CALCULATION POLICY – ADDITION AND SUBTRACTION
Foundation
Stage
Aim by end of
year:
- All can move
(count on or back)
up to 10 spaces
on a number
track.
-Some can add
two 1 digit
numbers showing
method used.
-All can subtract
small numbers by
taking away using
apparatus.
-Some can
discuss difference
mathematically
.
Addition
Subtraction
Make own marks or tallies to record numbers.
Begin to relate addition to combining two groups of
objects and counting on.
Adult to model number sentences in context.
Begin to relate subtraction to taking objects away from
a group and counting what is left. Find own way of
recording for subtraction e.g. cross-outs.
Begin to record numbers and number sentences, when
ready.
3 + 2 = 5
Select two groups of objects to make a given total
e.g. Find dominoes with 6 dots on.
Adults scribe number sentences.
◦
2+4=6
1+5=6
Adults model use of number tracks and number lines.
1
2
3
4
5
6
7
8
9
10
4+2=6
Find own way of recording for addition. Using
pictures, symbols, apparatus e.g.
3
5
2
5
Sing nursery rhymes and simple songs.
Solve practical problems in a real or role play context
and talk about own ideas, methods and solutions.
E.g. Sarah wants 3 grapes and you want 4 grapes. How
many grapes do I need altogether?
Year 1
Aim by end of
year:
-All can add two
1 digit numbers
-Some can add a
1 digit number to
a 2 digit number
Showing method
used.
-All can count
Relate addition to combining two groups and counting
on and record in a number sentence using + and =
signs.
Record addition by:
- showing jumps on prepared number lines
- drawing own number line
e.g. 6 + 5 = 11
6
7
8
9
7–2=5
Children record number sentences related to practical
work, when ready.
Experience subtraction in the context of counting back
along a number track
e.g. jumping backwards two jumps along a floor number
track game.
Adults model use of number tracks and number lines.
Use a number track to find one more than a number.
Say the number one more than when playing a board
game.
Experience addition as counting on, e.g. rolling a dice
and moving along a number track when playing snakes
and ladders.
Children to work practically with bead bars and bead
strings.
Number tracks and number lines to be available for
children to use in free flow activities.
3 and 2
Adults to model recording. (After practical work, in
context and in conjunction with apparatus).
10
Page 1
11
1
2
3
4
5
6
7
8
9
10
6–2=4
Use a number track to find one less than a number.
Children to work practically with bead bars and bead
strings.
Number tracks and number lines to be available for
children to use in free flow activities.
Start to develop the concept of difference by
comparing objects by the number in two sets or in the
context of measures and saying if they are the same or
different e.g.

