Addition
Year 1
Year 2
Progression in calculations
U+U
Teen numbers + U
TU + U
TU + U crossing the tens boundary
Strategies
Relate addition to counting on, and that it can be done in any
order
3+2=5
2+3=5
+1 +1
_______________________________________
0
1
2
3
4
5
6
7
8
9
Number bonds practice
Add a teen to a one-digit number, using number lines and
bead strings
12 + 5
0 1
2
Progression in calculations
TU + U
TU + U crossing the tens
boundary
Doubles
TU + TU crossing the 100
boundary
TU + 11
Near doubles
TU + 9
Strategies
+ = signs and missing numbers
Add three numbers: 32 +  + 
= 46; 35 = 1 +  + 5
Count on in tens and ones
Use knowledge of bonds to 10:
24 + 8 = 24 + 6 + 2 = 30 + 2 =
32
Partition into tens and ones,
add and recombine
23 + 34
3 4
5
6 7
8 9
20 + 30 = 50
3+ 4= 7
50 + 7 = 57
10 11 12 13 14 15 16 17 18 19 20
Refine the larger number first:
34 + 23 = 34 + 20 + 3
= 54 + 3
= 57
+ = signs and missing numbers
3+4=
3+=7
+4=7
+=7
=3+4
7=+4
7=3+
7=+
Add 9 or 11 by adding 10 and
adjusting by 1
35 + 9 = 44
+10
35
44
-1
45
Addition
Year 3
Year 4
Pupils will continue to use empty number lines and/or partitioning with
increasingly large numbers, including adding to the nearest multiple of 10
and adjusting, where appropriate.
Progression in calculations
TU + TU crossing the 100 boundary
HTU + TU not crossing the 1000 boundary
HTU + HTU not crossing the 1000 boundary
Strategies
Partitioning into hundreds, tens and ones, adding and
recombining
Refining to partitioning the second number only:
53 + 36 =
53 + 30 = 83
83 + 6 = 89
+30
83
89
Counting on from the largest number irrespective of the order
of the calculation.
38 + 86 = 124
+ 30
+4 +4
116 120 124
86
Adding a near-multiple of 10 to a 2-digit number and
adjusting
(e.g. 35 + 19 is the same as 35 + 20 – 1)
+ 20
-1
35
54 55
Adding multiples of 10 to any 2-digit number, including those
that are not multiples of 10
48 + 36 = 84
+30
+2
48
78 80
+4
84
Progression in calculations
HTU + TU crossing the 100 boundary
HTU + HTU crossing the 1000
boundary
£ .pp + pp
Strategies
Partitioning and recording on empty
number lines with increasingly large
numbers, including adjusting where
appropriate.
374 + 248 = 374 + 200 + 40 + 8
+6
53
Pupils will continue to use a number line for
adding a three- and two-digit number and they
will also continue to develop their mental
calculation strategies.
374
574
614 622
Introducing the expanded vertical
method
374
+ 248
12 (4 + 8)
110 (70 + 40)
500 (300 + 200)
622
Always referring to the actual value of
the digits concerned (e.g. not ‘7 + 4 is
11’, but ‘70 + 40 is 110’).
Extending to decimals in the context of
money
£3.59 + 78p
3.59
+ 0.78
0.17 (0.09 + 0.08)
1.20 (0.50 + 0.70)
3.00 (3 + 0)
4.37
Addition
Year 5
Year 6
Pupils will continue to use a number line for adding a
three- and two-digit number and they will also continue
to develop their mental calculation strategies.
Pupils will continue to use a number line for adding a three- and
two-digit number and they will also continue to develop their
mental calculation strategies.
Progression in calculations
ThHTU + HTU
TU.tths + U.tthshdths
Progression in calculations
ThHTU + HTU
ThHTU + ThHTU
Strategies
Extending to numbers with at least four digits
Strategies
Extending the carrying method to any
number of digits
3587 + 675 =
3587
+ 675
12 (7 + 5)
150 (80 + 70)
1100 (500 + 600)
3000 (3000 + 0)
4262
7648 + 1486 =
42 + 6432 + 786 + 3 + 4681 =
7648
+ 1486
9134
111
Extending the expanded vertical method to the
compact method
3587
+ 675
4262
NB: Revert to expanded
methods if pupils
experience any difficulty.
111
Applying these strategies to decimals (in context
of money & measures):
£23.70 + £48.56 =
23.70
+ 48.56
0.06
1.20 (0.7 + 0.5)
11.00 (3 + 8)
60.00 (20 + 40)
72.26
23.70
+ 48.56
72.26
11
42
6432
786
3
+ 4681
11944
121
Pupils will continue to use this method when adding
decimal (1, 2 and/or 3-decimal places) and larger
numbers.
