A Guide to Calculation
Whilst Mathematics may now be taught differently in school when compared to when many adults were
themselves in school, the number system itself has, of course, not changed and many of the strategies and
techniques that we developed during our own childhood remain very valuable. However, the lessons that we
teach in school today are much more about collaboration, investigation and understanding the processes
involved, just as much as an ability to apply them. Ultimately, the strategies that our children develop will be
similar to those that we ourselves developed, but our hope is that they fully understand the maths involved.
Included within this document are explanations (with examples) of some of the strategies that your child uses
in school in order to carry out addition, subtraction, multiplication and division calculations.
We hope that you find the content of this booklet helpful.
Addition
Progression of skills and methods
(addition)
Add money using coins
Can be demonstrated
visually as in diagram
but this should not be
used as a written
method.
Partition is a mental method, but it is useful for children to record jottings as in the diagram:
48 + 36 =84
40 + 30 = 70
8+6 = 14
70 + 14 = 84
It is useful for children to use apparatus
to support them when they first begin
to use this method. When they have
shown an understanding of the process,
apparatus may not be necessary.
Digits should be carried underneath the
answer box to avoid confusion
Children at level 4 should also be expected to:
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use this method for larger numbers (to at least 4 digits)
use this method to add numbers with up to 2 decimal places.
solve addition problems involving measures and money.
Using the standard written method:
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add decimals (including those which do not have the same amount of decimals digits).
solve addition problems involving measures and money.
use as an inverse operation to check subtraction calculations.
Subtraction
Progression of skills and methods
(subtraction)
Subtract 1 or
multiples of 10 from
any two-digit number.
Continue to use a
number line to find the
Children may choose to add on different quantities
first. They may prefer to add on 5 to begin with to
get themselves to the nearest tens number.
42 – 25 =
difference by adding on
+10
from the smaller to the
+5
(including bridging
through tens boundary).
*This method is a
mental method, but
it is useful for
children to record
jottings as in the
diagram.
10 + 5 + 2 = 17
+2
larger number.
25
35
40
42
This method can be
used where
children find it
difficult to grasp
the standard
written method but
will not be
necessary for all
children.
Apparatus can be
used to
demonstrate taking
from the tens
column.
Children at level 4 should also be expected to:



use this method for larger numbers (to at least 4 digits)
use this method to subtract numbers with up to 2 decimal places.
solve subtraction problems involving measures and money.
Using the standard written method:



subtract decimals (including those which do not have the same amount of decimals
digits).
solve subtraction problems involving measures and money.
use as an inverse operation to check addition calculations.
Multiplication
Progression of skills and methods
(multiplication)
The grid method should be introduced
during Year 3 for those children who are
working at a level 3 or above.
Use partitioning to solve TU x U calculations
x
Expanded standard
38 x 7 =
written method
38
x
7
56
210
266
A zero must be placed in the second row, rather than a
dash or a space.
38 x 7 =
Standard written
method
38
x
7
266
5
38 x 27 =
38
x
27
This method can then be used
to multiply TU by TU numbers.
266
760
1026
1
This step involves adding the 56 and 210 mentally. Carried
digits re placed underneath the answer box.
Carried numbers from the
multiplication should be placed
on the top line, as indicated by
the arrow. Carried numbers
from the addition should be
placed underneath the answer
box.
Using the standard written method:



multiply decimals (including those which do not have the same amount of decimals
digits).
solve multiplication problems involving measures and money.
use as an inverse operation to check division calculations.
Expectations of times tables knowledge
Year 1 – counting sequences (which follow times tables e.g. 2, 4, 6, 8 10 … for x2). By the end of year 1,
children can start learning 2, 10 and 5 times tables.
Year 2 – Learn 2, 10, 5 times tables. Begin 3 and 4 times tables.
Year 3 – Learn 2, 10, 5, 3, 4 times tables. Begin 11 and 6 times tables.
Year 4- Learn 2, 10, 5, 3, 4, 11, 6 times tables. Begin 7, 8, 9, 12 times tables.
Year 5- Learn all times tables up to 12 x 12.
Year 6 – continue practice of all times tables up to 12 x 12, use these to inform division and to work out
other times tables higher than 12 (e.g. double 12 times tables to generated 24 times tables).
From Year 2 to Year 6 times tables tests are conducted on a weekly basis.
Division
Progression of skills and methods
(division)
Chunking method – This is only used if
children find the standard written
method too difficult.
Standard written
method (short division)
2 7
3 8 21
Children at level 4 should also be expected to:


use this method for larger numbers HTU ÷ U, ThHTU ÷ U
use this method to divide numbers with up to 2 decimal places.


