Download Maths Calculation Policy - Dunchurch Junior School

Maths Calculation Policy
DUNCHURCH BOUGHTON C of E
(VA) JUNIOR SCHOOL
Maths Calculation Policy
Recognising its historic foundation, the school will preserve and
develop its religious character in accordance with the principles of
the Church of England and in partnership with the church at parish
and diocesan level.
The Christian Faith, and its practical expression, form a major part of
the whole school ethos. The school aims to give children both
knowledge and understanding of the Christian Faith while respecting
and understanding other religions and cultures.
The school aims to: School Aim
Statement:
Review History:

ensure that all children receive their entitlement to a broad,
balanced National Curriculum, encouraging them to have high
expectations in all areas of the curriculum and to reach their
full potential.

provide a secure and relaxed environment in which the
children are encouraged to have a healthy lifestyle, to be
tolerant and to grow in confidence and self-esteem.

ensure that pupils develop an open and enquiring mind and
are encouraged to be creative, imaginative and inventive.

work in partnership with parents and the wider community.
Reviewed by Governors: April 2006, April 2008, April 2011
Next review date:
Issue Date:
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Printed: 11 July 2012
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DUNCHURCH BOUGHTON C of E
(VA) JUNIOR SCHOOL
Maths Calculation Policy
Purpose
This policy has been developed to enable a consistent approach to be taken in the
teaching and learning of written mathematical calculations. This should ensure that
the methods taught allow progression in dealing with larger numbers and are
consistent with mental strategies taught.
The strategies adopted are taken from the National Numeracy strategy following
advice from The Warwickshire County Council Numeracy advisor.
To ensure familiarity with traditional calculations, children will be shown alternative
methods, where appropriate, before they complete Key Stage 2.
Aims
For children to be taught one clear method to complete each calculation type.
For methods taught to link to mental strategies taught.
For children, teachers and parents to all use the same calculation methods.
Multiplication
Children should know and use multiplication facts to 10x10. When sufficient facts
are known children may progress to multiplying larger numbers as shown below.
Questions should initially be written horizontally to enable children to make a
sensible estimate before calculating.
16 x 5
(Partition 16 into 10 + 6, then set the calculation out as below.)
X
5
10
50
6
30
= 80
The steps within the calculation are as follows
10 x 5 =50
6 x 5 = 30
50 + 30 = 80
Hence 16 x 5 = 80

3 digit x 1 digit (HTU X U )
256 X 8 is approximately 260 x 10 = 2600
X
8
200
1600
50
400
6
48
= 2048
( The final calculation of 1600 + 400 + 48 can be done mentally or with appropriate
jottings, or using the method children are using for addition. )

Decimals with one decimal place multiplied by a single digit integer.
4.9 X 3 is approximately 5 x 3 = 15
X
3
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Printed: 11 July 2012
4
12
0.9
2.7
Page 2
= 14.7
DUNCHURCH BOUGHTON C of E
(VA) JUNIOR SCHOOL
Maths Calculation Policy

2 digit x 2 digit (TU x TU)
23 X 37 is approximately 20 x 40 = 800
X
30
7
20
600
140
3
90
21
= 690
= 161 +
851
Add numbers from left to right Then total.
(Children should be aware that whichever order they add the numbers the
answer will be the same because of the commutivity of addition. Eg 600 + 140 +
90 + 21 = 851 )

