Download calculation policy - St Stephen`s, Church of England Primary School

ST STEPHEN’S C of E PRMARY SCHOOL AND CHILDREN’S CENTRE
CALCULATION POLICY
Progression towards a standard written method of calculation
INTRODUCTION
This calculation policy complies with the expectations set out in the National Curriculum for
Mathematics (2014). It provides guidance on appropriate calculation methods and
progression from EYSF to Year 6 under the following headings: addition, subtraction,
multiplication and division.
Children will use mental methods as their first port of call when appropriate, but for
calculations that they cannot do in their heads, they will need to use an efficient written
method accurately and with confidence.
AIMS OF THE POLICY
The aims of the policy are:
 to show the progression of calculation methods from early years to end of key stage
two: from informal to formal methods
 to ensure progression and consistency in teaching calculation methods across the
school
 to ensure that children develop efficient, reliable, formal written methods of
calculation for all operations and can use them effectively
MENTAL METHODS
Early practical, oral and mental work must lay the foundations by providing children with
good understanding of how the four operations build on efficient counting strategies and a
secure knowledge of place value and number facts.
Later on children must recognise how the operations relate to one another and how the
rules and laws of arithmetic are to be used and applied.
The ability to calculate mentally forms the basis of all methods of calculation.
A good knowledge of numbers or a ‘feel’ for numbers is the product of structured practice
and repetition.
An understanding of number patterns and relationships develops through directed enquiry,
use of models and images and the application of acquired number knowledge and skills.
1
PROGRESSION OF NUMBERLINES
Number track
Has the numbers
inside the
sections, rather
than on the
divisions
Calibrated,
numbered
numberline
Equal divisions
marked on the
numberline and
each division is
numbered
Calibrated,
unnumbered
numberline
Equal divisions are
marked, but left
unnumbered for
children to add
relevant numbers
to
Blank
numberline
No divisions or
numbers marked
for the children
ADDITION
Early Years (EYFS)
Objectives:
22-36 months: To know that a group of things changes quantity when something is
added.
ELG:
To begin to relate addition to combining two groups of objects.
To find one more than a given number.
Children engage in variety of maths songs, games and activities. They use mathematical
language related to addition through practical tasks involving a range of equipment including
small world play, role play, counters/cubes, etc.
2
1. Pupils engage in singing songs, rhymes when objects are added e.g. One potato, two
potato....
1, 2, 3, 4, 5, ...
Counting children coming and going from a group activity.
2. 6+2=8
‘I have 6 lollies and you have 2 lollies. How many altogether?
(see the methods outlined in the next year)
Year 1
Objectives:
 Read, write and interpret mathematical statements involving addition (+) and
equals (=) signs.
 Identify 1more/10more than any number.
 Add one-digit and two-digit numbers to 20, including zero.
 Solve missing number problems such as 7 = +4
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Practise counting on from any number, e.g. put 5 in your head and count on 3.
5+3=8
2. Use number track to count on for addition (numbers up to 20):
6+4=10
‘Put your finger on
number 6 and count on 4.’
3. Use marked number line (numbers up to 20):
7+3=10
7+3=10
Put your fingers on number 7 and
move 3 to the right.
Ensure pupils are confident using marked number line before moving on to the empty
number line.
(see the methods outlined in the next year)
3
Year 2
Objectives:
 Add numbers using concrete objects, pictorial representations, and mentally,
including:
-a two-digit number and ones
-a two-digit number and tens
-two two-digit numbers
-adding three one-digit numbers
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Use empty number line adding ones
(numbers within 100):
+1 +1 +1 +1
27
27+4=31
2. Use empty number line adding 10s
(numbers within 100):
+10 +10 +10 +10
27
31
Children count on in 1s
27+40=67
67
Children count on
in 10s
3. Use empty number line with partitioning: 4. Use empty number line adding
multiples of 10.