number of sweets in different size jars.
or

when playing with cars make two rows and discuss
that the row of 12 cars is longer than the row of 8
cars. “Can you make them the same length? How?”
Sing nursery rhymes, involving something being taken
away in each verse e.g. 5 little men in a flying saucer.
Solve practical problems in a real or role play context
and talk about own ideas, methods and solutions
e.g. In a play shop put 10 pennies in a purse, pay for
something and say how much money they have left
Relate subtraction to taking away by counting back and
as counting on and record in a number sentence using
the – and = signs.
Record simple subtraction in a number sentence using
the – and = signs e.g.
There were 8 cakes on a plate. Mary ate 3 of them.
How many were left?
8–3=5
May 2009
CALCULATION POLICY – ADDITION AND SUBTRACTION
back on a number
line to subtract 1
digit numbers
from a 1 or 2
digit number.
-Some can count
on when the
difference is
small.
Addition
Subtraction
Using the empty number line to add 10 to a single
digit number.
e.g. 8 + 10 = 18
+10
Use objects to develop idea that the number of objects
started with and those taken away can be represented
by a subtraction calculation.
8
18
Use a number line to add a pair of single digit
numbers to bridge through 10 e.g.
8 + 5 = 13
Model this
strategy.
2 3
+2
+3
8
10
13
(see Framework – section 5 p.40)
Shows 9 + 1 + 5 = 15
or
9 + 6 = 15
Bridge through a multiple of 10 e.g. add a single digit
to a teen’s number bridging through 20.
18 + 5 = 23
2
10
15
Or record as:
18 + 5 = 18 + 2 + 3
= 20 + 3
= 23
3
+2
18
+3
20
23
1 2 3
4
5
6
7 8
9 10 11 12
What is the difference between 5 and 12?
on) – marked line
1 2 3 4
Represent number line calculations in a number
sentence
e.g.
+1
+5
9
Use a marked or empty number line to count back (take
away) or to count on (find the difference) e.g.
12 – 7 (counting back) - marked line
5
6
(counting
7 8 9 10 11 12
What is the difference between 5 and 12? (counting on)
– empty line
5
12
Children need to begin to understand when it is sensible
to count back e.g. 18 – 5
13
14
15
16
17
18
And when it is sensible to count on e.g. 18 – 13
13
14
15
16
17
18
Say the number that is one more than any given
number and ten more than a multiple of ten.
Add 9 by adding 10 and subtracting 1.
Say the number that is 1 less than any given number or
10 less than a multiple of 10.
Find the difference between two numbers by comparing
them using apparatus or on number lines
e.g. What is the difference between 4 and 7?
17 + 9
With cubes:
+ 10
17
26
-1
Partition numbers using place value cards
1
7
How many
more?
27
10
7
17
=
10
+
7
And use calculator to confirm that numbers such as
57 are made up of 50 and 7 to develop their
understanding of place value.
Be able to complete number sentences where a
missing number is shown by a symbol e.g.
5+2= ∆
∆ =5+2
5+∆=7
7=∆+2
∆ + 2 =7
7=2 +∆
etc.
Generate equivalent calculations for given numbers
and record e.g. 6 =2 + 4 = 1 + 5 = 3 + 3
Page 2
or on two number lines:
4
7
or on one number line:
4
7
Be able to complete number sentences where a missing
number is shown by a symbol e.g.
6-2=∆
∆ =6-2
6-∆=4
4=∆-2
∆ -2=4
4=О-∆
etc.
May 2009
CALCULATION POLICY – ADDITION AND SUBTRACTION
Year 2
Aim by end of
year:
-All can add 1
digit number to a
2 digit number.
-Some can add
two 2 digit
numbers showing
method used.
-All can use a
number line to
subtract 2 digit
numbers
-Some can
subtract numbers
that cross 100.
Addition
Subtraction
Derive and recall pairs of numbers with a total of 10
and addition facts for totals to at least 5.
Solve simple problems explaining methods and
reasoning orally or in pictures in the context of
measures or money.
Use the language of addition accurately. Read 19 + 15
= 34 as nineteen add fifteen equals 34. Decide the
best strategy for addition: put the larger number
first and count on; look for numbers that total 10 or
20; partition and recombine.
Use prepared number lines then progress on to
drawing own empty number lines to: e.g.
Solve simple problems involving subtraction in the
context of measure or money explaining reasoning
orally or in pictures
e.g. This bottle holds 5 cups of water but this bottle
holds 7 cups. How much more is in the bigger bottle?

count in tens 23 + 20
+10
+10
23

33
Use marked, partly marked or empty number lines to
count back (take away) or to count on (find the
difference) – as Y1. Understand when it is sensible to
count back and when to count on. e.g.

93 – 5 (count back) 93 - 88 (count on)
88
43
count in multiples of ten
+20
27 + 20
93
Use number lines or jottings to count back.
76 – 15
27
47
-5
To add tens and units by partition second number
(not crossing the tens or hundreds barrier) using
different methods of recording:

Use language of subtraction accurately. Read 16 – 4 =
12 as sixteen subtract 4 equals twelve.
number line 45 + 13 =
+10
+3
-10
61
66
76
Record in number sentences : 76 – 10 = 66
66 – 5 = 61
Bridge through multiple of 10 when counting back.
45
55
Record in number sentences
45 +10 = 55 55 + 3 = 58

-4
Lead to partitioning
- second number only.
35 + 20 + 3
55 + 3 = 58
50 + 8 = 58
Bridge through a multiple of 10, explaining
method
16 + 7 = 23
4
16
+4
46
-1
50
-20
51
71
Record in number sentences: 71 -20 = 51
51 – 1 = 50
50 – 4 = 46
Subtract 1 or 10 from any given number.
using drawing
= 50
35 + 23
=8

71 – 25
not using number line, partitioning both numbers
35 + 23
30 + 20 = 50
5+ 3=8
50 + 8 = 58

