Baddow Hall Junior School
Written Calculations in Mathematics Policy
Baddow Hall Junior School is a fun, educational experience for all our children
in a happy and safe environment.
This is a working document which will be monitored and reviewed annually.
Adoption Date ………………………………………………
Signed ..……………………………………………..
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
Baddow Hall Junior School’s Policy for Written Calculations in Mathematics
This policy is to ensure written methods of calculation that children will be taught to use at
BHJS for the four mathematical operations (add, subtract, multiply and divide) are clear.
We have developed a consistent approach to the teaching of written calculations in order to
establish continuity and progression throughout our school and to meet the requirements of
the National Curriculum 2014 in Mathematics.
Informal written recording, to aid mental calculations, is a vital step in learning and
understanding when using the four operations and formal written methods can only be applied
once children have a sound knowledge of mental calculation strategies and informal jottings.
Children should only move onto the next step in the operation when they have mastered the
previous step, regardless of age or year group.
Once children have a secure knowledge of calculations, ensure they check answers using the
inverse operation.
Give the children as many opportunities as possible to apply their calculations within word
problems and real life situations.
All year groups will need to consolidate learning from the previous year, as well as extending
where necessary.
Before children are taught to use formal written methods it is important for them to have a
sound understanding of the following mental calculation strategies:
Addition and Subtraction
• Secure knowledge of number bonds to 10.
• Recall all addition pairs to 9+9.
• Addition and subtraction facts to 20.
• Understanding place value of numbers with up to 3 digits and partitioning these correctly.
• Adding three single digit numbers mentally.
• Add and subtract multiples of 10.
• Explaining their mental strategies orally and recording them using informal jottings.
Multiplication and Division
• Know the result of multiplying by 1 and 0.
• Knowledge of 2,3,4,5, 6, 7, 8, 9 and 10 times tables.
• Understanding of 0 as a place holder.
• Doubling and halving 2 digit numbers mentally.
• Multiplying two and three digit numbers by 10 and 100.
• Explaining their mental strategies orally and recording them using informal jottings.
The general progression in this policy is:
• Establish mental methods, based on a good understanding of place value.
• Use of informal jottings to aid mental calculations.
• Use partitioning and recombining to aid informal methods.
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
Refer to National Curriculum September 2014 for further examples of what children are
expected to do.
ADDITION
Year 3 -First stages of column addition
Introduction to vertical layout. Using partitioning, without breaking 10s and 100s barriers.
For example: 425 + 373
H
T
U
TOTAL
4
0
0
+
2
0
+
5
3
0
0
+
7
0
+
3
7
0
0
+
9
0
+
8
=
7
9
8
Vertical layout, using partitioning, breaking the 10s and 100s barriers.
For example: 487 + 378
H
T
U
TOTAL
4
0
0
+
8
0
+
7
3
0
0
+
7
0
+
8
7
0
0
+
1
5
0
+
1
5
=
8
6
5
Year 4 -Second stage of column addition
Introduction to formal column addition. Children must have sound understanding that units
line up below units, tens below tens etc
No carrying
H
T
U
3
4
2
1
+
5
5
With carrying
H
T
U
2
7
4
8
+
7
5
1
Place carried amounts under the ‘door step’ so
as not to miss them out in adding process.
Year 5 & 6 - Consolidate column method of addition, apply to decimals
Column Addition with Decimals
Extend to problems with more than 2 rows and those involving decimals.
H
+
T
2
6
9
1
U
6
9
6
1
t
3
8
1
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
When solving decimal problems, line up the decimal points first. Also put decimal point in
first when writing the answer. Decimal points do not have their own column.
SUBTRACTION
Year 3 -First stages of column subtraction
Begin to solve subtraction sums in a vertical layout, using partitioning without exchanging.
For example: 563 - 241
H
5
0
0
2
0
0
3
0
0
T
6
4
2
0
0
0
-
U
5
3
2
TOTAL
=
3
2
2
Leading to:
Then start to introduce the concept of exchanging from one column, using tens and units only
e.g. 63 – 28
T
U
5
0
6
0
1
3
2
0
8
3
0
5
=
3
5
We have exchanged 10 from the 60, so the 60 becomes 50 and the 3 becomes 13.
-
Year 4 -Second stages of column subtraction
-
H
5
2
3
T
6
4
2
Leading to:
U
3
1
2
H
-
T
U
6
2
3
13
5
8
5
Then introduce the concept of exchanging from more than one column, using hundreds, tens
and units.
