Maths Calculation Policy
This policy sets out the progression for maths calculation within
Newchurch Primary School
Each stage follows the logical next steps in mathematical understanding
and offers help and guidance to support your child.
Once children become secure with one method they will be encouraged to move on to the next stage.
Addition
Subtraction
Multiplication
Division
Addition
No formal written notation will be used until Stage 3
Stage
Method
Objective and vocabulary
• Counting to find the total number of objects.
• Setting out neatly to avoid double counting.
• Conservation of number (same number even when
set out in a different pattern).
Counting sets of objects
1
= 3
count, number, total
What can you do at home?
also = 3
• Count objects at home (How many teddies are
there on your bed? How many flowers?)
• Remember to mix objects. How many toys on the
floor?
Addition
Stage
2
Method
Combining two sets of objects into one group to find
the total.
+
=
Extend to numbers up to 20 using multilink/cubes.
Children will be asked to find one group of 5 cubes
and then one group of 9 cubes and then combine to
find the total.
Objective and vocabulary
• To be able to add groups to a total of 9.
• To be able to add groups to a total of 20.
Add, total, group, altogether
What can you do at home?
• Add different coloured toys or different
coloured pencils/pens.
• How many blue cars/pencils? How many red
cars/pencils? How many altogether?
Addition
Stage
Method
Objective and vocabulary
Drawing pictures/dots – informal jottings.
3
Then counting the total.
**** + ***** = *********
Extend to using numbers to represent the jottings.
4
+
5
=
9
• To be able to count a series of objects and
represent them with abstract jottings (dots,
lines etc) and then find the total.
• To use numbers (symbols) to represent the
dots.
symbol, represents, equals
What can you do at home?
• Count objects at home and record results using
jottings (dots or marks).
• Encourage setting out correctly.
• Extend to represent the jottings with
numbers.
Addition
Stage
Method
Counting on, on a number line (with numbers)
4
4 more than 3 is 7
Objective and vocabulary
To be able to count on from the highest
number in the calculation (3 + 6 - hold 6 in
their head and count/jump on 3).
• To count on one ’jump’ at a time to check
understanding of number system.
•
number line, count on, more than
What can you do at home?
• Encourage your child to make or draw their
own number line.
Addition
Stage
Method
Objective and vocabulary
Use number lines to record steps in a calculation.
5
• To carry out an addition calculation (TU + U)
using an empty number line (one which holds less
This extension of Stage 4 will help children to add
information – using the higher number at the
beyond ten. Steps will then bridge through multiples
beginning of the number line).
of ten.
• To use partitioning in a TU + TU calculation
16 + 7 = 23 (7 is broken down into 4 and 3)
1. Partition the lower number into ten and units
(place value should be secure at this stage
e.g. 36 is 3 tens and 6 ones).
2. Add the tens to you calculation.
3. Add the ones to your calculation.
Moving on to partitioning TU + TU:
47 + 35 = 82
47 + 30 + 5
steps, jump, bridge,
partition, tens, units
What can you do at home?
• Make/draw an extended number line
• Give 2 digit numbers, e.g. 23 - How many tens?
How many ones?
Addition
Stage
6
Method
Continue to use partitioning without the use of a
number line.
23 + 34 = 57
Objective and Vocabulary
• To use written partition methods to support
calculations (TU + TU, extending to HTU)
partition, written method, columns
What can you do at home?
• Practise written method using partitioning.
• Encourage children to take care that numbers
are written neatly in the correct HTU columns.
Addition
Stage
Method
Written column method – continuing to use
partitioning.
Always starting using the
column on the right.
Objective and vocabulary
• To use column addition with partitioning for
numbers up to 1 decimal place.
columns, hundreds, tens,
ones/units, decimal (tenths)
What can you do at home?
7
• Encourage children to take care that numbers
are written neatly in the correct HTU.1/10
columns.
Extend to decimals:
23.7
+ 12.9
1.6
5.0
30.0
36.6
(0.7 + 0.9)
Addition
Stage
Method
Moving on to efficient written methods
8
Objective and vocabulary
• To use an efficient written method for adding 2
and 3(or more) digit numbers including up to 2
decimal places.
carry
What can you do at home?
Use and apply knowledge of decimals to adding
money.
• Give opportunities for adding money both
mentally and using written methods
• Reinforce 0.09 represents 9/100 = 9 pence
whereas 0.9 represents 9/10 = 90/100 = 90
pence
• Place value should be secure at this stage
H T U . 1/10 1/100 (tenths/hundredths)
Subtraction
No formal written notation need be used until Stage 3
Stage
Method
Counting sets of objects
1
Objective and vocabulary
•
•
•
To be able to count sets of objects
To recognise groups with fewer objects.
Find the total number of objects in a group,
remove some, and find the new total.
count, number, take away,
more, less, total
What can you do at home?
Take away 1 teddy which leaves:
objects
•
•
•
Count objects at home (How many teddies are
there on your bed? How many flowers? etc.)
Remove one of the objects and recount.