58
3
Count on to the nearest 10.
23 – 18 = 5
+2
+3
18
20
23
Develop into calculations that count on in three jumps.
+3
20
Relate finding a difference to subtraction.
Understand difference is the same as subtraction and
work out small differences by counting on.
23
or record as
16 + 7 = 16 + 4 + 3
= 20 + 3
= 23
91 – 65 (counting on)
+5
65
Page 3
+20
70
+1
90
= 26
91
May 2009
CALCULATION POLICY – ADDITION AND SUBTRACTION
Addition
Subtraction
Add 1 or 10 to any given number.
Add 19 or 21 by adding 10 and adjusting.
e.g. 27 + 19 = 27 + 20 -1
= 47 -1
= 46
Using partitioning (second number only)
-not crossing 10
-crossing 10
48 – 23 = 48 – 20 – 3
73 – 25 = 73 -20 - 5
= 28 – 3
= 53 - 5
= 25
= 48
Or using empty number line
+20
27
46
-1
47
Subtract 9 or 19, by subtracting 10 or 20 and
adjusting.
E.g. 45 – 9 = 45 – 10 +1
= 35 +1
= 36
0r using empty number line
-10
35
Year 3
Aim by end of
year:
-All children add
two 2 digit
numbers.
-Some can add 2
and 3 digit
numbers, showing
method used.
-All children
should be able to
use a method to
subtract 2 and 3digit numbers.
-Some should be
able to use
expanded
decomposition as
shown.
Use knowledge of facts to identify missing numbers
in sentences.
9 + ∆ = 13
∆+ 4 = 13
∆ + ◊ = 13
40 +  = 100
 +200 = 400 etc
Extend to 3 numbers:
and:
5 + ∆ + 4 = 13
13 + 5 = ∆ + 10
50 + ∆ + 3 = 73
12 + ∆ = 14 + 4 etc
13 = ∆+ ◊+ 3 etc
Generate equivalent calculations for a given number.
e.g. 20
20 = 10 + 10 = 11 + 9 etc
Derive and recall all addition facts for each number
to at least 10, all pairs which total 20 and multiples of
10 with totals up to 100.
Solve problems involving addition in contexts of
measures or pounds and pence explaining methods and
reasoning orally and where appropriate in pictures and
writing.
Use of mathematical vocabulary is more precise.
Develop methods for adding two digit and three digit
numbers by partitioning second number only.
246 + 87
246 + 80 + 7 or 246 + 7 + 80
leading to:
= 756 + 20 +7
= 776 + 7
= 783
Use knowledge of place value and partitioning of
three digit numbers to develop written methods for
addition of two and three digit numbers using
expanded methods of recording.
375 + 67
300
70
+
60
300 130
5
7
12 = 442
Solve problems involving subtraction in contexts of
measures or pounds and pence explaining methods and
reasoning orally and where appropriate in pictures and
writing
e.g. In the sales my coat was reduced from £15.50 to
£12.99. What was the difference in price?
Use of mathematical vocabulary is more precise.
Use a number line to count back alongside an informal
written method.
246 -47
-7
199
-40
206
246
246 – 40 = 206
206 - 7 = 199
Begin to record calculations in preparation for an
efficient standard method.
Expanded decomposition (see Framework – section 5
p45)
E.g. 81 – 57
leading to:
81
- 57
Page 4
45
+1
Use knowledge of facts to identify missing numbers in
number sentences.
13 - ∆ = 9
∆-4 =9
∆ - ◊= 9 etc
Extend to:
13 + 5 = ∆ - 10 etc
356 + 427 = 356 + (400 + 20 + 7)
First step:
356 + 400 =756
756 + 20 = 776
776 + 7 = 783
36
81 and 1 = 70 and 11
50 and 7 = 50 and 7
20 and 4
= 24
May 2009
70
1
80 1
50 7
20 4 = 24
CALCULATION POLICY – ADDITION AND SUBTRACTION
Addition
67
+ 24
80
11
91
83
+ 42
120
5
125
Subtraction
Add most significant
digits first.
Add mentally from top.
This leads onto most
significant digits first.
Bridge through a multiple of 10 to add, explaining
method e.g.
68 + 7
2
5
= 68 + 2 + 5
= 70 + 5
= 75
Add 1, 10 or 100 to any given number.
Add a near multiple of 10 to a two digit number and
show on a number line e.g.
45 + 28
+30
45
73
-2
75
Count up when the difference is small (complementary
addition) (Framework - Section 5 p45)
e.g. 216 -187
+13
+16
= 29
187
200
216
216
- 187
13 to make 200
16 to make 216
29
Subtract 1, 10 or 100 from any given number.
Subtract a near multiple of 10 from a 2-digit number,
explaining the method used
e.g. 96 – 39 = 96 – 40 +1
= 56 +1
= 57
or
-40
56
Apply understanding of inverse relationship between
addition and subtraction to generate pairs of
statements to find unknowns in number sentences.
4 + ∆ = 33
33 – 4 =
Use knowledge of number facts to find unknowns.
347 + ∆ = 447
Use 3 numbers e.g.
10 + ∆ + 50 = 100
∆ + ◊ + O = 100
Recall pairs of numbers with totals of 100 and
addition facts for totals to at least 20.
Solve problems explaining methods and reasoning
orally and where appropriate in pictures and writing,
in the context of measures money and time.
Year 4
Aim by end of
year:
-All can use an
efficient written
method to add
and subtract 2
and 3 digit whole
numbers and £.p.
but continue to
use counting up
method where
appropriate.
Note: ‘compact’
method is not
appropriate for
adding two 2-digit
numbers – this is a
mental method.
Use symbols and missing numbers:Continue to develop as in Y1, 2 and 3 but with
appropriate numbers. Develop use of empty number
lines, partitioning and other informal recording
methods developed in Y1,2 and 3 to support and
explain calculations where appropriate e.g.

