Kentisbeare Primary School- Mathematics
Calculations Policy
Published Autumn Term 2014
To be reviewed Autumn Term 2015
Kentisbeare Primary School Calculation Policy
This policy has been created to meet the requirements of the New Primary Curriculum for 2014. It outlines the development that we expect the children to make as they
pass through each year group. At its core is a desire to give children quality, consistent and smooth learning of calculations in mathematics from their point of entry to the
time they leave us.
Early Years Foundation Stage (EYFS)
EYFS works developmentally to support the children to play and explore, actively learn, create and think critically the expectation is that children will meet the Early
Learning Goals (ELGs) in Mathematics by the end of EYFS. We realise, that if children do not meet the ELGs, further provision at this level is needed in Key Stage One.
Key Stage One and Two
Although this policy is broken down into year groups we understand that all children develop at different rates and it is critical to enabling children to reach their maximum
potential that we teach by stage not age.
Using Written Methods
Written methods enable children to demonstrate their approach to calculations for the four number operations which they cannot complete mentally and help pupils to
improve their methods of working out;
 It is good practice when first introducing a method for the range of numbers to be within what the pupil can calculate mentally so that they can self-assess their
success at using a method.
 Once pupils are able to perform a written method successfully they should be encouraged to complete calculations independently choosing the most appropriate
way of doing so.
 Children are to be encourage to calculate mentally, part of this policy is aimed at giving children models for mathematic they can visualise.
Progression of Written Methods
The written methods for each of the four operations demonstrate progression by building upon skills and knowledge learnt in each year at school;
 A pupil should not be targeted at achieving an age-expected method if they are not able to successfully use the method for a previous age-group.
 As a school we are taking an approach which ensures consistency across the school using the same few methods across both key stages.
 With this in mind, it should be easier for pupils to work on calculations using the method for their appropriate ability.
 When teaching number operation it is fundamental to the development of conceptual understanding in mathematics that addition and subtraction are taught in
tandem as well as multiplication and division. All children need to be supported to use the inverse operation to check their calculations at all stages of
development.
Context for calculations
At Kentisbeare Primary School we believe in teaching mathematics with a meaningful context. A meaningful context helps children understand the importance of
mathematics. Initially children will be given a context for their mathematics, it is expected that, as they progress, they can offer their own meaningful contexts.
For example a year six child said recently “I would like to know more about adding with decimals as it would help me know what change I should get when shopping.”
Choosing a calculation
Children need to be taught and encouraged to use the following processes in deciding what approach they will take to a calculation, to ensure they select the most
appropriate method for the numbers involved. We aim that, as children become more confident, this is done with increasing independence. At all stages children should be
encouraged to think:
Can I do it in my head with a mental strategy?
Approximate
Could I do it using some jottings?
Calculate
Should I use a written method?
Check it
Early Years and Foundation Stage
Mental
calculations:
Recall
- Numbers from 0-20
EYFS
Number operation
Say which number + 1
is one more or one - 1
less than any
given number.
Using quantities
and objects add
and subtract two
single double
numbers and
count on or back
to find the answer
e.g.
7+ 3 = 10
9-3 = 6
Strategies
Using a range of resources to add and subtract
Use classroom routines to add and subtract
Use doubling and halving
Children begin to record in the context of play or practical
activities and problems.
Multiplication and division
Number operation
Use of games, songs and practical activities t o begin using vocabulary
Solve simple word problems using their fingers
Can find one more to ten.
Begin to relate addition to combining two groups of objects
• Make a record in pictures, words or symbols of addition activities
already carried out.
• Construct number sentences to go with practical activities
Higher Begin to relate subtraction to ‘taking away’
• Make a record in pictures, words or symbols of subtraction
activities already carried out
• Use of games, songs and practical activities to begin using vocabulary
• Construct number sentences to go with practical activities
• Relate subtraction to taking away and counting how many objects
are left.
Mental Calculations
Adding single digit numbers
Subtracting single digit numbers
Doubling, halving, sharing
Example workings
Can find one less to ten.
Higher Ability/ Gifted and Talented Progression:
Multiplication
2,4,6,8,10,12,14,16,18,20
5,10,15,20,25,30,
35,40,45.50
Counting backwards along a number line using finger.
Children progress to using a number line. They jump forwards along the
number line using finger
Real life contexts and use of practical
equipment to count in repeated groups
of the same size:
• Count in twos; fives; tens
10, 20, 30, 40, 50, 60, 70,
80.90.100
Also maths songs on 2s, 5s and 10s.
Playing game with lots of
Solve problems
using doubling
Doubling numbers
e.g.
2 + 2 =4
3+3=6
Real life concepts of doubling
How many sweets would you get?
Watching doubling video clips
Playing IT games about doubling
Make things with doubles
Solve problems
with Sharing
Split into 2, 3 ,5 6 etc
Share objects into equal groups
Use related vocabulary
Activities might include:

Sharing of milk at break time

Sharing sweets on a child’s birthday

Sharing activities in the home corner

Count in tens/twos

Separate a given number of objects into two groups
(addition and subtraction objective in reception being
preliminary to multiplication and division)
Count in twos, tens
How many times?
How many are left/left over?
Group
Answer
Right, wrong
What could we try next?
How did you work it out?
Share out
Solve problems
with halving
Half
Half practical resources and use related vocabulary
Activities might include:
Cutting a cake in half
Cutting up paper in half
Splitting groups of children in half
Use vocabulary half and halve
Year One
Mental calculations:
addition and subtraction
Recall:
National Curriculum:
Addition
Subtraction
Year One
+ = signs and missing numbers
- = signs and missing numbers
Number and place value
Children need to understand the concept of equality before using the
‘=’ sign. Calculations should be written either side of the equality sign
so that the sign is not just interpreted as ‘the answer’.
7-3=
=7-3
7-=4
4=-3
-3=4
4=7-
-=4
4=-
•count to and across 100,
forwards and backwards,
beginning with 0 or 1, or from
any given number
•count, read and write numbers
to 100 in numerals, count in
multiples of twos, fives and tens
Strategies
– all pairs of numbers with a total of 10, eg 3 + 7;
– addition and subtraction facts for all numbers to at least 5;
– addition doubles of all numbers to at least 5, eg 4 + 4.
2 = 1+ 1
– count on or back in ones;
– reorder numbers in a calculation;
– begin to bridge through 10, and later 20, when adding a single-digit number;
– use known number facts and place value to add or subtract pairs of single-digit
numbers;
– add 9 to single-digit numbers by adding 10 then subtracting 1;
– identify near doubles, using doubles already known;
– use patterns of similar calculations.
2+3=4+1
3=3

Understand subtraction as 'take away'

Find a 'difference' by counting up;
2+2+2=4+2
•given a number, identify one
more and one less
•identify and represent numbers
using objects and pictorial
representations including the
number line, and use the
Missing numbers need to be placed in all possible places.
3+4=
=3+4
language of: equal to, more than,
less than (fewer), most, least
3+=7
7=+4
+4=7
7=3+
+=7
7=+
I have saved 5p. The socks that I want to buy cost 11p. How much more do I need in
order to buy the socks?
+6
Addition and subtraction
•read, write and interpret
mathematical statements
involving
addition (+), subtraction (–) and
equals (=) signs
The Number Line
0
Children use a numbered line to count on in ones. Children use
number lines and practical resources to support calculation and
teachers demonstrate the use of the number line.
1 2 3
4
5
6
7 8
9
10 11 12