Remember to mix objects. How many toys on
the floor? If I take one away, how many are
there left?
Subtraction
Stage
Method
Objective and vocabulary
Record calculations using drawings of objects.
2
6 - 3 = 3
• To be able to use drawings to represent
calculations – moving on to numerical symbols.
take away, subtract,
less, symbol (6,-,=)
What can you do at home?
• Talk through calculation to aid understanding
of method and vocabulary.
• Draw pictures at first progressing onto
symbols.
Subtraction
Stage
3
Method
Counting back from a given number on a number line
(with numbers).
Objective and vocabulary
• To count back, using the number line for
support (discussing number of ‘jumps’ moved
back).
number line, backwards, forwards,
count back, subtract, minus,
less than, steps, jump
What can you do at home?
Use of multilink/dienes as reinforcement initially.
3 less than 7 = 4
• Make/draw a number line at home (highlighting
each ten).
Subtraction
Stage
Method
Use number lines to record steps in a calculation.
4
This extension of Stage 3 will help children to
subtract higher number. Steps will often mark a
bridge through a multiple of 10.
Objective and vocabulary
To count differences by counting back
(breaking down numbers into tens and ones
where necessary).
• To check calculation by using the inverse
calculation or counting on.
•
47 – 23 = 24
number line, count back, steps,
jumps, bridge, tens, units/ones,
difference, inverse
Partition smaller numbers - 2 tens and 3 ones.
What can you do at home?
Encourage your child to make/draw their own
number line.
• Partition smaller numbers.
• Encourage a wide range of vocabulary is used
to describe calculations.
•
82 – 35 = 47
47 count on to 82
Subtraction
Stage
5
Method
Objective and vocabulary
Partitioning using symbols – writing numbers in
groups below one another.
76 - 34 = 42
70
- 30
6
4
40
2
bridge, tens, units/ones,
difference, inverse
What can you do at home?
Check using number line (counting on).
Extend to larger numbers.
2543 - 1321 = 1222
-
2000
1000
1000
500
300
200
• To carry out calculations using partitioning
(extending to larger numbers where no
borrowing is required).
40
20
20
3
1
2
• Partition numbers.
• Ensure column subtractions lined up correctly.
• Ensure smaller number is subtracted from
larger number.
Subtraction
Stage
Method
72 – 47 = 25
6
Objective and vocabulary
• To carry out calculations using partitioning
where borrowing is used (ensure method is fully
secure before introducing decomposition
/borrowing).
• Extend to larger numbers when secure.
bridge, tens, units/ones,
difference, inverse
What can you do at home?
• Practise written method using partitioning to
check initially.
• Ensure columns are lined up correctly and neatly
Subtraction
Stage
7
Method
Continue to use partitioning until secure then move
on to column subtraction
89 – 64 = 25
89
- 64
25
Extend to larger numbers
Objective and vocabulary
• To use efficient written methods to support
calculations (TU - TU, extending to HTU).
• To use efficient written methods.
• Once column subtraction is secure, move on to
using decomposition.
partition, column, borrow across
Stage
Method
Extend to decimals:
8
8.6 - 4.2
8.6
- 4.2
4.4
Objective and vocabulary
• To use column subtraction using decimals up to
two places.
• Ensure columns are lined up correctly.
columns, hundreds, tens, ones/units,
decimal (tenths) (hundredths)
Extend to 2 decimal places linking to money.
£33.24 - £ 21.12 = £12.12
33.24
- 21.12
12.12
Decomposition can be used when secure.
In a calculation giving change from whole £, it is
more sensible to use the counting on number line
method.
What can you do at home?
• Encourage children to take care that numbers
are written neatly in the correct HTU.1/10 1/100
columns.
• Give opportunities for handling money and
giving change (encourage mental methods).
Multiplication
No formal written notation need be used until Stage 3
Stage
1
Method
Counting groups of objects
Objective and vocabulary
• To be able to count groups of objects.
count, number, groups
What can you do at home?
• Count a group of objects at home by breaking
down into groups of 2, 3, 4 or 5.
• Emphasis should be on counting and grouping
rather than finding totals.
Groups of 4
Multiplication
Stage
Method
Breaking the total into groups.
2
12 = 3 lots of 4
Objective and vocabulary
• To be able to multiple by breaking the total
into groups.
group, lots of
What can you do at home?
• Talk through calculation to aid understanding
of method and vocabulary.
• Use objects and manipulate into groups.
Multiplication
Stage
Method
Objective and vocabulary
Set out calculations as arrays
3
*****
*****
*****
*****
****
****
****
****
****
4x5
5x4
Both total 20
• To learn the relationship between a number
and its factors.
• To know the order of digits in a calculation
does not make a difference to its total.
array, times tables
What can you do at home?
• Arrange items into arrays.
• Set arrays out neatly.
• Count items and show that different patterns
total the same.
• Link to times tables.
Multiplication
Stage
Method
Multiplication as repeated addition.
4
Objective and vocabulary
•
Identify that 5 x 3 = 15 is the same as:
To record multiplications and repeated
additions in formal notation
5x3=3+3+3+3+3
lots of, groups of, times,
repeated addition
What can you do at home?