H
T
U
-
4
15
5
2
2
6
7
8
13
8
5
First exchange from one column and then, once confident, exchange from more than one. To
extend further, include a double exchange i.e. 1100 – 296.
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
Year 5 and 6
Column subtraction with decimals. Extend to problems involving decimals. When writing in the
number to be subtracted, line up the decimal point first. Also put the decimal point in first
when writing the answer. Decimal points do not need their own column.
MULTIPLICATION
Year 3 -First stages of multiplication
Consolidate previous year’s work including repeated addition.
Consolidate understanding of the following mental calculation strategies:
• Knowledge of 2,3,4,5 and 10 times tables.
• Explaining their mental strategies orally and recording them using informal jottings.
• Understanding 0 as a place holder.
• Doubling and halving 2 digit numbers mentally.
• Know the result of multiplying by 1 and 0.
• Multiplying two and three digit numbers by 10 and 100.
Learn additional multiplication facts
Work on different ways to derive new facts from those that they already know
Know by heart multiplication facts for x2, x5, x10
Begin to learn/consolidate facts for x3, x4
Understand effect of multiplying by 10
Multiply a single digit by 1, 10, 100.
Understand and use, when appropriate, the principles (but not the names) of the commutative
and distributive laws as they apply to multiplication.
Example of commutative law (multiplication works in any order)
8 x 15 = 15 x 8
Example of distributive law (partition one number and then multiply each part separately)
18 x 5 = 90
(10 x 5) + (8 x 5) = 50 + 40 = 90
Grid Method
Before introducing the grid method, the children need to have practised multiplying
multiples of 10. E.g. For 30 x 40, take off the 2 zeroes, 3x4=12, then put back the 2 zeroes =
1200.
Another way of thinking of 3 x 215 is 3 x 200, plus 3 x 10, plus 3 x 5. Some children prefer
to break calculations up into smaller parts.
This can be done in a grid.
The largest number goes on the top. One way to help the children to remember this is to
imagine the grid is a bus; ‘The biggest number is being bossy, so he gets to see the sights.
The smallest number has to drive.’
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
2 digits by 1 digit.
Start with using 2’s, 5’s and 10’s.
x
2
1
0
2
0
Leading to multiples of 10 E.g. 25 x 2
x
2
Work out totals using column addition
5
1
2
0
4
0
0
=
3
0
5
1
0
=
5
0
method.
Leading to any 2 digits x 1 digit, such as 37 x 4.
x
4
1
3
0
2
0
3 digits by 1 digit.
x
3
7
2
8
=
Total
1
4
8
E.g. 215 x 3
2
0
0
1
6
0
0
30
0
5
1
5
=
6
4
5
So, 3 x 215 = 645. Work out totals using column addition method.
Year 4 -Grid Method of Multiplication
To be taught once children have understood column addition.
2 digits by 1 digit -
As in year 3, but use column addition to add the totals.
3 digits by 1 digit -
As in year 3, but use column addition to add the totals.
2 digits by 2 digits - Always have the largest number on the top. Beginning with teens
number multiplied by another teens number, then move onto any 2 digit numbers.
46 x 34 is done as follows.
x
30
4
1
4
0
2
0
0
1
6
0
(30 x 40)
(4 x 40)
6
1
8
0
2
4
(30 x 6)
(4 x 6)
1
2
1
1
1
5
1
0
8
6
2
6
0
0
0
4
4
Add up the parts of the 4 answers. Make sure these 4 numbers’ Th, H, T and U are lined up.
Now perform column addition to give you the answer to the multiplication question.
Extend to 3 digits multiplied by 2 digits where appropriate.
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
Year 5
Short Multiplication - This is for 1 digit multiplied by 2 or more digits.
Make it very clear that the units must be multiplied first. Always put the largest number on
top.
H
T
2
x
7
1
U
6
3
8
Firstly, 3 x 6 is 18, carry the one.
Secondly, 3 x 2 is 6, and then add the carried 1.
Repeat method of Short Multiplication for 3 digits by 1 digit.
Long Multiplication –
This is for 2 or more digits multiplied by 2 or more digits.
Put the largest number on top, as before. Multiply the units on the top first BUT you multiply
them by the 10s on the bottom. This way, the first thing they are doing is putting in the
place holding zero, so they are less likely to forget it! Also, they then have the largest
number on top when it comes to do the column addition at the end.
For the calculation 32 x 24:
+
First insert the place holding zero.
x
6
1
7
3
2
4
2
6
2
4
0
8
8
(2
0
(4
x
x
3
3
0)
2)
Secondly. 2 x 2 is 4. (This is really 20 x 2 = 40)
Thirdly. 2 x 3 is 6. (This is really 20 x 30 = 600)
Now complete the second row in the same way you did short multiplication, then add up the 2
rows using column addition for your final answer.