Use practical and informal written methods to support the subtraction of a onedigit number from a one digit or two-digit number and a multiple of 10 from a two-digit
number.
•represent and use number
bonds and related subtraction
facts within 20
•add and subtract one-digit and
two-digit numbers to 20,
including zero
I have 11 toy cars. There are 5 cars too many to fit in the garage. How many cars fit in
the garage?
7+ 4
0
1
2
•solve one-step problems that
involve addition and subtraction,
using concrete objects and
pictorial representations, and
missing number problems such
3
4
5
6
7
8
9
10
11
-5
12
Use the vocabulary related to addition and subtraction and symbols to describe and
record addition and subtraction number sentences
as 7 = _ –29
Recording by
- drawing jumps on prepared lines
- constructing own lines
Multiplication
Division
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
Through grouping and sharing
small quantities, pupils begin
to understand: multiplication
and division; doubling
numbers and quantities; and
finding simple fractions of
objects, numbers and
quantities.
Multiplication is related to doubling and counting groups of the
same size.
Sharing
Requires secure counting skills
-see counting and understanding number strand
Develops importance of one-to-one correspondence
See appendix for additional information on x and ÷ and aspects of number
Looking at columns
Looking at rows
2+2+2
3+3
3 groups of 2
2 groups of 3
Counting using a variety of practical resources
Counting in 2s e.g. counting socks, shoes, animal’s legs…
Counting in 5s e.g. counting fingers, fingers in gloves, toes…
Counting in 10s e.g. fingers, toes…
Sharing – 6 sweets are shared between 2 people. How many do they have each?
 
  
  
Practical activities involving sharing, distributing cards when playing a game, putting
objects onto plates, into cups, hoops etc.
Grouping
Sorting objects into 2s / 3s/ 4s etc
They make connections
between arrays, number
patterns, and counting in 2s,
5s and 10s.
Pictures / marks
How many pairs of socks are there?
There are 3 sweets in one bag.
How many sweets are there in 5 bags?
There are 12 crocus bulbs. Plant 3 in each pot. How many pots are there?
Jo has 12 Lego wheels. How many cars can she make?
Year Two
Mental calculations:
addition and subtraction
Recall:
Strategies
– addition and subtraction facts for all numbers to at least 10;
– all pairs of numbers with a total of 20, eg 13 + 7;
– all pairs of multiples of 10 with a total of 100, eg 30 + 70;
– multiplication facts for the 2 and 10 times-tables and
corresponding division facts;
– doubles of all numbers to ten and the corresponding halves;
– multiplication facts up to 5 x 5 eg 4 x 3.
– count on or back in tens or ones;
– find a small difference by counting up from the smaller to the larger number;
– reorder numbers in a calculation;
– add three small numbers by putting the largest number first and/or find a pair
totalling 10;
– partition additions into tens and units then recombine;
– bridge through 10 or 20;
– use known number facts and place value to add or subtract pairs of numbers;
– partition into ‘5 and a bit’ when adding 6, 7, 8 or 9, then recombine;
– add or subtract 9, 19, 11 or 21 by rounding and compensating;
– identify near doubles;
– use patterns of similar calculations;
– use the relationship between addition and subtraction;
– use knowledge of number facts and place value to multiply or divide by 2, 5 or
10;
– use doubles and halves and halving as the inverse of doubling.
National Curriculum:
Addition
Subtraction
- = signs and missing numbers
Year Two
Number and place value
+ = signs and missing numbers
•count in steps of 2, 3 and 5
from 0 and in tens from any
number, forward and backward
Continue using a range of equations as in Year 1 but with appropriate,
larger numbers.
•count in tens from any number,
forward and backward
14 + 5 = 10 + 
Extend to
Continue using a range of equations as in Year 1 but with appropriate numbers.
Extend to 14 + 5 = 20 - 
Find a small difference by counting up
42 – 39 = 3
+1
+2
and
•recognise the place value of
each digit in a two-digit number
(tens, ones)
•use place value and number
facts to solve problems
32 +  +  = 100 35 = 1 +  + 5
39
Partition into tens and ones and recombine
12 + 23 = 10 + 2 + 20 + 3
40
42
Subtract 9 or 11. Begin to add/subtract 19 or 21
35 – 9 = 26
= 30 + 5
•count to and across 100,
forwards and backwards,
beginning with 0 or 1, or from
any given number
+1
= 35
26
25
Count on in tens and ones
35
-10
23 + 12 = 23 + 10 + 2
•count, read and write numbers
to 100 in numerals
= 33 + 2
Use known number facts and place value to subtract (partition second number
only)
= 35
•given a number, identify one
more and one less
+10
37 – 12 = 37 – 10 – 2
+2
•identify and represent numbers
using objects and pictorial
= 27 – 2
23
representations including the
number line, and use the
language of: equal to, more than,
less than (fewer), most,least
35
33
= 25
25
27
37
The Empty Number Line:
Bridge through 10 where necessary
Partitioning and bridging through 10.
Addition and subtraction
•solve problems with addition
and subtraction:
–using concrete objects and
pictorial representations,
including those involving
numbers, quantities and
measures
–applying their increasing
knowledge of mental methods
•recall and use addition and
subtraction facts to 20 fluently,
The steps in addition often bridge through a multiple of 10
15
e.g.
-5
Children should be able to partition the 7 to relate adding the 2 and then
the 5.
8 + 7 = 15
8
20
10
15
Add 9 or 11 by adding 10 and adjusting by 1
e.g.
Add 9 by adding 10 and adjusting by 1
35 + 9 = 44
+10
35
44
45
22
-2
32
-10
-1
and derive and use related facts
up to 100
•add and subtract numbers using
concrete objects, pictorial
representations, and mentally,
including:
–a two-digit number and ones
–a two-digit number and tens
–adding three one-digit numbers



