is important that their
skills are broadened through their use and application in a
range of contexts, these include:
 using inverse
 missing box questions
 using units of measure including money and time
 word problems
 open ended investigations
Division
Stage 1: Practical (sharing)
 Sharing using objects between 2 and 4 leading to ½ and ¼
 Children will work practically with equipment sharing objects
one to one
1
2
3 4
1 2 3 4
1 2 3 4
12 cakes are shared equally between 3 people
 Using pictures and objects e.g. 12 divided by 3
Stage 2: Number lines (grouping)
Children will move from sharing objects practically to grouping them,
this will be mirrored on a number line, working from right to left so that
they see division as repeated subtraction. This will prepare them for
the abstract concept of dividing numbers rather than objects.
Each cake box holds 3 cakes, if I have 12 cakes, how many cake
boxes will I need?
How many times can I subtract 3
Using their knowledge of the inverse relationship between
multiplication and division, children can use their multiplication tables
when grouping on a number line, working from left to right.
How many groups of 3 are there in
First without and then with remainders and ensuring that divisors offer
an appropriate level of challenge.
Stage 3: Short division
 Short division method with carrying
372 ÷ 3 = 124
 Short division method with carrying and remainders (includ
remainders expressed as a fraction and a decimal)
78 ÷ 5 = 15 3/5
78 ÷ 5 = 15.6
Stage 4: Long division
432 ÷ 15 = 28 r12
28 r4/5
28.8
With long division, there is
the opportunity to teach an
expanded method first (i.e.
chunking).