+10
+1
23
33
+1
+30
35
53
23+12=35
+6
83
89
Partitioning the second number
53+36=89 More efficient way (adding a
multiple of 10; then a ones number)
6. Use partitioning bridging through
tens:
5. Use partitioning into tens and ones and
recombine:
12 + 23 = 10 + 2 + 20 + 3
= 30 + 5
23+39= 20+3+30+9
= 35
20+30=50
Refine to partitioning the second number:
3+9=12
23 + 12 = 23 + 10 +1 + 1
50+12=62
= 33 + 1 + 1
= 35
(see the methods outlined in the next
year)
4
Year 3
Objective:
 Add numbers with up to three digits, using formal written methods of columnar
addition.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Use an empty number line with
calculation that bridge through 100:
+50
67
125
+8
117
76+59=70+50+6+9
70+50=120
6+9=15
120+15=135
5. Use expanded written method:
36 + 43 = 79
36 = 30 + 6
43 = 40 + 3
Recombine
to get the
answer
+50
+8
167
67+58=125
3. Use partitioning bridging through
100:
Partition both
numbers
2. Using an empty number line to add 2
digit number to a 3 digit number:
217
225
167+58=225
4. Partition into hundreds, tens and ones
and recombine:
139+36 = 139+30+6
=169+6
=175
6. Then
53
+3 2
5 (3 + 2)
8 0 (50 + 30)
85
Add the least significant digits
(units) together first and then
the tens in preparation for the
formal written method.
Then Ensure secure place value as we add
units/ones to get 5 and 50+30 makes 80
153
so write 8 in tens column.
+ 32
185
7. Then use the same methods when adding numbers bridging through 10, e.g.
63+39=
When the children are ready, teach them to use the written methods bridging through
tens and hundreds, e.g. 76+47=
Then move to addition of 3 digit numbers and 2 digit numbers using formal method.
153
+ 39
192
1
(see the methods outlined in the next year).
30 + 40 6 + 3
5
Year 4
Objective:
 Add whole numbers with up to 4 digits, including using formal written methods
(columnar addition).
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Continue to teach the use of empty
number lines using 3 and 4 digit
numbers.
2. Revisit expanded method:
126+238=
100+20+6
200+30+8
300+50+14=364
(see the methods outlined in the
previous year).
3. Reduce the recording:
4. Formal written method (standard
compact form):
126
+ 238
Use the language of place
value when explaining
364
1
126
+ 238
14 (8+6)
+ 50 (20+30)
300 (100+200)
364
If the pupils are ready introduce the
addition of 4 digit numbers and 3 digit
numbers.
(see the methods outlined in the next year).
Year 5
Objective:
 Add whole numbers with more than 4 digits, including using formal written
methods (columnar addition).
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Continue to teach the use of empty number lines with larger numbers and decimals.
+50
367
+8
417
425
6
367+58=425
2. Use column method (standard compact
form):
3. Use formal written method to add
decimals:
154.75
+ 233.82
388.57
1
Year 6
There are no new methods for addition in year 6. Pupils, however, are expected to continue
to practise and use formal written methods for addition of larger numbers and decimals
when solving problems (see previous year’s methods for reference).
SUBTRACTION
Early Years (EYFS)
Objectives:
22-36 months: To know that a group of things changes quantity when something is taken
away.
ELG: Begin to relate subtraction to ‘taking away’ using objects to count how many are
left after some have been taken away.
Find one less than a given number.
Children engage in variety of maths songs, games and activities. They begin to use
mathematical language related to subtraction through practical tasks involving a range of
equipment including small world play, role play, counters/cubes, etc.
1. Pupils engage in singing songs, rhymes when objects are taken away, e.g. ten fat
sausages sizzling in a pan, one went pop and another went bang!
10, 9, 8, 7
7
2.
7- 3 = 4
‘Take 3 lollies away. How many are left?’ Visuals are essential.
(see the methods outlined in the next year)
Year 1
Objectives:
 Read, write and interpret mathematical statements involving subtraction (-) and
equals (=) signs.
 Identify 1 less/10 less than any number.
 Subtract one-digit and two-digit numbers to 20, including zero.
 Solve missing number problems such as 16 =
-5
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Practise counting back from any number using your fingers (small numbers), e.g. take
9 fingers out and count back 3 hiding the fingers.
9-3=6
2. Use number track to count back for subtraction (numbers up to 20):
10 – 3 = 7
‘Put your finger on
number 10 and count back 3.’
3. Use marked number line (numbers up to 20):
10 – 3 = 7
7+3=10
‘Put your finger on number 10 and
move 3 to the left.’
Ensure pupils are confident using marked number line before moving on to the empty
number line.
4. Use counting on to find the difference (small differences).
9 stars
5 stars
8
5. ‘Count up from the smallest number to find the difference.’
