Calculation Policy from September 2014
Year 1
Addition
Subtraction
+ = signs and missing numbers
3+4=
3+=7
+4=7
+=7
=3+4
7=+4
7=3+
7=+
Promoting covering up of operations and
numbers.
7+4
0
1
2
3
4
5
6
7
8
9
10
11
12
Recording by drawing jumps on prepared
lines and constructing own lines. ( Teacher
models number lines with missing numbers)
Division
Pictures and marks
Pictures and marks
Sam spent 4p. What was his change from
10p?
There are 3 sweets in one bag.
How many sweets are there in 5 bags?
12 children get into teams of 4 to play a
game. How many teams are there?
- = signs and missing numbers
(Recording on a number line modelled
by the teacher when solving problems)
7-3=
7-=4
-3=4
-=4
Number lines (numbered)
Multiplication
Pictures and marks
=7-3
4=-3
4=7-
4=-
Use of bead strings to model groups of.
A bag of 12 sweets is shared among 4
children. How many sweets will each
child get? (sharing)
12 sweets are placed in bags of 4. How
many bags can I make? (grouping)
Number lines (numbered)
11 – 7 (Counting back)
0
1
2
3
4
5
6
7
8
9
10
11
12
Number bonds to 10.
The difference between 7 and 11 (counting
on)
0
1
2
3
4
5
6
7
8
Experiencing division as sharing and
as grouping.
9
10
11
12
Recording by drawing jumps on prepared
lines and constructing own lines. ( Teacher
models number lines with missing numbers)
(Teachers model jottings appropriate for
larger numbers)
Calculation Policy from September 2014
Year 2
Addition
Subtraction
+ = signs and missing numbers
Continue using a range of equations as in
Year 1 but with appropriate, larger numbers.
Extend to
14 + 5 = 10 + 
35 =  + 5
Use Dienes blocks to support.
Partition into tens and ones and recombine
Use hundred square to consolidate mental image
i.e. counting down adds 10 – counting up
subtracts 10
12 + 23 = 10 + 2 + 20 + 3
= 30 + 5
= 35
Refine to partitioning the second number
only:
23 + 12 = 23 + 10 + 2
= 33 + 2
= 35
Multiplication
x = signs and missing numbers
÷ = signs and missing numbers
14 + 5 = 20 - 
32 +  = 50
Use Dienes blocks to support.
7x2=
7 x  = 14
 x 2 = 14
 x  = 14
6÷2=
6÷=3
÷2=3
÷=3
Find a small difference by counting on
Arrays and repeated addition
42 – 39 = 3


+1
 
 
2x4
+2
=2x7
14 =  x 7
14 = 2 x 
14 =  x 
=6÷2
3=6 ÷
3=÷2
3=÷
Understand division as sharing and
grouping
 4x2

Sharing – 6 sweets are shared between 2
people. How many do they have each?
or repeated addition
39
40
2 + 2 + 2 + 2 (or 4 + 4)
42
 
