Download Winford Calculation Policy-KS2

Winford Church of England
Primary School
Written Calculation Methods
Key Stage 2
At Winford Church of England Primary School, your child takes part in a daily Maths lesson.
During these lessons they have the opportunity to explore a wide range of areas of learning in
Maths, from counting to measures, handling data to shape and space. Throughout these
areas, they learn and apply mental and written calculation strategies to help them solve
problems, and advance their learning.
This booklet will explain the written methods which we use at Winford. Many of these
methods will be familiar, others may be new to you. In order for your child to learn best at
school and at home, it is important that there is consistency in the vocabulary and methods
used, and your child is encouraged to apply the same methods that they use in the classroom
to any Maths-based activities that they complete at home. The written methods for the four
operations (+ - x ÷) are presented in the order that they are taught. Some children will advance
quickly through the methods, whilst others will require more time at each stage to consolidate
their understanding. This means that the methods are not divided up according to year group.
Your child’s class teacher will be able to let you know which methods your child is currently
learning and using.
Although the focus of this booklet is on pencil and paper methods it is important to recognise
that the ability to calculate mentally lies at the heart of our teaching of Maths. Mental
methods will be taught systematically from Reception onwards and pupils will be given regular
opportunities to develop the necessary skills. In every written method there is an element of
mental processing and it is essential that pupils have a secure understanding of mental
methods in order to support this. There are lots of ways you can support your child to develop
their mental methods e.g. discussing the total cost of different items when you go shopping,
practising number bonds to 20 or memorising times tables. Our long-term aim is for your child
to be able to select an efficient method of their choice that is appropriate for a given task.
We hope that you will find this booklet useful when it comes to supporting your child with
their maths. If you do require any further information or support, please speak to your child’s
class teacher and they will be happy to help.
Addition – KS2
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
+6
53
83
89
Add a near multiple of 10 to a two-digit number
e.g. 35 + 19 is the same as 35 + 20 - 1.
+20
35
54
- 1
55
Expanded Written Method – teacher model only
Step by step process of column addition.
358
+273
11 (8+3)
120 (50 + 70)
500 (300 + 200)
631
Compact Written Method (carrying underneath)
3 5 8
+2 7 3
6 3 1
1
1
Extend to decimals in the context of money
£ 2.50 + £ 1.75 = £ 4.25
£ 2.5 0
+ £ 1.7 5
£ 4.2 5
1 1
Add the nearest multiple of 100 and adjust
262 + 99 = 361
+100
262
361
- 1
362
Extend to numbers with any number of digits and
decimals with 1 and 2 decimal places.
124.9 + 117.25 = 242.15
1 2 4.9 0 (note the addition of a zero)
+ 1 1 7.2 5
2 4 2.1 5
1 1
Add the nearest multiple of 10, 100 or 1000, then
adjust
Extend to add decimals e.g. 0.9, 1.9, 2.9
+ = signs and missing numbers
58 +64 =
23 +
= 25 + 13
= 35
45 =
+ 13
+ 753 = 1230
45 = 34.2 +
+
346 =
= 62
+
Subtraction – KS2
Use known number facts and place value to subtract
92 – 15 = 77
82
77
92
Find a small difference by counting up
e.g. 5003 – 4996 = 7
This can be modelled on an empty number line.
Compact Written Method
-5
2 14
- 10
Subtract mentally a ‘near multiple of 10’ from a twodigit number
Subtract 9 or 11 by subtracting 10, then adjusting.
35 – 9 = 26
+1
26
25
35
- 10
Extend to larger near multiples, for example;
78 – 49 is the same as 78 – 50 + 1
Complementary addition
84 – 56 = 28
+ 20
+4
56
60
+4
80
84
Or
+20
56
+8
76
84
1
352
-178
174
Extend to larger numbers and decimals.
2 1
7 3. 3 9
- 4 1. 5 7
3 1. 8 2
- = signs and missing numbers
3.7 – 0.9 =
100 -
= 46
= 174 - 27
250 =
- 75
+ 57 = 25
6.4 = 13.5 -
-
3.5 =
= 1000
-
Multiplication – KS2
Number lines
3x6
0
6
Expanded Written Method
– teacher model only
& provide as an alternative written method where
appropriate.
12
18
Partition and recombine
35 x 2
30 x 2 = 60
5 x 2 = 10
= 70
Estimate and then check.
Estimate and check
72 x 38 =
is approximately
70 x 40 = 2800
x
30
8
70 2
2100 60
560 16
= 2160
= 576 +
2736
1
Use known facts to 12 x 12 and place value to carry out
simple multiplications.
Compact Written Method
Carried numbers written below.
x
125
7
875
1 3
Extend to larger numbers, multiplying out the units
first each time.
125
x 27
875
1 3
2500
1_____
3375
1
Extend to decimals up to 2 decimal places.
1. 2 5
x 17
8. 7 5
1 3
1 2. 5 0
2 1. 2 5
x = signs and missing numbers
3x9=
4x
= 7 x 30
= 32
2500 =
x 0.3 = 24
6.3 = 9 x
x
49 =
= 81
-
x 50
Division – KS2
Understand division as sharing and grouping
18 ÷ 3 can be modelled as:
Pencil and paper procedures
‘Bus stop’ method
÷ = signs and missing numbers
18 ÷ 3 =
0 2 5r3
Sharing
18 shared between 3
5
Grouping
How many 3’s make 18?
Remainders
128 ÷ 5 = 25 r3 or 25 3/5 or 25.6
Quotients expressed as fractions or decimal fractions.
Sharing
16 shared between 3, how many left over?
Grouping
How many 3’s make 16, how many left over?
e.g.
-3
-3
13
10
7
4
-3
-3
16
-3
Grouping and sharing should be modelled using a
range of practical resources.
Where appropriate, relate division to multiplication as
the inverse operation, particularly from Y4, when
children should know most times tables facts and be
encouraged to use these to solve simple division
calculations.
=7
÷ 70 = 9
÷
With remainders
16 ÷ 3 = 5 r1
1
11 2 28
2.8 ÷
= 24 ÷ 2
=3
4 = 28 ÷
7=
÷3
0.8 =
÷