9 and 5 is 4’
7
‘The difference between
11
‘The difference between 7 and
11 is 4’
(see the methods outlined in the next year)
Year 2
Objectives:
 Subtract numbers using concrete objects, pictorial representations, and mentally,
including:
-a two-digit number and ones
-a two-digit number and tens
-two two-digit numbers
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Use 100 square
2. Use empty number line counting back in
ones (numbers within 100):
-1 -1 -1 -1
27
31-4=27
3. Use empty number line counting back
in 10s (numbers within 100):
-10 -10 -10 -10
27
Children count back in 1s
4. Use empty number line partitioning
second number:
-1
-1
--10
67
24 25
67 – 40 =27
31
Children count back in
10s
35 – 12 = 23
9
35
Partitioning the second number
5. Use empty number line subtracting
multiples of 10.
6. Count on to find a small difference.
‘Count up from the smallest number to the
largest number to find the difference.
Examples:
15 – 7 = 8 ‘Count on from 7 up to 15’.
‘The difference between 15 and 7 is 8.’
32 - 27 = 5 ‘Count on from 27 up to 32’.
‘The difference between 32 and 27 is 5’.
76 – 59 = 17 ‘Count on from 59 to 76....59 +10
is 69 add 7’ ‘The difference between 76 and
59 is 17’
(see the methods outlined in the next year)
Year 3
Objective:
 Subtract numbers with up to three digits, using formal written methods of columnar
subtraction.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Use an empty number line with
calculations that bridge through 100:
-5
2. Use an empty number line to subtract
multiples of ten (more efficient way):
-10
-5
-10
102
102
107
117
127
127 – 25 = 102
3. Subtraction using partitioning:
74 – 27 =
74 – 27 = 74 – 20 – 7 = 54 – 7 = 47
126 - 27=
126 – 27=126 – 20 – 7 =99
107
-20
127
127 – 25 = 102
When the pupils are ready extend to larger
numbers.
4. Count on to find the difference:
The mental method of counting up from
the smaller to the larger number can be
recorded using either number lines or
vertically in columns.
10
Partition the second number to subtract.
115- 97=18
115
so
97+10+8=
97
+10
107
+8
115
‘The difference between 215 and 197 is 18.’
5.
6.
You might replace the + sign with the word
‘and’ to avoid confusion.
7. Formal written method (column
8. Column subtraction involving
subtraction):
decomposition/exchange:
63
-32
31
6 13
73
- 16
57
Use the language of place value to ensure
understanding.
‘We can’t subtract six from three, so we need to
exchange a ten for ten ones to give us 60 + 13.’
Use base ten materials to support understanding.
9. Formal written methods with numbers over 100.
If children are confident, extend the use of the formal written method with larger
numbers (3 digits), returning to the expanded method first, if necessary.
(see the methods outlined in the next year).
Year 4
Objective:
 Subtract whole numbers with up to 4 digits, including using formal written methods
(columnar subtraction).
11
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Continue to teach the use of empty
number lines using 3 and 4 digit
numbers:
-5
2. Revisit expanded method:
226-18=
-20
127
10 16
102
107
200+20+6
Ensure pupils are secure
with partitioning
127 – 25 = 102
10+8
When the pupils are ready extend to larger
208=200+8
numbers.
3. Formal written methods involving
4. If the pupils are ready introduce the
decomposition:
subtraction of 3 digit numbers from 3
digit numbers:
1 15
258
Exchange from the tens and
537 – 142 = 395
hundreds column
-73
500 + 30 + 7
400 + 130 + 7
185
- 100 + 40 + 2 - 100 + 40 + 2
300 + 90 + 5 = 395
5. When children are confident develop subtraction using 4 digit numbers and decimals
(in the concept of money and measures) using methods above.
(see the methods outlined in the next year)
Year 5
Objective:
 Subtract whole numbers with more than 4 digits, including using formal written
methods (columnar subtraction).
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Continue to teach the use of empty
number lines with larger numbers
and decimals:
-5
272
2. Return to expanded method if necessary:
503-278=225
-50
277
327
327 – 55 = 272
12
When pupils are ready extend to larger
numbers.
