Partitioning is a method taught in Key Stage 1 for adding and subtracting large numbers by breaking them down into place value components. Numbers are written as a number sentence showing their tens and ones. The tens are added together first, then the ones, making large calculations easier to work out mentally. Partitioning helps children visualize math problems and understand that two-digit numbers are made up of tens and ones. While useful for addition, partitioning can cause errors for subtraction, so number lines are often used instead.

1. Partitioning and Number Sentences

2. What is Partitioning?
• Partitioning is a way of working out calculations that involve large numbers by splitting them
into smaller units so they’re easier to work with. So, instead of adding numbers in a column
(as you will probably be familiar with)
52
+46
128
• Children in KS1 will be taught to break the numbers into it component parts and write the
calculation in a number sentence like this:
50 + 2 + 40 + 6
• Then they will collect the ‘10s’ together and the ‘1s’
50 + 40 + 2 + 6 = 90 + 8 = 98

3. Why are children taught partitioning?
• Children are taught this method before they learn to add numbers in columns.
• Partitioning gives children a different way of visualising maths problems, and helps them
work out large sums in their head.
• By breaking numbers down into units that are easy for them to calculate mentally, they can
reach the correct answer without counting out tricky double or triple-digit numbers on their
fingers or trying to remember where a decimal point needs to be.
• Partitioning is taught in Key Stage 1, to make children aware that a two-digit number is made
up of tens and ones. Teachers often use arrow cards for this so that children can physically
make a number, such as 24, out of a 20 and a 4. The idea is that the child lines up the
arrows together to make the numbers fit:
There is a template at the
end of this section that you
can download and print to
use with your child

4. Look at this examples and then try some
for yourself
Addition
• 23 + 14 = 20 + 3 + 10 + 4
= 20 + 10 + 3 + 4 = 37
Subtraction
• 68 – 32 = 60 + 8 - 30 + 2
= 60 – 30 (and/+) 8 – 2
= 30 + 6 = 36
• 25 + 42 =
• 76 + 21 =
• 87 + 32 =
• 195 + 222 =
• 96 – 33 =

5. Link to next topic
• How did you find the partitioning calculations?
• You may have found that you got an incorrect answer to the subtraction calculation?
• Children often make a mistake when using partitioning for subtraction.
• This is because they have to add the partial sums which seems to be a contradiction. 90 - 30
(+) 6 – 3 = 60 + 3 = 63
• Due to this misconception partitioning is often not used for subtraction and children are
taught to use number lines instead.
• We will look at this method in the next topic.