146 +29
+30
146

175
-1
176
548 + 235
548 + 235 = 548 + 200 + 30 + 5
= 748 + 30 + 5
= 778 + 5
= 783
57
96
+1
Apply the understanding of the inverse relationship
between addition and subtraction to generate pairs of
statements to find unknowns in number sentences.
∆ - 15 = 19
19 – 15 =∆
Use knowledge of number facts to find unknown
numbers.
∆ - ◊= 19
20 - ∆ - ◊= 5
etc
Solve one and two step problems involving subtraction
in contexts of measures money and time, explain
methods and reasoning orally in pictures and writing
e.g. The bus left school at 8.30 and arrived at the
museum at 10.15. How long was the journey?
Continue to use counting up (complimentary addition)
method, with informal notes or jottings, when
appropriate e.g.

When subtracting from multiples of 100 or 1000

Finding a small difference by counting up
e.g. 5003 – 4996 =7. (can be modelled using an empty
number line or jottings)
+4
+3
=7
4996
5003
 To support or explain mental calculations
e.g. 754 – 86 =
+ 14 + 600 + 54 = 668
+14
86
Page 5
5000
+600
100
+54
700
May 2009
754
CALCULATION POLICY – ADDITION AND SUBTRACTION
Addition
Subtraction
Begin expanded method, adding least significant digit
first
625
205
358
If children find
+ 48
+ 176
+ 973
this difficult go
back to first
13
11
11
stage (see Y3)
60
70
120
600
300
1200
673
381
1331
Explaining the subtraction of the nearest multiple of 10
and adjusting (see Y2/3 examples)
Teach expanded decomposition leading to compact
decomposition. (see Framework – section 6 p50)
-
754
86
-
= 700 and 40 and 14
80 and 6
This leads to preparing for ‘carrying’ below the line
(compact recording).
(see Framework – Section 6 p48)
To tens
625
+ 48
673
1
to hundreds
783
+ 42
825
1
Cross out the
digit that has
been carried,
once it has been
added in.
11
Extend to decimals as appropriate e.g. money knowing
that the decimal points should line up under each
other.
Use knowledge of addition facts and place value to
derive sums of pairs of multiples of 10, 100 or 1000.
Solve problems explaining methods and reasoning.
Year 5
Aim by end of
year:
-Most children
are able to use
compact method
for addition and
compact
decomposition for
subtraction, when
appropriate,
(numbers up to
10,000 and
decimals) but
should continue to
use counting up
method, where
appropriate.
Use symbols and missing numbers:Continue to develop as in Y1, 2, 3 and 4 but with
appropriate number.s
Develop use of empty number lines, partitioning and
other informal recording methods to support and
explain calculations where appropriate (including
decimals).
125.64 + 56.7
125.64 + 50 + 6 + .7
175.64 + 6 + .7
181.64 + .7
182.34
50
6
0.7
125.64
= 600 and 140 and 14
80 and 6
tens and hundreds
367
+ 85
452
175.64
181.64
Leading to:
754
- 86
600
= 700
600
1
50 4
80 6
60 8
= 668
7 '5 8
- 8 6
668
Extend to decimals as appropriate e.g. money knowing
that the decimal points should line up under each other.
Solve problems explaining methods and reasoning.
Continue to use counting up (complimentary addition)
method, with empty number lines, when appropriate e.g.
When subtracting from multiples of 100 or 1000
Finding a small difference by counting up, or when
bridging across a boundary by a small amount.
e.g. 8006 – 2993 = 5013. (can be modelled using an
empty number line or jottings)
+7
+5000
+6
2993