3. Develop the stages of
4. Subtraction using larger numbers and
decomposition introducing ‘zero’:
decimals:
2 4 1
4 9 9
1
352
5000
-178
- 457
174
4543
Extend to up to 2 decimal places
48.42 – 37.61 =
4 78 . 14 2
3 7 . 6 1
1 0 . 8 1
Year 6
There are no new objectives set out for subtraction in year 6. Pupils, however, are expected
to continue to practise and use formal written methods for subtraction of larger numbers
and decimals when solving problems (see previous year’s methods for reference).
MULTIPLICATION
Early Years (EYFS)
Objectives:
 Count repeated groups of the same size.
 Share objects into equal groups and count how many in each group.
Children engage in variety of maths songs, games and activities. In practical activities and
through discussion they will begin to solve problems involving doubling.
3+3=6
‘Three lollies for me and three for you. How many altogether?’
(see the method outlined in the next year)
Year 1
Objectives:
 Count in multiples of twos, fives and tens (to the 10th multiple).
13
 Solve one-step problems involving multiplication and division, by calculating the
answer using concrete objects, pictorial representations and arrays with the support
of the teacher.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the EYFS.
1. Practise counting in 2s, 5s, 10s in real situations, engaging in practical problem
solving.
‘Three pairs of socks. How many
altogether? 2, 4, 6’
2. Use pictures and symbols:
There are 3 sweets in one bag.
How many sweets are there in 5 bags?
3 make 15 sweets.’
3. Use of bead strings to model groups of: 4. Use
arrays
multiplication:
‘4 groups of 5. How many beads?
15, 20’
5 groups of
to
support
early
‘Four groups of 2 faces.
5, 10, How many faces altogether?’ ‘2, 4, 6, 8’
(see the methods outlined in the next year)
Year 2
Objectives:
 Recall and use multiplication and division facts for the 2, 5 and 10 multiplication
tables, including recognising odd and even numbers.
 Calculate mathematical statements for multiplication and division within the
multiplication tables and write them using the multiplication (×), division (÷) and
equals (=) signs.
 Show that multiplication of two numbers can be done in any order (commutative)
and division of one number by another cannot.
 Solve problems involving multiplication using materials, arrays, repeated addition,
mental methods, and multiplication and division facts, including problems in
contexts.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
14
1. Combining groups (repeated addition):
2. Using arrays:
‘3 boxes of crayons. 10 crayons in each box.
How many crayons altogether?
10+10+10=30
3 groups of 10 is 30
3 times 10’
3. Use empty number line.
0
5
10
15




 
 
 
 
Reinforce the concept of multiplication
being done in any order.
4. x = signs and missing numbers
7x2=
7 x  = 14
 x 2 = 14
 x  = 14
20
‘4 x 5=20 4 jumps of 5’
‘5+5+5+5=20 repeated addition’
  5+5+5+5=20
  four rows of 5
  four groups of 5
  4 x 5=20
5 x 4=20
=2x7
14 =  x 7
14 = 2 x 
14 =  x 
(see the method outlined in the next
year)
Year 3
Objectives:
 Recall and use multiplication facts for the 3, 4 and 8 multiplication tables.
 Write and calculate mathematical statements for multiplication and division using
the multiplication tables that they know, including for two-digit numbers times onedigit numbers, using mental and progressing to formal written method.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Continue to use number lines and arrays 2. Doubling multiples of 5 up to 50:
to support multiplication, as
appropriate:
‘15 x 2 = 30 double 15 is 30’
0
4
8
12
‘3x4=12 3 jumps of 4’
15
3.
4. Partitioning:
15x4=60
(10 x 4) + ( 5 x 4)
40 +
20 = 60
5. Partition using a grid method:
6. Expanded short multiplication:
14x8= 112
13 x 8 = 104
x
8
10
80
10 + 3
x8
2 4 (3 x 8)
+ 8 0 (10 x 8)
104
(see the methods outlined in the next
year).
4
32
80+32=112
Year 4
Objectives:
 Recall multiplication facts up to 12 x 12.
 Multiply two-digit and three-digit numbers by a one-digit number using formal
written layout.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Continue to use empty number lines, as
appropriate.
2. Partition to multiply using a grid
method:
34x8= 272
x
30
8 240
4
32
240
+32
=272
16
3. Expanded short multiplication:
4. Formal short multiplication:
34 x 4 = 136
36 x 4=
Use the language of place value
to ensure understanding. Ensure
that the digit ‘carried over’ is
written under the line in the
correct column.
