Methods for Maths at
St John the Baptist Catholic
Primary School
“They didn’t do it like that in my day!”
Do your children ask for help with their maths
homework and start talking in a foreign
language, using words like ‘partitioning’,
‘chunking’, ‘grid multiplication’…..?
If so, you may feel the need for some translation.
The purpose of this booklet is to outline the various calculation methods
that children are taught as they progress through the school, many of
which are different to the methods that you may have been taught in
your primary school days.
As children progress through school, they are building up a bank of
strategies that can be applied when appropriate.
Each strategy can be refined or extended to suit the calculation needed.
We hope the explanations and examples help you to assist your child at
home.
Addition
Progression
of skills



Subtraction
Use of language: more, less, bigger, smaller, different, same
Begin to relate addition to combining two groups of objects
e.g.

Investigate the different ways a number can be broken up
e.g. 4; 4and 0 , 3and1, 2and 2 , 1and 3 , 0and 4
 Begin to understand subtraction as ‘taking away’
e.g. 5 take away 4

Know one more; +1



Add single digit numbers using fingers

Use equipment to add up
Use practical resources to record number sequences




e.g..
6
+
4
=
4 + 5=9
10
e.g. the difference between 5 and 3 is 2
 Use pictures and visual aids to record calculations.
e.g. how many are left when 3 bricks are taken away?
Vary position of missing numbers in number sentences.
Develop understanding of addition as counting steps along a number line
Use structured number lines to record calculation.
 Use structured number lines and 100 squares.
 Vary position of missing numbers in number sentences.
 Begin to use and apply the inverse operation
e.g. 6 + 5 = 11 11 – 5 = 6

7 + 4 = 11

0
Know one less; -1
Continue to develop vocabulary including ‘difference between’ and ‘how
many less is … than
1
2
3
4
5
6
7
8

9
10
Put the largest number first when adding.
 Know that addition can be done in any order
e.g. 15 + 4 is the same as 4 + 15.
Learn number facts (number bonds) to 10
e.g. 1+9 =10 , 9+1=10 , 2+8=10 , 8+2=10
11

Find out ‘how many more make …?’ by counting on (complementary
addition)
Count back from any number up to 100
Subtract one digit numbers from 2 digit numbers
Addition
Progression
of skills






Subtraction

Count on in 10’s from any two digit number
Continue to use practical resources
Use 100 square to support counting on.
Count on in 1s
Count on in 10s (e.g. 60 + 30)
Count on in 10s and 1s (e.g. 41 + 24)

e.g. There are 34 children in the class, 17 go to the hall. How many are left?
Using a number sentence
34 – 17
becomes 34 – 10 = 24
24 - 4 = 20
20 - 3 = 17
Begin to partition and recombine using number
Partition the 2nd number and subtract
sentences e.g. seeing 12+15 as 10+10 and 2+5, then 20+7=27
 Adding two 2 digit numbers either as a number sentence or on a number
line
e.g.
24+12
20+10=30
4+ 2= 6
Therefore 30+6=36



Using an empty number line (from right to left)
34 – 17 =
20
30
34
36
10+11 (10+10+1=21)
Mental methods including partitioning and recombining.
e.g. 31
+ 17 is 30 + 10 + 7 + 1
31 + 17 is 30 + 18



Continue using informal written methods.
Use number lines, particularly empty number lines to model and support
addition.
Begin to use expanded written method
e.g. 45+17=
Therefore
?
40+10=50
5+ 7=12
50+12=62
17

Use number lines and empty number lines to support calculations
Using doubles and near doubles (then adjusting by one)
e.g. 10+10+20
Continue to develop vocabulary of difference, less than, fewer than, minus
and counting back
Number lines and empty number lines to count back and begin to count on
to find the difference.
20
24
34
Partition numbers in different ways to support calculations using a 100
square.
e.g.
56 can be partitioned into 50+6 or 10+10+10+10+10+6

e.g.


Mental methods including partitioning and recombining
31 – 17 is 30 – 10 -7 - 1
31 – 17 is 30 – 16
Use number lines counting in multiples of 10 then units.
Informal counting on
e.g. 66
– 54 = 12
Addition
Progression
of skills


Begin to partition larger numbers to add.
Begin to record on squared paper.