Encourage your child to make/draw their own
number line.
• Count up to a total by grouping/jumping in 2,
3, 4, 5 etc.
•
Use a number line to aid understanding
Multiplication
Stage
Method
Partitioning into composite parts
5
13 x 5
(10 x 5) + (3 x 5)
50 + 15
= 65
Objective and vocabulary
• To multiply by partitioning.
• To calculate brackets first.
partition, brackets, tens, units
What can you do at home?
Pupils will know method for multiplying by 10 by
moving digits to left and using zero as place holder.
• Practise calculations by partitioning numbers
and showing brackets.
• Ensure children use knowledge of place value
to x 10 etc.
Multiplication
Stage
6
Method
Objective and vocabulary
Continue to use partitioning to multiply using grid
method.
• To use the grid method for multiplying TU x U
then extend to TU X TU and HTU X TU.
23 x 8 = 184
160
+ 24
184
63 x 24
x
60
3
20
1200
60
4
240
12
1440 + 72
= 1512
What can you do at home?
• Practise using the grid method for TU x U
until secure.
• Encourage your child to recognise that 20 x 30
is (2 x 10) x (3 x 10) and the calculation is 2 x
3 x 10 x 10 so there would be 2 zeros in the
answer 600.
Multiplication
Stage
7
Method
TU X U showing calculations and multiplying by the
units first.
39
X 7
63
210
273
(7 x 9)
(7 x 30)
Extend to short multiplication TU X U.
Objective and vocabulary
• To use short multiplication for TU X U and
including decimals.
• Ensure columns are lined up correctly
especially the decimal point.
tens, units, carry
What can you do at home?
• Encourage children to take care that numbers
are written neatly in the correct H T U.1/10
1
/100 columns.
Multiplication
Stage
Method
TU x TU long multiplication for some children.
8
Use grid method alongside initially to show
calculation link.
63
X 24
12
240
60
1200
1512
Objective and vocabulary
• To use the long multiplication method when x
TU.
• Refer to number of zeros.
What can you do at home?
(4 x 3)
(4 x 60)
(20 x 3)
(20 x 60)
• Encourage children to take care that numbers
are written neatly in the correct H T U
columns.
• Encourage checking using the grid method
initially.
Division
No formal written notation need be used until Stage 3.
Stage
Method
Sharing
Objective and vocabulary
• To be able to share objects
share
1
What can you do at home?
• Share objects at home between family
members.
Share the apples between the teddies.
How many each?
Division
Stage
Method
Objective and vocabulary
Sharing/grouping - breaking the total into groups.
2
• To be able to share by breaking the total into
groups.
share, group, divide, fair, equal
What can you do at home?
12 ÷ 4 = 3
12 apples
3 teddies
• Talk through calculation to aid understanding
of method and vocabulary.
• Use objects and manipulate into groups.
Division
Stage
Method
Recognise grouping as repeated subtraction.
3
Objective and vocabulary
• To be able to share and group using a number
line.
share, share equally, group,
lots of divide, divided by,
divided into, division, grouping,
number line, left, left over
What can you do at home?
• Encourage your child to make/draw a number
line.
Division
Stage
Method
Short division with no remainders.
4
Objective and vocabulary
•
To use short division to divide TU by U with no
remainders.
Show partition.
84 ÷ 2 = 42
(80 4) ÷ 2 = (40 2)
short division, partition, place
value, divide, bus-stop method,
inverse
What can you do at home?
• Talk through calculation to aid understanding
of method and vocabulary.
• Reminder of place value.
• Encourage checking using inverse.
Remind children of correct place value:
How many 2s in 8? Record above the 8 tens.
How many 2s in 4? Record above the 4 units.
Division
Stage
5
Method
Short division with remainders once Stage 4 is
secure.
Objective and vocabulary
• To use short division TU by U with remainders.
Short division, partition, place
value, divide, bus-stop method,
inverse, remainder
What can you do at home?
Continue to develop with decimal numbers.
• Talk through calculation to aid understanding
of method and vocabulary.
• Reminder of place value.
• Encourage checking using inverse until secure.
Division
Stage
6
Method
Division using the chunking method.
Remind children division is repeated subtraction.
Objective and vocabulary
• To divide HTU by TU.
division, divide, chunk, repeated
subtraction, groups of, halving,
doubling, multiples of 10
What can you do at home?
• Talk through calculation to aid understanding
of method and vocabulary.
• Encourage checking using inverse until secure.
• Once secure, encourage children to subtract
the highest amount possible by finding 10x the
divisor, then doubling to find 20x and so on.
Division
Stage
7
Method
Once secure with chunking, introduce long division
alongside Stage 6.
Objective and vocabulary
• To divide by a single digit using long division.
• To divide by 2 digits using long division.
Introduce initially by a single digit then move on to
dividing by 2 digits.
What can you do at home?
• Talk through calculation to aid understanding
of method and vocabulary.
• Encourage checking using inverse until secure.