30 + 4
x4
36
16 (4 x 4)
x 4
+ 120 (4 x 30)
144
2
136
5. If children are confident, continue to develop short multiplication with three-digit
numbers multiplied by a one-digit number.
136x4=
If needed revisit expanded short multiplication and/or grid method.
Year 5
Objective:
 Multiply numbers up to 4 digits by a one- or two-digit number using a formal written
method, including long multiplication for two-digit numbers.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year, especially formal method of short multiplication.
1. Partition to multiply using a grid 2. Expanded long multiplication
method:
34 x 14 = 476
15x32= (10+5) x (30+2) = 480
34
X14
x
10
5
16 (4 x 4)
30 300 150
+ 120 (4 x 30)
2 20
10
40 (10 x 4)
300 (10 x 30)
476
3. Compact formal method:
4. When children are confident with long
multiplication extend with three-digit
34 x 14 = 476
numbers multiplied by a two-digit
number, returning to the grid method first,
34
if necessary.
X14
136 (4 x 34)
340
476
132x23= 3036
132
X 23
17
Use previous methods if needed to multiply
larger 2 digit numbers, e.g. 26x52=
396 (3x132)
2640 (20x132)
3036
(see the method outlined in the next year)
Year 6
Objective:
 Multiply multi-digit numbers (including decimals) up to 4 digits by a two-digit whole
number using the formal written method of long multiplication.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year, especially formal method of short and long multiplication.
1. Compact long multiplication with three- 2. Formal written method for long
digit numbers multiplied by a two-digit multiplication involving decimals:
number:
34.2 x 14 =
132x23= 3036
34.2
X14.0
132
136.8 (4 x 34.2)
X 23
+
342 (10 x 34.2)
396 (3x132)
478.8
2640 (20x132)
3036
3. Use the grid method:
If children show lack of understanding, please
refer to earlier stages of multiplication
DIVISION
Early Years (EYFS)
Objectives:
30-50 months: To be able to separate a group of 3 or 5 objects in different ways and
begin to see
that the total is still the same.
ELG:
To begin to talk about sharing and halving.
18
1. Children engage in games or group activities where the teddies have a tea party and all
the 3 bears get a cake each. Then one bear gives his to another, .... Are there still 3
cakes?
2.
‘Share eight lollies between two children. How many do they each get?’
Visuals are key.
(see the method outlined in the next year)
Year 1
Objectives:
 Solve one-step problems involving division; by calculating the answer using
concrete objects, pictorial representations and arrays with the support of the
teacher.
 Count in multiples of two, five and ten.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the EYFS.
1. Explore concept of sharing objects into equal groups, engaging in practical problem
solving.
‘Share these 6 cookies between 2 children. How
many will each child get?’
2. Use grouping:
‘Put 15 sweets into groups of 3. How
many groups do you have?’
3. Use arrays to support early division:
‘How many groups of 2?
Four groups of 2
’15
sweets make 5 groups of 3.’
faces.’
(see the methods outlined in the next year)
Year 2
Objectives:
19
 Solve problems involving division, using materials, arrays, repeated subtraction,
mental methods, and multiplication and division facts, including problems in
contexts.
 Recall and use multiplication and division facts for the 2, 5 and 10 multiplication
tables.
 Calculate mathematical statements for division within the multiplication tables
they know and write them using the division (÷) and equals (=) signs
Before progressing to the following methods ensure pupils are secure in the methods
outlined in year 1.
1. Sharing and grouping:
2. Using arrays:




‘30 pencils shared between 3 pots’.
‘We have 30 pencils. We need to put ten in
each pot. How many pots do we need?’
30 ÷ 3=10
30 ÷ 10=3
3. Use empty number line (repeated
subtraction):
-5
0
-5
5
-5
-5
10
15
 
 
 
 








20 ÷ 5 = 4
20 ÷ 4 = 5
How many groups of 4?
How many groups of 5?
4. ÷ = signs and missing numbers:
6÷2=
6÷=3
÷2=3
÷=3
20
’20 ÷ 5=4 4 jumps of 5’
20–5-5-5-5=0 repeated subtraction’
=6÷2
3=6 ÷
3=÷2
3=÷
(see the method outlined in the next year)
Year 3
Objectives:
 Recall and use division facts for the 3, 4 and 8 multiplication tables.