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 2
numbers can be done in
Multiplication
Division
x = signs and missing numbers
÷ = signs and missing numbers
7x2=
=2x7
6÷2=
=6÷2
7 x  = 14
14 =  x 7
6÷=3
3=6 ÷
 x 2 = 14
14 = 2 x 
÷2=3
3=÷2
 x  = 14
14 =  x 
÷=3
3=÷
Arrays and repeated addition
    4 x 2 or 4 + 4
   
2 x 4 or 2 + 2 + 2 + 2
Grouping
Link to counting and understanding number strand
Count up to 100 objects by grouping them and counting in tens, fives or twos;…
Find one half, one quarter and three quarters of shapes and sets of objects
6  2 can be modelled as:
any order
(commutative) and
division of 1 number by
another cannot

solve problems
involving multiplication
and division, using
materials, arrays,
repeated addition,
mental methods, and
multiplication and
division facts, including
problems in contexts
There are 6 strawberries.
0
1
2
3
4
5
6
7
How many people can have 2 each? How many 2s make 6?
8
6  2 can be modelled as:
Doubling multiples of 5 up to 50
15 x 2 = 30
Partition
Children need to be secure with partitioning numbers into 10s
and 1s and partitioning in different ways: 6 = 5 + 1 so
e.g. Double 6 is the same as double five add double one.
AND double 15
10
+
0
1
2
3
4
5
6
In the context of money count forwards and backwards using 2p, 5p and 10p coins
Practical grouping e.g. in PE
5
12 children get into teams of 4 to play a game. How many teams are there?
20
+
10
X
10
5
2
20
10
= 30
OR
= 30
Years Three and Four
Mental calculations:
addition and subtraction
Recall:
Strategies
addition and subtraction facts for all numbers to 20;
– all pairs of multiples of 100 with a total of 1000;
– all pairs of multiples of 5 with a total of 100;
– multiplication facts for the 2, 5 and 10 times-tables and
corresponding division facts.
– multiplication facts for 2, 3, 4, 5 and 10 times-tables;
– division facts corresponding to tables of 2, 3, 4, 5 and 10.
– count on or back in repeated steps of 1, 10 and 100;
– count up through the next multiple of 10, 100 or 1000;
– reorder numbers in a calculation;
– add 3 or 4 small numbers, finding pairs totalling 10;
– add three two-digit multiples of 10;
– partition into tens and units, adding the tens first;
– bridge through 100;
– use knowledge of number facts and place value to add or subtract any pair of
two-digit numbers;
– add or subtract 9, 19, 29, 11, 21 or 31 by rounding and compensating;
– add or subtract the nearest multiple of 10 then adjust;
– identify near doubles;
– continue to use the relationship between addition and subtraction;
– double any two-digit number by doubling tens first;
– use known number facts and place value to multiply or divide, including
multiplying and dividing by 10 and then 100;
– partition to carry out multiplication;
– use doubling or halving;
– use closely related facts to carry out multiplication and division;
– use the relationship between multiplication and division.
National Curriculum:
Addition
Subtraction
+ = signs and missing numbers
Continue using a range of equations as in Year 1 and 2 but with appropriate,
larger numbers.
Partition into tens and ones

Partition both numbers and recombine.