3 digit x 2 digit (HTU X TU)
324 X 43
X
40
3
300
12000
900
20
800
60
4
160
12
= 12960
= 972 +
13932
Care should be taken when selecting numbers in calculations. For example, when
multiplying decimals for the first time using the grid method, use numbers such as
4.5 x 5.
Children who do not know all of their tables can use the grid method to multiply
larger numbers based on tables they should be familiar with. Eg 253 x 4 requires
knowledge of 2, 5 and 3 times tables and understanding of place value.
Subtraction
This method, also called complementary addition, builds on mental methods taught.
It is based on finding the difference between 2 numbers by counting on from the
smallest to the largest.
The two numbers being subtracted are positioned at each end of a number line. An
addition to the smallest number is made to the nearest 10, this is noted on the line.
Further additions are made, and noted, until the second of the two numbers being
subtracted is reached. All the additions are then added mentally, giving the final
answer.
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Printed: 11 July 2012
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DUNCHURCH BOUGHTON C of E
(VA) JUNIOR SCHOOL
Maths Calculation Policy
56 – 27 (TU –TU)
This is approximately 56 – 30 = 26
+3
+10
+ 10
+6
= 29
--------------------------------------------27
30
40
50
56
The size of jump may vary according to confidence. The next stage in the
understanding of this calculation would be to make a more efficient jump of 20 from
30 to 50.
.
157 –78 (HTU – TU)
+2
+20
+57
= 79
----------------------------------------78
80
100
157
763 – 285 (HTU – HTU)
+15
+400
+63
= 478
----------------------------------285 300
700
763
12.5 – 3.6 (Decimals to 1 decimal place)
+0.4
+8.5
= 8.9
------------------------------
3.6
4.0
12.5
8.37 – 3.59 (Decimals to 2 decimal places)
+0.41
+4.37
= 4.78
--------------------------------3.59
4.0
8.37
It may be appropriate for some children at the end of year 6 to investigate other
methods of subtraction, including decomposition.
Division
The aim is that children should know and use multiplication facts to 10x10, and
know and use the corresponding division facts.
However, children need to be dividing even when they don’t know the number facts
ie tables. Children should be able to count on, for example, in 2`s even if they don’t
know by heart their 2 x tables. As children move on from counting on in groups of
the divisor, they need to use key facts to help them.
The key facts needed, will be 10x, 5x and 2x. Known facts can be used to make
fewer steps. This enables children to more efficient in their calculations, and
eliminates the need to always start counting on from zero.
The number being divided is positioned at the right end of a number line, 0 is placed
at the other end. Jumps along the line are made in multiples of the divisor (the
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Printed: 11 July 2012
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DUNCHURCH BOUGHTON C of E
(VA) JUNIOR SCHOOL
Maths Calculation Policy
number being divided by), 7 in the example below. The number of jumps is totaled
and recorded along with any remainder.
68  7
7
7
7
7
7
7
7
7
7
“ nine sevens are sixty three remainder 5”
(R5)
----------------------------------------------------0 7 14 21 28 35 42 49 56 63 68
68  7 = 9 R 5
A more efficient method would be to use key facts as a starting point.
“I know that 5 x 7 = 35, so that will be my first jump”.
5
x7
7
7 7 7 (R5)
x1 x1 x1 x1
------------------------------------------------------0
35 42 49 56 63 68
As confidence increases children may use other known tables facts to help them in
their calculation.
I know 7 x 7 = 49 and I know 2 x 7 = 14
68  7
7
x7
2
x7
R5
-------------------------------------------------------0
49
63
68
68  7 = 9 R 5
Leading to 3 digits divided by 2
216  13
10
x13
5
x13
1
x13
R8
216÷13 = 16R8
------------------------------------------------------------------------0
130
195
208
216
The remainder can alternatively be recorded as a quotient 216 ÷ 13 = 16 8/13
This method of recording the answer should be clearly modeled to support
understanding.
Addition
Children will be taught to mentally add number bonds for all numbers to 10, then 20.
As they progress to adding two 2 digit numbers, they will be taught to partition the
numbers, then add.
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Printed: 11 July 2012
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Maths Calculation Policy
DUNCHURCH BOUGHTON C of E
(VA) JUNIOR SCHOOL
Addition sums should be written horizontally, initially. Each mental step in the
calculation should be recorded on a separate line.
A number of steps will be taught, confidence with one is necessary before moving to
the next. Some children will not progress to step 5.
The method used is based on understanding of partitioning and recombining
numbers.
E.g.
13 + 16 =
is 10 + 3 + 10 + 6
so 10 + 10 = 20
3+6=9
20 + 9 = 29
Step 1
48 + 53 =101
40 + 50 = 90
8 + 3 = 11
90 + 11 = 101
Partition each number then add tens, then units
Mentally add the sum of the two partitioned parts
When children are confident with this method and can apply it to 3digit numbers,
and can use it to solve problems, subsequent steps can be taught.
Step 2
48 + 53 = 101
The process of step 1 along side the usual addition layout
48 (40 + 8)
+ 53 (50 + 3)
-------------90 (40+50)
The most significant digit is added first i.e. 10’s
11 (8 + 3)
-------------101
The answer is then transferred to complete the original sum
Step3
48 + 53 = 101
The process of step 2 not showing the partitioning.
48
and adding the most significant digits first
+ 53
--90
+ 11
--101
Step 4
48 + 53 =101 As step 3 but adding the least significant digits first
48
+ 53
---11
+ 90
---101
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Printed: 11 July 2012
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Maths Calculation Policy
DUNCHURCH BOUGHTON C of E
(VA) JUNIOR SCHOOL
Step 5
48 + 53 = 101 The compact method
48
+ 53
---101
---Children will be at different stages in their understanding of the process and should
move on when they are secure at using a particular stage.
Care should be taken when selecting numbers for calculations as progression is
important.





Numbers that do not bridge 10
Numbers that bridge 10
Numbers that do not bridge 100
Numbers that bridge 100
Numbers that bridge both 10 and 100
All calculation methods taught will be modeled to support children`s understanding
so that they have a good sense of the size of numbers and a clear understanding of
the operations being used.
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Printed: 11 July 2012
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