Year 6
Consolidate Grid Multiplication of Multiplication (2 digit by 1 digit, 3 digit by 1 digit, 2
digit by 2 digit and 3 digit by 2 digit)
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
To extend Grid Multiplication, use decimals:
E.g. 34.7 x 8
x
8
2
3
0
4
0
3
4
0
7
2
5
6
=
2
7
7
6
=
1
7
3
5
2
3
0
1
4
2
7
And then with 2 decimal numbers:
E.g. 34.7 x 5.9
x
5
0
1
9
3
0
5
0
2
7
4
2
7
0
3
6
3
5
0
6
3
=
+
1
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
3
3
DIVISION
Year 3
Consolidate previous year’s work
Consolidate understanding of the following mental calculation strategies:
• Knowledge of 2,3,4,5 and 10 times tables.
• Explaining their mental strategies orally and recording them using informal jottings.
• Understanding 0 as a place holder.
• Doubling and halving 2 digit numbers mentally.
• Know the result of multiplying by 1 and 0.
• Multiplying two and three digit numbers by 10 and 100.
Derive division facts corresponding to 2, 10 (extension 5) times tables
Use a number line to illustrate grouping
To find how many 2s are in 8 (8 ÷ 2), the children need to understand that you are taking 2
away from the main group to make smaller groups (the beginnings of repeated subtraction).
This could be recorded as follows.
2
0
2
2
2
4
2
6
8
Grouping through chunking
Then, move onto taking groups of 2 away. E.g. the children know that 10 2s are 20, so they
can take away 20 at a time rather than individual 2s.
For 42 ÷ 2 = 21
-2
0
-20
2
-20
22
10 + 10 + 1 = 21
42
Understand division as sharing and grouping
(Children must fully understand these methods before moving onto written methods)
18 ÷ 3 can be modelled as:
Sharing – 18 shared between 3. If we share 18 sweets into 3 groups, how many sweets will
there be in each group? What goes into 18 3 times?
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
AND
Grouping - How many 3’s make 18? If we have 18 sweets, how many groups of 3 can we make?
How many 3s in 18?
Year 4- Consolidate Sharing through Chunking Method
148 ÷ 4 = 37
1
1
-
4
4
0
4
6
4
2
2
0
8
0
8
0
8
0
8
8
0
(1
0
x
4)
(1
0
x
4)
(1
0
x
4)
(7
x
4)
H
T
1
1
1
+
U
0
0
0
7
7
3
Using column addition to add up the multiple chunks
Year 5- Extend to long division
96 ÷ 3 = 32
3
-
3
9
9
0
0
0
128 ÷ 4 = 32
2
6
6
6
0
4
-
0
1
0
1
1
0
3
2
2
8
2
2
0
0
0
8
8
0
Year 6 -Short Division
The chunking method needs to have been taught before using this method.
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx
When teaching this method for the first time, use hundreds, tens and units apparatus.
Less able may need this support for longer.
For the question 795 divided by 3, set the calculation out as follows:
3
3
H
T
U
2
7
19
5
H
T
U
2
7
H
3
2
7
First, how many 3s go into 7. Or the way you would explain it to start
with, if we have 7 ‘hundreds’ blocks and shared them into 3 equal groups,
how many blocks would be in each group, or, how many groups of 3 can we
make from 7? Write the answer above the 7. ‘Carry’ the one left over
into the tens column.
6
19 15
T
U
6
5
19 15
Next, how many 3s go into 19. Or the way you would explain it to start
with, if we have 19 ‘tens’ sticks and shared them into 3 equal groups, how
many sticks would be in each group. Write the answer above the
19. ‘Carry’ the one left over into the units column.
How many 3s go into 16. Or the way you would explain it to start with, if
we have 16 ‘units’ cubes and shared them into 3 equal groups, how many
cubes would be in each group. Write the answer above the 16.
Further extension would see children dividing decimal numbers and 3 or more digit numbers
by 2 digit numbers.
734 ÷ 4 = 183.5
4
H
T
U
t
1
7
8
33
3
34
5
20
Rather than have a remainder of 2, more able children can carry
the two into the tenths column or even the hundredths and add it
to the pace holder 0.
This would give an answer of 183.5 (1 dp).
R:\2. Office 2, Office 3, Assessment and Senco\Policies\3 The Curriculum\Written Calculations in Mathematics Policy.docx