Count on by partitioning the second number only e.g.
36 + 53 = 53 + 30 + 6
= 83 + 6
- = signs and missing numbers
Continue using a range of equations as in Year 1 and 2 but with appropriate numbers.

add and subtract numbers
mentally, including:
o
a three-digit
number and 1s
Find a small difference by counting up
Continue as in Year 2 but with appropriate numbers e.g. 102 – 97 = 5
Subtract mentally a ‘near multiple of 10’ to or from a two-digit number
o
o



a three-digit
number and 10s
a three-digit
number and 100s
add and subtract numbers
with up to 3 digits, using
formal written methods of
columnar addition and
subtraction
estimate the answer to a
calculation and use inverse
operations to check
answers
solve problems, including
missing number problems,
using number facts, place
value, and more complex
addition and subtraction
= 89
Continue as in Year 2 but with appropriate numbers e.g. 78 – 49 is the same as 78 – 50 + 1
+30
+6
83
53
89
Add a near multiple of 10 to a two-digit number
Secure mental methods by using a number line to model the method.
Continue as in Year 2 but with appropriate numbers
e.g. 35 + 19 is the same as 35 + 20 – 1.
Children need to be secure adding multiples of 10 to any two-digit number
including those that are not multiples of 10.
48 + 36 = 84
+30
+2
48
+4
78 80
84
pencil and paper procedures
83 + 42 = 125
either
or
1. Vertical expansion
83
+ _42
5
120
125
2. Horizontal expansion
80 + 3
+ 40 + 2
120 + 5 = 125
Add the nearest multiple of 10, then adjust
Continue as in Year 2 and 3 but with appropriate numbers e.g. 63 + 29 is
the same as 63 + 30 - 1
Pencil and paper procedures
367 + 185 = 431
either
or
367
+185
12
140
400
552
300 + 60 + 7
100 + 80 + 5
400 +140+12 = 552
Use known number facts and place value to subtract
Continue as in Year 2 but with appropriate numbers e.g.97 – 15 = 72
82
87
97
-5
-10
With practice, children will need to record less information and decide whether to count back
or forward. It is useful to ask children whether counting up or back is the more efficient for
calculations
such as 57 – 12, 86 – 77 or 43 – 28.
Pencil and paper procedures
Complementary addition (inverse operation)
84 – 56 = 28
+20
+4
+4
56
60
80
84
Find a small difference by counting up
e.g. 5003 – 4996 = 7
This can be modelled on an empty number line (see complementary addition below).
Children should be encouraged to use known number facts to reduce the number of steps.
Subtract the nearest multiple of 10, then adjust.
Continue as in Year 2 and 3 but with appropriate numbers.
Use known number facts and place value to subtract
92 – 25 = 67
72
67
leading to
367
+185
552
11
Extend to decimals in the context of money.
92
-5
-20
Pencil and paper procedures
Complementary addition
754 – 86 = 668
+600
+14
86
+54
100
754
700
For those children with a secure mental image of the number line they could record the
jumps only:
754 – 86 = 668
14 (100)
600 (700)
54 (754)
668