3000
8000 8006
Using known number facts and place value to
subtract e.g. 4.1 – 1.8 = 2.3
+0.2
+2.0
+0.1
182.34
-
2.0
4.0
4.1
to support or explain mental calculations
to support or explain the subtraction of the
nearest multiple of 10 or 100 then adjust e.g.
4005 – 1997 = 4005 – 2000 +3
= 2005 +3
= 2008
Page 6
= 668
Leading to:
1.8
Note: ‘compact’
method is not
appropriate for
adding two 2-digit
numbers – this is a
mental method.
= 700 and 50 and 4
80 and 6
May 2009
CALCULATION POLICY – ADDITION AND SUBTRACTION
Addition
Subtraction
Use compact (‘carrying’) method.
See (see Framework – section 6 p49 – Method C)
587
3587
+ 475
+ 675
1062
4262
Continue to develop compact decomposition with
different numbers of digits and decimals.
Note: Children should understand the importance of
lining up units digits under units digits, tens under tens
etc.
11
111
HTU + HTU then ThHTU + ThHTU
Children may need to return to expanded method
when first carrying out addition of decimals - least
significant digits first.
Ensure that children know the importance of ‘lining
up’ the decimal points particularly when adding mixed
amounts e.g. 16.4 m. + 7.68 m.
16.4
+ 7. 68
2 4 . 0 8m.
4
3
5 '7 6 4 .' 0
- 821. 6
4 942. 4
Children may need to return to expanded method when
first carrying out subtraction involving decimal
numbers. This reinforces understanding of place value,
particularly with decimals.
1 1
Year 6
Aim by the end
of Year 6:
-All children
should be able to
use carrying
method for
addition and
decomposition
method for
subtraction,
accurately and
reliably – when
appropriate but
should be able
use counting up
method, with
jottings, where
appropriate.
Note: ‘compact’
method is not
appropriate for
adding and
subtracting two 2digit numbers – this
is a mental method
Solve problems, explaining methods and reasoning
orally and in writing.
Solve problems, explaining methods and reasoning orally
and in writing.
Use symbols and missing numbers:Continue to develop as in earlier years but with
appropriate numbers (including decimals)
Develop use of empty number lines, partitioning and
other informal recording methods developed in
earlier years to support and explain calculations
where appropriate (including decimals).
Use compact (‘carrying’) method. As Y5, extend
method to any number of digits and decimal places
Use symbols and missing numbers:Continue to develop as in earlier years but with
appropriate numbers (including decimals)
Develop use of empty number lines, partitioning and
other informal recording methods developed in earlier
years to support and explain calculations where
appropriate (including decimals).
Continue to use complimentary addition, using an empty
number line, informal notes or jottings when
appropriate with appropriate numbers e.g.
For those children who have not mastered compact
method (see Framework – section 6 p49 Method C) or
are unable to use it reliably, use expanded method,
but teach again when appropriate.
 0.5 – 0.31
+0.09
= + 0.09 + 0.1 = 0.19
+0.1
0.31
0.40
0.50
 Subtracting the nearest multiple of 10,100, 1000
 Subtracting from any multiple of 1000, 10,000 etc
Solve problems explaining methods and reasoning
orally and in writing.
Page 7
i.e. where using decomposition would be very
complicated.
Continue to develop compact decomposition with
different numbers of digits and decimals.
Note: Children should understand the importance of
lining up digits.
May 2009