13.86 + 9.481 = 23.341
13.86
+ 9.481
23.341
1 1 1
Subtraction
Year 1
Year 2
Progression in calculations
U–U
TU – U not crossing the tens boundary
TU – 10 or a multiple of it
TU – U crossing the tens boundary
Strategies
Understand subtraction as ‘take away’, counting back
6–3=3
-1 -1
-1
____________________________________
0
1
2
3
4
5
6
7
8
9
Progression in
calculations
TU – 10 or a multiple of it
TU – TU not crossing the
tens boundary
TU – TU crossing the tens
boundary
Strategies
Find a small difference by
counting on
42 – 39 = 3
13 – 5 = 8
Subtract 9 or 11 by
subtracting 10 and adjust
Find the difference by counting on
Use known number facts
and place value to subtract,
partitioning the second
number only
35 – 9 = 35 – 10 + 1 = 26
-1-1-1-1-1
5 – 3 = 2 as 3 +  = 5
+1 +1
_______________________________________
0
1
2
3
4
5
6
7
8
9
37 – 12 = 37 – 10 – 2 = 25
Count on or back on empty
number lines
Progression in counting
back:
47 – 23 = 24
– = signs and missing numbers
7-3=
7-=4
-3=4
-=4
=7-3
4=-3
4=7-
4=-
Crossing the tens bounday:
42 – 25 = 17
Subtraction
Year 3
Year 4
Pupils will continue to use empty number lines and/or
partitioning with increasingly large numbers, including
subtracting to the nearest multiple of 10 and adjusting,
where appropriate.
Progression in calculations
TU – TU crossing the tens boundary
HTU – TU crossing the tens boundary
HTU – HTU not crossing the tens boundary
HTU – HTU crossing the tens boundary
Strategies
Find a small difference by counting up
102 – 97 = 5
Subtract mentally a ‘near multiple of 10’ from a
2-digit number and adjust
45 – 19 = 45 – 20 + 1 = 26
Pupils will continue to use a number line for subtracting
increasingly large numbers and they will also continue to develop
their mental calculation strategies.
Progression in calculations
HTU – HTU not crossing the tens boundary
HTU – HTU crossing the tens boundary
ThHTU – HTU not crossing the hundreds boundary
ThHTU – HTU crossing the hundreds boundary
£ .pp – pp not crossing £1
£ .pp – pp crossing £1
Strategies
Find a small difference by counting up
1003 – 996 = 7
Subtract mentally a ‘near multiple of 10’ from a 2-digit
number and adjust
Continue as in Year 3 with appropriate numbers
Use the empty number line as in Year 3
374 - 248 = 126
+ 52
+ 70
+4
Use known number facts and place value to
subtract, partitioning the second number only
97 – 15 = 97 – 10 – 5 = 82
Count on or back on empty number lines
It is important that children should decide
which method of subtraction is efficient for
each calculation, such as in 57 – 12 or 74 – 27.
248
300
370
Extending to decimals in the context of money
£8.95 - £ 4.34 = £ 4.61
57 – 12 = 45
74 – 27 = 47
– = signs and missing numbers
– 86 = 668
– = signs and missing numbers
53 –
= 24
Written column method up to 4 digits.
Written column method up to 3 digits.
438
- 215
223
2
1
632
- 417
215
2
2942
- 821
2121
1
2532
- 1317
1215
374
Subtraction
Year 5
Year 6
Pupils will continue to develop the use of a number line for
subtracting increasingly large numbers and they will also
continue to develop their mental calculation strategies.
Pupils will consolidate and extend Year 5 work including
decimals to three decimal places.
Progression in calculations
ThHTU – HTU not crossing the hundreds
boundary
ThHTU – HTU crossing the hundreds boundary
£ .pp – .pp not crossing £1
£ .pp – .pp crossing £1
Progression in calculations
ThHTU – HTU not crossing the hundreds
boundary
ThHTU – HTU crossing the hundreds boundary
.pp –. pp crossing the unit boundary
.ppp – .ppp not crossing the unit boundary
.ppp –. ppp crossing the unit boundary
Strategies
Find a difference by counting up
Strategies
Find a difference by counting up
1209 – 388 = 821
3002 – 1997 = 1005
Subtract mentally a ‘near multiple of 10 or 100’
from a number and adjust
Subtract mentally a ‘near multiple of 10, 100 or
1000’ from a number and adjust
Use known number facts and place value to
subtract
Use known number facts and place value to
subtract
6.1 – 0.4 = 5.7
61 – 4 = 57
Subtract using partitioning
72.5 – 45.7 = 26.8
72.5 – 40 = 32.5
32.5 – 5 = 27.5
27.5 – 0.7 = 26.8
0.5 – 0.31 = 0.19
50 – 31 = 19
Written method
Introduce the compact method once children are
secure
741 – 367 = 374
Written method
Introduce the expanded form of decomposition for
subtraction
741 – 367 = 374
Recognise the most efficient method to use
– = signs and missing number
– = signs and missing numbers
Children should be encouraged to check
calculations using the inverse.
Children should be encouraged to check
calculations using the inverse.