recall and use
multiplication and division
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
one-digit numbers, using
mental and progressing to
formal written methods
solve problems, including
missing number problems,
involving multiplication
and division, including
positive integer scaling
Multiplication
Division
x = signs and missing numbers
Continue using a range of equations as in Year 2 but with appropriate
numbers.
÷ = signs and missing numbers
Continue using a range of equations as in Year 2 but with appropriate
numbers.
Understand division as sharing and grouping
18 ÷ 3 can be modelled as:
Sharing – 18 shared between 3 (see Year 1 diagram)
OR
Grouping - How many 3’s make 18?
Arrays and repeated addition
Continue to understand multiplication as repeated addition and continue
to use arrays (as in Year 2).
Doubling multiples of 5 up to 50
35 x 2 = 70
Partition
X
30
5
2
60
10
=70
0
3
Remainders
6
9
12
15
18
problems and
correspondence problems
in which n objects are
connected to m objects
Use known facts and place value to carry out simple multiplications
Use the same method as above (partitioning), e.g.
32 x 3 = 96
x
3
30
90
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.
2
6
= 96
0
3
6
9
12
15 16
Continue to use arrays:
30 ÷ 6 can be modelled as:
grouping – groups of 6 placed on no. line and the number of groups counted e.g.
+6
0
+6
6
+6
12
+6
18
+6
24
30
sharing – sharing among 6, the number given to each person
18 x 9 = 162
18 x 9 = (10 x 9) + (8 x 9) = 162
Remainders
41 ÷ 4 = 10 r1
+40
+1
10 groups
41 = (10 x 4) + 1
Pencil and paper procedures- Chunking.
72 ÷ 5 lies between 50  5 = 10 and 100  5 = 20
 Partition the dividend into multiples of the divisor:
e.g
72 = 50 + 22
50 ÷ 5 = 10
22 ÷ 5 = 4r2  10 + 4r2 = 14 r 2
OR
72
50 (10 groups)
22
20
(4 groups)
2
Answer : 14 remainder 2
Years Five and Six
Mental calculations:
addition and subtraction
Recall:
National Curriculum:
Addition
Subtraction

+ = signs and missing numbers
Continue using a range of equations as in Year 1 and 2 but with appropriate
numbers.
Find a difference by counting up
e.g. 8006 – 2993 = 5013
> add and subtract whole numbers
with more than 4 digits, including
using formal written methods
(columnar addition and subtraction)
> add and subtract numbers
mentally with increasingly large
numbers
> use rounding to check answers to
calculations and determine, in the
context of a problem, levels of
accuracy
– multiplication facts to 14 x 14:
– division facts corresponding to tables up to 14 x 14.
– squares of all integers from 1 to 10.
Partition into hundreds, tens and ones and recombine
Either partition both numbers and recombine or partition the second
number only e.g.
358 + 73 = 358 + 70 + 3
= 428 + 3
= 431
Strategies
– consolidate all strategies from previous years;
– use knowledge of number facts and place value to add or subtract pairs of
three-digit multiples of 10 and two-digit numbers with one decimal place;
– add or subtract the nearest multiple of 10, 100 or 1000, then adjust;
– continue to use the relationship between addition and subtraction;
– use factors;
– partition to carry out multiplication;
– use doubling and halving;
– use closely related facts to carry out multiplication and division;
– use the relationship between multiplication and division;
– use knowledge of number facts and place value to multiply or divide.
This can be modelled on an empty number line (see complementary addition below).
Subtract the nearest multiple of 10 or 100, then adjust.
Continue as in Year 2, 3 and 4 but with appropriate numbers.
Use known number facts and place value to subtract
6.1 – 2.4 = 3.7
> solve addition and subtraction
multi-step problems in contexts,
deciding which operations and
methods to use and why.
+70
+3
428
358
4.1
3.7
431
Add or subtract the nearest multiple of 10 or 100, then adjust
Continue as in Year 2, 3 and 4 but with appropriate numbers e.g. 458 + 79 =
is the same as 458 + 80 - 1
6.1
-2
-0.4
0.5 – 0.31 = 0.19
0.2
0.19
Pencil and paper procedures
Extend to numbers with at least four digits
3587 + 675 = 4262
0.5
-0.3
-0.01
Pencil and paper procedures
Complementary addition
754 – 286 = 468
3587
+ 675
4262
111
Revert to expanded methods if the children experience any difficulty.
Extend to up to two places of decimals (same number of decimals places)
and adding several numbers (with different numbers of digits).
72.8
+54.6
127.4
1
1
286
300
+54
700
35.8 + 7.3 = 35.8 + 7 + 0.3
= 42.8 + 0.3
= 43.1
+0.3
Pencil and paper procedures
35.8
42.8
754
Find a difference by counting up
e.g. 8000 – 2785 = 5215
To make this method more efficient, the number of steps should be reduced to a minimum
through children knowing:
 Complements to 1, involving decimals to two decimal places ( 0.16 + 0.84)
 Complements to 10, 100 and 100
Moving on to numbers with decimals:
+7
+400
+14
43.1
Add the nearest multiple of 10, 100 or 1000, then adjust
Continue as in Year 2, 3, 4 and 5 but with appropriate numbers including
extending to adding 0.9, 1.9, 2.9 etc
Complementary addition
6467 – 2684 = 3783
+16
Pencil and paper procedures
Extend to numbers with any number of digits and decimals with 1, 2 and/or
3 decimal places.
13.86 + 9.481 = 23.341
13.86
+ 9.481
23.341
1 1 1
Revert to expanded methods if the children experience any difficulty.
2684
+3467
+300
2700
3000
6467
OR
6467 – 2684 = 3783
16 (2700) can be refined to
316 (3000)
300 (3000)
3467 (6467)
3467 (6467)
3783
3783
Reduce the number of steps to make the calculation more efficient.
Extend to 2 places of decimals
Multiplication
Division
Partition
47 x 6 = 282
Sharing and grouping
Continue to understand division as both sharing and grouping (repeated subtraction).