solve division problems involving measures and money.
use as the inverse operation to check multiplication calculations.
Standard written
method (long division)
As we are dividing by 51, children may find
it useful to write their 51 times tables down
the side of there page to support them. This
can be done using mental repeated
addition.
To calculate 748 divided by 51,
First, set the sum out as shown:
We work out 74 divided by 51, and write the answer (1) above the 4.
1 × 51 = 51, so we write this underneath 74.
Subtract 51 from 74 to get the remainder (23).
We now bring down the next digit (8) and write it on the end of the 23. This is the same as writing the
remainder at the top:
We now work out 238 divided by 51, and write the answer (4) above the 8. You use estimation skills
here: 51 is roughly 50 and 4 × 50 = 200. You can work out 51 × 4 = 204 separately.
We write 204 underneath the 238 and subtract to find the remainder. There are no more digits to bring
down, so we have our answer:
r34
The full answer including the remainder
should always be placed above the question.
So the answer is 14 remainder 34.
NB: In Year 6, children working at a level 5 may also be expected to convert their remainder to a
decimal or fraction answer.
Children working at Level 5 should also be expected to:



solve division problems involving measures and money.
use as an inverse operation to check multiplication calculations.
convert remainders to decimal remainders.
Homework Advice
The most important thing that you can do as a parent is show an interest in your child’s work. If you can,
support them in completing it, but never worry about referring your child back to his/her teachers for
help. We hope that the information contained within this booklet will support you in supporting them, but
would discourage any parent from trying to ‘muddle through’ when a conversation with, or note to, the class
teacher would be welcomed.
Helpful homework habits include...

working out the best time (not always the most immediate) to complete homework;

gathering all relevant equipment and materials before beginning;

finding a quiet, comfortable environment, away from distractions;

reading and following instructions carefully;

presenting work as it is done in the classroom, avoiding any confusion over place value or strategies;

checking through carefully upon completion of work.
General advice on standard written methods

When setting out standard written methods from addition, subtraction and multiplication,
answers should be between two sets of lines.
E.g. 54
X6
______


Answers to word problems should always include the units e.g. cm, $ etc.
Digit columns should be labelled the following:
M
HTh
TTh
Th
H
T
U

When setting out digits, one digit should occupy one square in Maths books, with no
additional space for a decimal point; this should occur on the line between the units and
tenths.
Fractions should be written with one digit per square, with a horizontal line between the
numerator and denominator.

E.g.
Other Useful Information...
100 square
The 100 square is a visual tool to help children in a variety of ways:
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Place Value: the 100 square clearly shows the pattern of where the tens rows are and where the
units columns are.
+1/-1: using the 100 square to jump right/left one space to add/subtract 1.
+10/-10: Using the 100 square to jump up or down one space encourages mathematicians to stop
adding/ subtracting in 10 single units.
+9: Jump down one space (+10), then left one space (-1) = easy strategy for adding 9;
+11: Jump down one space (+10), then right one space (+1) = easy strategy for adding 11;
-9: Jump up one space (-10), then left one space (+1) = -9
-11: Jump up one space (-10), then right one space (-1)= -11.
The variations are now endless: +20 (jump down 2 squares), -40 (jump up 4 squares), + 19 (jump
down 2 squares and
Games & Activities to Use at Home
There are a number of helpful props that will provide opportunities for talking about maths in the family
home. This process alone helps enormously when it comes to understanding some of the concepts that are
taught in school. These include...

A prominent clock

A traditional calendar

Board games involving dice or spinners

A pack of traditional playing cards

A calculator

Measuring jugs with scales

Dried beans, pasta shapes and Smarties – good for sharing and creating arrays

A tape measure or ruler

A bar of chocolate – great for discussing fractions!

Fridge magnet numbers, letters and symbols

Weighing scales

A dartboard

Dominoes

Guess Who? – perfect for dividing things into categories, or for thinking about probability

An indoor or outdoor thermometer
Key vocabulary
Array: Arrays are a pictorial representation to help children understand times tables:
3 x 5 = 15
Factor: A factor is one of two or more numbers that divides a given number without a remainder.
In the number sentence 4 x 5 = 20, both 5 and 4 are factors of 20.
Grid method: The grid method is a written technique used to teach children multiplication. It
involves partitioning numbers into tens and units before they are multiplied, and placing them in a
grid. The numbers are then multiplied two by two and the results are added together to give a
total answer.
Inverse operation: Inverse operations are opposite operations – one reverses the effect of the
other. In primary maths we talk about the inverse to explain how addition and subtraction are
linked and how multiplication and division are linked.
Multiple: A multiple is a number that can be divided by another number a certain number of times
without a remainder. In the number sentence 4 x 5 = 20, 20 is a multiple of 4 and a multiple of 5.
Number bonds: Number bonds are also often referred to as 'number pairs'. They are simply the
pairs of numbers that make up a given number. E.g. number bonds to 10 are: 1 + 9, 2 + 8, 3 + 7, 4 +
6, 5 + 5
Number facts: Number facts are basic addition, subtraction, multiplication and division
calculations that children should learn to recall instantly.
Partitioning: Partitioning is a way of working out maths problems that involve large numbers by
splitting them into hundreds, tens and units etc. If we partition 34, it becomes 30 + 4.
Place value: Place value is the value of each digit in a number. It means understanding that 582 is
made up of 500, 80 and 2, rather than 5, 8 and 2.
Repeated addition: Repeated addition is a method of helping children understand multiplication.
Children are asked to work out, for example, what 3 'lots of' 5 are. They will be shown that this
can be written as 5 + 5 + 5 (repeated addition number sentence) as well as 3 x 5 (multiplication
number sentence).