  
Subtract 9 or 11. Begin to add/subtract 19 or 21
35 – 9 = 26
  
+1
0
+10
+2
26
25
23
35
33
Add 9 or 11 by adding 10 and adjusting by 1
35 + 9 = 44
+10
Counting back where appropriate
Use known number facts and place value to
subtract (partition second number only)
-1
2
3
4
5
6
7
8
6  2 can be modelled as:
Grouping – There are 6 sweets. How many
people can have 2 each? (How many 2’s
make 6?)
37 – 12 = 37 – 10 – 2
= 27 – 2
= 25
27
25
44
1
35
-10
35
Division
- = signs and missing numbers
37
45
-2
-10
0
2
4
6
Calculation Policy from September 2014
Year 3
Addition
Subtraction
+ = signs and missing numbers
Continue using a range of equations as in
Year 1 and 2 but with appropriate, larger
numbers.
58 +  = 100
35 =  + 9
Division
- = signs and missing numbers
Continue using a range of equations as in
Year and 2 but with appropriate numbers.
x = signs and missing numbers
Continue using a range of equations as
in Year 2 but with appropriate numbers.
÷ = signs and missing numbers
Continue using a range of equations as
in Year 2 but with appropriate numbers.
Find a small difference by counting on
Continue as in Year 2 but with appropriate
numbers e.g. 102 – 97 = 5
Number lines
Understand division as sharing and
grouping
18 ÷ 3 can be modelled as:
Sharing – 18 shared between 3
Grouping - How many 3’s make 18?
Subtract mentally a ‘near multiple of 10’
to or from a two-digit number
Continue as in Year 2 but with appropriate
numbers
e.g. 78 – 49 is the same as 78 – 50 + 1
Partition into tens and ones and
recombine
Partition both numbers and recombine.
Refine to partitioning the second number
only e.g.
36 + 53 = 53 + 30 + 6
= 83 + 6
= 89
+30
Multiplication
Subtract 9 or 11 to whole numbers. Begin to
add/subtract 19 or 21, 29 or 31.
6
Doubling multiples of 5 up to 50
Partition using grid method to present
87
30
60
x
97
2
-5
84 – 56 = 28
+ 20
+4
60
20
+ 10 = 30
Use known facts and place value to
carry out simple multiplications. Use
the Grid Method as above (partitioning)
+4
80
7
14 = 60 + 14 = 74
OR
Partition:
15 x 2
-10
Counting forward (complementary
addition)
56
18
Arrays and repeated addition
Continue to understand multiplication
as repeated addition and continue to
use arrays.
89
Add a near multiple of 10 to a two-digit
number
Continue as in Year 2 but with appropriate
numbers
e.g. 35 + 19 is the same as 35 + 20 – 1.
12
0
3
6
9
12
15
18
Remainders
Sharing - 16 shared between 3, how
many left over?
Grouping – How many 3’s make 16,
how many left over?
35 x 2 = 70
97 – 15 = 82
+6
83
0
Counting back in ‘jumps’
82
53
6x3
84
X
3
30
90
e.g. 32 x 3 =96
2
6 = 90 + 6= 96
0
3
16 ÷ 3 = 5 r1
6
9
12
15 16
Calculation Policy from September 2014
Year 4
+ = signs and missing numbers
- = signs and missing numbers
Continue using a range of equations as in
Year 3 but with appropriate numbers.
x = signs and missing numbers
Continue using a range of equations as
in Year 3 but with appropriate numbers
Add the nearest multiple of 10
Continue as in Year 2 and 3 but with
appropriate numbers e.g. 63 + 29 is the
same as 63 + 30 - 1
Find a small difference by counting up
e.g. 5003 – 4996 = 7
This can be modelled on an empty number
line
Pencil and paper: The Grid Method
Expanded pencil and paper method
To support the step towards column
addition the children will be taught to
partition within the standard written form.
Use known number facts and place value
to subtract mentally
3
+
6=93
82
20
7
140
8
-10
Pencil and paper procedures
Complementary addition
754 – 86 = 668
+0.7
8.5
+600
+14
9.2
3
21
0
+6
6
+6
12
+6
18
+6
24
30
=140+21=161
Pencil and paper: Chunking
114 ÷ 6
92
-5
+3.0
+6
x
30
500 + 40+ 7
+ 300+ 80+ 9
800+120+16 = 936
5.5
23 x 7 =
x
Adding decimal numbers
5.5 + 3.7=
Grouping
Recall methods from year 3
30 ÷ 6 can be modelled as:
92 – 15 = 77
77
547+389=
÷ = signs and missing numbers
86
100
2
2100
60
560
16
= 2160
= 576
Recombine using thousands,
hundreds, tens and units:
2000 + 600 + 130 + 6 = 2736
Estimate and check.
+54
700
70
754
x10
0
x9
60
114
Calculation Policy from September 2014
Year 5
+ = signs and missing numbers
Add the nearest multiple of 10, then
adjust
Continue as in Year 3 and 4 but with
appropriate numbers e.g. 630 + 299 is the
same as 630 + 300 - 1
Use formal methods of addition:
- = signs and missing numbers
Continue using a range of equations as in
Year 4 but with appropriate numbers.
Pencil and paper procedures:
Counting back
Pencil and paper: Grid method
920 – 150 = 770
372 x 24 is approximately 400 x 20 =
8000
820
770
920
358 + 73 =
3 5 8
+ 7 3
4 3 1
1 1
x = signs and missing numbers
Continue using a range of equations as
in Year 4 but with appropriate numbers,
including decimal numbers.
-50
-10 0
x
300
70 2
20 6000 1400 40 = 7440
4 1200 280 8 = 1488
+ 8928
Complementary addition
Begin to use short multiplication
754 – 186 = 668
+500
+14
186
200
+54
700
754
÷ = signs and missing numbers
Recall methods from year 4
Remainders
Quotients expressed as fractions or
decimal fractions
61 ÷ 4 = 15 ¼ or 15.25
41÷ 4 = 10 r1
x10
0
41
OR
40
41 = (10 x 4) + 1
Remainders
Quotients expressed as fractions or
decimal fractions
676 ÷ 8 = 84.5
41÷ 4 = 10 r1
8006 – 2993 = 5013
Short Division
Beginning to use decomposition
2 4 1
352
-178
174
+1
Calculation Policy from September 2014
Year 6
+ = signs and missing numbers
Continue using formal methods of
addition
- = signs and missing numbers
Continue using a range of equations as in
Year 5 but with appropriate numbers.
x = signs and missing numbers
Continue using a range of equations as in
Year 5 but with appropriate numbers,
including decimal numbers.
Pencil and paper: decomposition
Pencil and paper procedures
Short Multiplication
Add the nearest multiple of 10, 100 or
1000, then adjust
Continue as in Year 2, 3, 4 and 5 but with
appropriate numbers including extending to
adding 0.9, 1.9, 2.9 etc
Add the nearest multiple, then adjust
Continue as in Year 5 but with appropriate
numbers e.g. 6389 + 1299 is the same as
6390 + 1300 - 2
Pencil and paper procedures
Extend to numbers with any number of
digits and decimals with 1 and 2 decimal
places.
124.9 + 117.25 = 242.15
124.90 (note the addition of a zero)
+ 117.25
242.15
11
Solve problems involving decimal numbers.
Long Multiplication
÷ = signs and missing
numbers
Use formal method for
division when appropriate:
long division