Partitioning will then become a mental strategy as the children progress
throughout the school.
Subtraction


Begin to use zigzag method to subtract by counting on.
Begin to record on squared paper.
Addition
Progression
of skills




Using formal methods to add.
Column addition
Can be used to add large numbers and decimals.
Can be used to add several numbers together at once.
Subtraction




Using formal methods to subtract.
Column subtraction (decomposition)
Can be used to subtract large numbers and decimals.
Can only be used to subtract pairs of numbers.
Multiplication
Progression
of skills
Division
 Vocabulary: Jumps, hops, steps.
 Share objects into equal groups
e.g. share the fruit for a snack; give out one cup to each person, sweets into bowls
 Use of practical equipment to count in repeated groups of the same size
e.g. Make a bead necklace 2red, 2blue, 2 red, 2 blue etc. A pair of socks, gloves, etc.
 Draw pictures to show equal sets:
e.g. how many wheels on 3 bikes?
 Count on and back in twos, fives and tens from any number.
 Know doubles of numbers to 20
 Sort objects into groups to count.
 Solve practical problems that combine groups of twos, fives and tens.
 There are 2 socks in one pair, how many socks are there in 4 pairs?

Count confidently in steps of two to 100, five to 100 and ten from any
number, and begin to count in steps of 3 and 4.
e.g. There are 4 apples in one box.
How many apples in 6 boxes?
 Create groups of objects and record as repeated addition and a number
sentence
e.g. 5 x 3 (Said as 5 ‘lots of 3’)
=3+3+3+3+3
= 5 x 3 = 15
 Use of visual support such as Number lines, empty number lines, 100
square etc.
4x2
 Draw pictures to show sharing and grouping:
e.g. I have 8 wheels, how many bikes can I make?
 Solve practical problems sharing groups into twos, fives and tens.
e.g. 6 shared between 2 people



Know halves of numbers to 20
Recognise odd and even numbers
Develop vocabulary involved in division, divided by / between, repeated
subtraction, how many groups of … in …
 Count confidently in steps of two, five and ten.
 Using practical equipment to share into equal groups
e.g. 12 people get into 4 teams to play a game. How many in each team

Relate grouping to arrays and use a number line to illustrate grouping and
repeated subtraction
e.g. 8 ÷ 2=
2x4
8÷4=

Understand multiplication as repeated addition and making arrays using
practical equipment
e.g. 3 x 3=
 Know the inverse of multiplication and division
e.g. 2 x 4 = 8 so 8 ÷ 2 = 4




Know that dividing by 2 is the same as halving ½
Know that dividing by 4 is the same as finding a quarter ¼
Know that dividing by 3 is the same as finding a third 1/3
Begin to understand the concept of a remainder
Multiplication
Progression
of skills


Use partitioning to multiply 2 digit numbers by a single digit.
Record on squared paper.

Partitioning will then become a mental strategy as the children progress
throughout the school.
Division



Using formal methods for division
Chunking
Used when calculations go outside table knowledge.
Multiplication
Progression
of skills



Using formal methods for multiplication
Grid Method
Can be used to multiply larger numbers or decimals.
Division



Using formal methods for division
Chunking.
Can be used to divide larger numbers.
Which is more important?:
or
This will depend on the numbers involved and the individual child.
When faced with a calculation, no matter how large or difficult the numbers may appear to
be, all children should ask themselves:
Can I do this in
my head?
If I can’t do it
wholly in my
head, what do
I need to write
down in order
to help me
calculate the
answer?
Do I know the
approximate
size of the
answer?
Will the written
method I know be
helpful?
When do children need to start recording?
The following table shows how some sort of recording is relevant throughout the primary
years with mental strategies playing an important role throughout.
Reception Year 1
Year 2
Year 3
Year 4
Year 5
Year6
Making a record of a calculation
Jotting to support a mental strategy
Explaining a mental strategy
Developing written methods
All the written skills shown above can then be applied to problem solving. It is important to
encourage children to look first at the problem and then get them to decide which is the
best method to choose – pictures, mental calculation with or without jottings, structured
recording or calculator.
Children attempting to use formal written methods without a
secure understanding will try to remember rules, which may
result in unnecessary and mistaken applications of a standard
method.