1. Maths Workshop – Calculation methods
In the Alice Smith School at JB, our process of delivering Maths to the
children follows the format: Teach, Practise, Apply, Review. We often find
that the children have difficulties with the Applying part of this process:
being able to apply their Maths knowledge and skills to real-life situations
and problem solving, and often it comes down to them not having a firm
foundation of understanding of number and the number systems. They need
to be able to manipulate numbers confidently and, to use the shortened,
more formal versions of calculations methods, they must first understand
clearly what they are doing. Many adults were taught these formal methods
of calculation but how many of us actually understood what we were doing or
why we were putting something ‘on the doorstep’ or ‘borrowing one from next
door’?! We do aim for the majority of the children to be using the formal
methods of calculation by the time they leave JB but the initial methods
that are taught help children develop this crucial first understanding of
what is happening, therefore helping to set the children up so that they will
be able to move on easily to calculate problems using larger, more complex
numbers – and choosing the methods that they are happiest and most
proficient at using.
* Please remember that these methods are in the back of your child’s
Link Book or Homework Diary.
2. Calculation in early Primary
At this stage we may ask the children to ‘put something down on paper’ about
what they have done or have found out. This will allow them to choose how
to record or whether to: e.g. use a picture, some kind of tally or write a
number. Children are most likely to want to ‘put something down’ when the
record has some purpose for them e.g. making labels to show the number of
bricks in a tin. Some children may choose to record their thinking in number
sentence form.
Mental skills:
• Say and use number names
• Count reliably up to 10 objects
• Recognise numerals 1 to 9
• Use more and less, greater and smaller, heavier and lighter
• Begin to use the vocabulary of addition and subtracting
• Find a number 1 more and 1 less
• Begin to relate addition to combining two groups of objects and
subtraction as ‘taking away’
• Use developing mathematical ideas and methods to solve practical
problems
Initially only addition and subtraction are taught. The children’s experience
of these operations will be a mixture of words, pictures and symbols. When
recording simple mental calculations in a number sentence they are always
set out horizontally. Initially calculations should be carried out practically
first, then build on visually through using written digits, symbols and shapes.
3. Addition
We use many methods to teach children about addition. These methods include
interactive whiteboard games, board games, mental and written methods and
problem solving but the best way for them to become confident with the process is
practice! The children are taught methods they can use for mental and written
calculations, the most common are:
Number line: 39 + 22
+ 20 (or 2 lots of 10) + 2 (or add on the 1 up to the next
10 and then the extra units)
39 49 59 60 61
Partitioning and recombining
add the tens add the units
98 + 73 = (90 + 70) + (8 + 3)
= 160 + 11
= 171
Children can use both of the above methods for mental and written calculations.
Column Addition 87 + 45
Then progressing on to
1) H T U 2) H T U
8 7 8 7
4 5 + 4 5 +
1 2 (7+5) 1 3 2
1 2 0 + ( 80 + 40 )
1
1 3 2
This method can progress on to adding several numbers and adding decimals (i.e.
money).
4. Subtraction
We use many methods to teach children about subtraction which link closely with
the teaching of addition. The most common methods for mental and written
calculation of subtraction questions are:
Number line (easiest to add on) 57 – 36
+ on 4 to round to next 10 + on 7 for remaining units
+ on 10 to round to closest 10
36 40 50 57
Expanded method of subtraction
Basic: 47 – 36 = crossing the 10 75 – 47 =
47 – (30 – 6) = 75 – (40 – 7) =
47 – 30 = 17 75 – 40 = 35
17 – 6 = 11 35 – 7 = 28
Decomposition (Column Subtraction)
And finally:
75 – 47 = (70 + 5) – (40 + 7) 6 7 14 5 1 4
6 6 5 -
70 + 5 60 + 15
40 + 7 - 40 + 7 - 0 8 9
20 + 8
This method can also be extended to
= 28 decimals.
5. Multiplication (1)
We use many methods to teach children about multiplication, these will include
calculator techniques but it is important that the pupils understand how to work out
multiplication questions independently. The most useful skill for the understanding of
complex multiplication sums is quick recall of times tables.
The most common methods for mental and written multiplication calculations are:
Pictures are also a great way of visualizing multiplication: 3x5
Repeated addition on the number line: 3 x 5
+ 1 lot of 5 +2 lots of 5 +3 lots of 5
0 5 10 15
Repeated addition: 6x4=
6 + 6 + 6 + 6 = 24
moving on to 12 x 6 =
(adding in pairs)
12 + 12 24
12 + 12 24 = 72
12 + 12 24
Partitioning: 14 x 3
14 x 3 = (10 x 3) + (4 x 3)
= 30 + 12
= 42
6. Multiplication (2)
The Grid Method – this shows the children in a more visual way which numbers they
are multiplying together and what the actual values of these numbers are.
14 x 3
X 10 4
3 30 + 12 = 42
27 x 34
X 20 7
30 600 + 210 = 810
7 140 + 49 = 189 +
= 999
42 x 4.6
X 40 2
4 160 + 8 = 168.0
0.6 24 + 1.2 = 25.2
= 193.2
When ready, the children would move onto the vertical expanded method and then
the shortened column method:
5 6 3 9 4
2 7 x 3 x
4 2 (6 x 7 = 42) 1 1 8 2
3 5 0 ( 50 x 7 = 350)
1 2 0 ( 6 x 20 = 120) 2 1
1 0 0 0 ( 50 x 20 = 1000)
1 5 1 2
1
7. Division
We use several methods to teach children about division but this still seems to be
the operation they find most challenging. As with multiplication, the most useful
skill is for the children to know their times tables and have the ability to derive
division facts from these. The most common methods for written division
calculations are:
Sharing using drawings 12 ÷ 2
Division as repeated subtraction 15 ÷ 5 (opposite of repeat addition)
- 3 lots of 5 - 2 lots of 5 - 1 lot of 5
0 5 10 15
Using known multiplication facts 12 ÷ 3
“I know that 3 x 4 = 12, therefore 12 ÷ 3 must = 4”
Chunking 128 ÷ 4
4 1 2 8 (use known facts to divide)
4 0 - (10 x 4) then add together 10+20+2 = 32
8 8
8 0 - (20 x 4)
8
8 - (2 x 4)
0 128 ÷ 4 = 32
This method works with remainders too.
Long division (bus stop method) 127 ÷ 7
0 1 8 r. 1 There are zero 7s in 1, but there is
5 one 7 in 12 with 5 remaining, carry the
7 1 2 7 5 and put it next to the unit 7. There
are eight 7s in 57 with 1 remaining
therefore, 127 ÷ 7 = 18 remainder 1.
8. Maths Games
There are lots of easy ways to help your child with their maths, quick fire
questions when on long journeys, questions in the supermarket, counting small
change at home. Real life problems are particularly important for improving
mathematical skills; money, time, measure. There are also lots of games on safe
and fun sites on the internet, including:
www.sums.co.uk
www.funbrain.com
www.primarygames.co.uk
www.bbc.co.uk/schools/revisewise
www.whizzeducation.com
www.gamequarium.com
www.counton.org
www.woodlands-junior.kent.sch.uk/maths
www.apples4theteacher.com
www.topmarks.co.uk/mathsgames
www.rainforestmaths.com
www.ictgames.co.uk
www.mad4maths.com/parents/
