Princeville Primary School
Guide for Parents
Calculations Policy
Pencil and paper procedures
Key Stages 1 & 2
1
Addition
Year 2
Year 3
Partitioning the second number only:
Paper and pencil procedures
23 + 12 = 23 + 10 + 2
= 33 + 2
= 35
83
+42
------5
120
-------125
Year 1
+ = signs and missing numbers
3+4=
3+ =7
+4=7
+∇=7
=3+4
7= +4
7=3+
7= +∇
+10
Promoting covering up of operations and
numbers.
Using the symbols < > ≤ ≥
83 + 42 = 125
7+4
1
3
2
4
5
6
7
8
9
10
11
12
Recording by - drawing jumps above on
prepared lines
-
2
constructing own lines
35
33
Then
Pencil and paper procedures
Number lines (numbered)
0
23
+2
80 + 3
+ 40 + 2
---------------120 + 5 = 125
then
83
+42
------5
120
-------125
358 + 73 = 431
358
73 +
------11
120
300
------431
Addition
Year 4
Pencil and paper procedures
Column addition up to 4 digits without carrying
1346
1232+
------2578
3
then
1672
1598 +
---------3270
---------111
Year 5
Year 6
Pencil and paper procedures
Column addition up to 4 digits with carrying
3587 + 675 = 4262
3587
+ 675
4262
111
Extend to decimals (same number of decimals places) and adding several
numbers (with different numbers of digits).
In Year 6 the expectation is the
children learn to apply the
methods they have learnt in
previous years
Subtraction
Year 2
Year 1
Pictures / marks
Sam spent 4p. What was his change from 10p?
Year 3
Find a small difference by counting up
Pencil and paper procedures
42 – 39 = 3
Column subtraction without “borrowing”
+1
- = signs and missing numbers
7-3=
=7-3
7- =4
4= -3
-3=4
4=7-∇=4
4= -∇
+2
40
39
11 – 7
(Counting back)
+ 20
+4
1
2
3
4
6
5
8
7
9
10
11
The difference between 7 and 11
(Counting up)
To reinforce concept. Practical strategies essential to
see ‘difference’.
1
2
3
4
5
6
7
8
9
10
11
12
Recording by - drawing jumps on prepared lines
- constructing own lines
(Teachers model jottings appropriate for larger numbers)
4
60
+4
80
159
26 –
_____
133
Then decomposition (modelled using base ten) 2 digit2 digit then 3 digit – 2 digit
12
56
0
42
Pencil and paper procedures
Complementary addition
84 – 56 = 28
Number lines (numbered)
0
159 – 26 =133
84
Subtraction
Year 5
Year 4
Pencil and paper methods
Pencil and paper methods
3 digit – 2 digit (modelled using base ten)
Subtraction of decimals (modelled using base ten)
1 1
2 5 1
3.64
- 1.75
_____
1.89
_____
Then up to 4 digits
Following this the children must then complete
application activities
5
Year 6
In Year 6 the expectation is the children learn to apply
the methods they have learnt in previous years
Multiplication
Year 2
Year 1
Pictures and symbols
There are 3 sweets in one bag.
How many sweets are there in 5 bags?
(Recording on a number line modelled by the
teacher when solving problems)
Arrays and repeated addition
    4 x 2 or 4 + 4
   
2x4
or repeated addition
2+2+2+2
Year 3
Arrays and repeated addition
Pencil and paper methods
    4 x 2 or 4 + 4
   
2x4
or repeated addition
Then partitioning from the units:
2+2+2+2
Pencil and paper methods
16 x 3 =
1.
2.
3.
4.
3 x 6 = 18
3 x 10 = 100
100 + 18
118
Then partitioning from the units:
16 x 3 =
1.
2.
3.
4.
3 x 6 = 18
3 x 10 = 30
30 + 18
48
Then
32 x 3
32
x3
6
90
96
Then
32 x 3
32
x3
96
6
Multiplication
Year 5
Year 4
Pencil and paper procedures
1.
252 x 3
Pencil and paper procedures
1524 x 4
Step 1
Step 1
2x3=
6
50 x 3 = 150
200 x 3 = 600 +
756
1524
4x
6096
Year 6
Pencil and paper procedures
43
12 x
86
430
516
1
21
Step 2
252 x
3
6
150
600
756
43 x
12
6
80
30
400
516
(2x3=6)
(2x40=80)
(10x3=30)
(10x40=400)
Step 3
252 x
3
756
1
Step 3
143 x
12
6 (2x3)
80 (2x40)
200 (2x100)
30 (10x3)
400 (10x40)
1000 (10x100)
1716
1
7
38.85 x
17
1432 x
13
Step 2
.35
5.60
56.00
210.00
6
90
1200
3000
20
300
4000
10000
18616
1
(10x2)
(10x30)
(10x400)
(10x1000)
.50
8.00
80.00
300.00
x7p
x10p
660.45
121
Then move onto 3 and 4 digit x 2 digit as method one
Extend to decimals with up to 2 decimal places
(using money to aid understanding)
This needs to be modelled
Division
Year 1
Pictures / marks
12 children get into teams of 4 to play a game.
How many teams are
Year 2
Year 3
Pencil and Paper procedures
Grouping – There are 6 sweets. How many people can have
2 each? (How many 2’s make 6?)
Pencil and Paper procedures
Division with remainders
16 ÷ 3 = 5 r1
Sharing - 16 shared between 3, how many left over?
Grouping – How many 3’s make 16, how many left over?
e.g.
there?
0
Children can use small world objects and/or any
counting equipment to physically share between a
given number.
2
4
6
Understand division as sharing and grouping
Sharing – 6 sweets are shared between 2 people.
How many do they have each?
0
3
6
9
12
15
r1
Grouping - How many 3’s make 18?
32 ÷ 3
0
3
6
9
12
15
 
  
  
10 x 3
30
r3
Division with remainders
7÷2
0
8
18
2
4
6
r1
Year 4
Year 5
Pencil and paper procedures
Year 6
Pencil and paper procedures
Pencil and paper procedures
As year 4 (3 digit ÷ 1 digit)
2 digit ÷ 1 digit
61 ÷ 4
Children need to be secure in the numberline
chunking method before moving onto chunking
method below.
Then
3 digit ÷ 2 digit
eg 362 ÷ 14
1.
Children write x tables for the dividing number
10 x 4
Eg
5x4
40
5 x 14 = 70
10 x 14 = 140
20 x 14 = 280
r1
+180
Children then use column addition to add up the jumps to
give the answer 15 r 1
977 ÷ 36 is approximately 1000 ÷ 40 = 25
20 x 14
20 x 14
180
10 x 4
Method is then repeated for 4 digit ÷ 2 digit numbers
40
split the remainder
Children then use column addition to add up the jumps
Splitting the remainder:
When dividing by 4 the remainder of 1 would be split
by calculating 1 ÷ 4 = either 0.25 or ½ giving the answer
15.25 or 15 ½
9
r2
5x4
2.
3.
360
Repeat method for 3 digit ÷ 1 digit
977
360 (10 groups)
617
360 (10 groups) refine 257
to
- 180
(5 groups)
77
72
(2 groups)
5
Answer: 27 5/36
-
977
720
257
180
77
72
5
(20 groups)
(5 groups)
(2 groups)