partitioning explained

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.