>identify multiples and factors,
including finding all factor pairs of a
number, and common factors of two
numbers
> know and use the vocabulary of
prime numbers, prime factors and
composite (non-prime) numbers
> establish whether a number up to
100 is prime and recall prime
numbers up to 19
> 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
> multiply and divide numbers
mentally drawing upon known facts
> 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
47 x 6 = (40 x 6) + (7 x 6) = 282
Remainders
Quotients expressed as fractions or decimal fractions
61 ÷ 4 = 15 ¼ or 15.25
OR
Use the grid method of multiplication (as below)
+20
+40
10 groups
Pencil and paper procedures
Grid method
72 x 38 is approximately 70 x 40 = 2800
x
30
8
70 2
2100 60
560 16
2100 + 60 = 2160
560 + 16 = 576
2160
5 groups
Pencil and paper procedures- Chunking
256 ÷ 7 lies between 210  7 = 30 and 280  7 = 40
 Partition the dividend into multiples of the divisor:
e.g.
256 = 210 + 46
210 ÷ 7 = 30
46 ÷ 7 = 6r4  30 + 6r4 = 36r4
OR
256
- 210
46
- 42
(30 groups)
(6 groups)
+1
> multiply and divide whole numbers
and those involving decimals by 10,
100 and 1000
4
560+
2736
Expanded Column Multiplication
>recognise and use square numbers
and cube numbers, and the notation
2
3
for squared ( ) and cubed ( )
> solve problems involving
multiplication and division including
using their knowledge of factors and
multiples, squares and cubes
> solve problems involving addition,
subtraction, multiplication and
division and a combination of these,
including understanding the meaning
of the equals sign
> solve problems involving
multiplication and division, including
scaling by simple fractions and
problems involving simple rates.
Children should describe what they do by referring to the actual values of
the digits in the columns. For example, the first step in 38 × 7 is ‘thirty
multiplied by seven’, not ‘three times seven’, although the relationship 3 × 7
should be stressed.
30 + 8
x 7
56 (8 x 7 = 56)
210 (30 x 7 = 210)
266
38
x 7
56
210
266
Short Column Multiplication
The recording is reduced further, with carry digits recorded below the line.
Answer: 36 remainder 4
977 ÷ 36 is approximately 1000  40 = 25
 Partition the dividend into multiples of the divisor:
e.g.
977 = 720 + 180 + 77
720 ÷ 36 = 20
180 ÷ 36 = 5
77 ÷ 36 = 2r5  20 + 5 + 2r5 = 27r5
OR
977
- 720 (20 groups)
257
- 180 (5 groups)
77
72 (2 groups)
5
Answer: 27 5/36
Pencil and Paper procedures- Short Division Method
38
x 7
266
5
Children who are already secure with multiplication for TU × U and TU × TU
should have little difficulty in using the same method for HTU × TU or
applying decimals.
286
x 29
2574
5720
8294
1
Write down how many times your divisor goes into the first number of the dividend. If there is a
remainder, that's okay.
Write down your remainder to the left of the next digit in the dividend.
Continue. Repeat steps 1-3 until you are done.
(9 x 286 = 2574)
(20 x 286 = 5720)
Both methods above are necessary by year 6, to deal with the wide range of problems experienced at the
end of key stage.