 Write and calculate mathematical statements for division using the multiplication
tables that they know, including for two-digit numbers divided by one-digit numbers,
using mental and progressing to a formal written method.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in year 2.
1. Use an empty number line to count
forward:
+4
+4
+4
+4
+4
2. Continue to use number lines (repeated
subtraction):
-4
+4
20
-4
-4
-4
-4
-4
0
24
4
8
12
16
20
0
24
4
8
12
16
20
’24 ÷ 4= 6 How many jumps of 4 are
’24 ÷ 4= 6 6 jumps of 4’
there in 24?’
3. Introduce the formal layout using multiplication/division facts that the children know:
24 ÷ 4 = 6
6
4 24
’24 divided by 4 is 6’ ‘How many 4s are there in
24?’
(see the method outlined in the next year)
Year 4
Objectives:
 Recall multiplication and division facts up to 12 x 12.
 Use place value, known and derived facts to divide mentally.
 Divide two-digit and three-digit numbers by a one-digit number using formal written
layout (not explicitly stated in the programmes of study but implied in the nonstatutory guidance).
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Continue using the formal written
layout for division using multiplication
tables that pupils know:.
40 ÷ 8 = 5
5
8 40
2. Use empty number line to work out
division with remainders.
’40 divided by 8 is 3’ ‘How many 8s are
there in 40?’
3. Formal written method with
remainders:
4. Division using partitioning (2 digit by 1
digit):
96 ÷ 6 = 16
10 6 = 16
6 60 + 36
Partition 96=60+36. The pupils need to
practise partitioning and know their times
Remainders are not specifically referred to tables well.
until Y5 in the National Curriculum.
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However, this may be an appropriate point Six ‘goes into’ 60 ten times and
to introduce them using familiar six ‘goes into’ 36 six times.
Ten add six equals 16’
multiplication facts.
5. Formal written method of short
division:
96 ÷ 6 = 16
1 6
6 9 ³6
Use the vocabulary of
place value to ensure
understanding and
make a link to
partitioning.
6. If children are confident, develop further
by dividing three-digit numbers by a one
digit number using the formal method of
short division with whole number (no
remainders).
(see the method outlined in the next year)
Year 5
Objective:
 Divide numbers up to 4 digits by a one-digit number using the formal written method
of short division and interpret remainders appropriately for the context.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year, especially formal method of short division.
1. Continue to practise the formal written
method of short division with whole
number answers:
2. Short division with remainders:
253 ÷ 4 = 63 r1
6 3r1
4 2 5¹3
168 ÷ 7 = 24
24
7 1 6²8
The remainder can also be expressed as a
fraction, (the remainder divided by the
Use the language of place value to ensure
divisor):
understanding.
253 ÷ 4 = 63¼
Make a link to the partitioning method (see (see the method outlined in the next year)
Y4 guidance).
Year 6
Objectives:
 Divide numbers up to 4 digits by a two-digit number using the formal written method
of short division where appropriate, interpreting remainders according to the
context.
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 Divide numbers up to 4 digits by a two-digit whole number using the formal written
method of long division, and interpret remainders as whole number remainders,
fractions, or by rounding, as appropriate for the context.
Before progressing to the following methods ensure pupils are secure in the methods
outlined in the previous year.
1. Continue with Short division with or
without remainders:
253 ÷ 4 = 63 r1
2. Formal written method of long division
(dividing by 1 digit numbers):
6 3r1
4 2 5¹3
The remainder can also be expressed as a
fraction, (the remainder divided by the
divisor):
253 ÷ 4 = 63¼
3. Formal written method of long division
(dividing by 2 digit numbers):
4.
Our aim is that by the end of Y6 children
use mental methods (with jottings) when
appropriate, but for calculations that they
cannot do in their heads, they use an
efficient formal written method accurately
and with confidence.
Multiples of the divisor (12) have been
subtracted from the dividend (197)
‘10 (lots of 12) + 5 (lots of 12) + 1 (lot of
12)= 16 (lots of 12)’ ‘5 is the remainder’
Reference:
Southwark Council, Written Calculation Policy for Southwark Primary Schools, 2014.
Agreed by Governors
(Chair Signature):
Policy Due for Review:
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