What is partitioning?
Partitioning is a way of working out maths problems 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, like this…
…younger students will first be taught to separate each of these numbers into units, like this…
70 + 9 + 30 + 4
…and they can add these smaller parts together. For instance, they can pick out all the tens and work down to single units, making the problem more and more manageable, like this…
70 + 30= 100
9 + 4 = 13
100 + 13 = 113
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 (and us!) 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.
When do children start to partition numbers?
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:
Partitioning in addition
These are two commonly used methods for adding larger numbers:
567 + 199 = 766
A teacher might start teaching children to add two-digit and three-digit numbers in Year 2 by partitioning. The reason for this is that it helps children to mentally add multiples of ten (70 + 50 for example) and multiples of 100 (400 + 800 for example). Later children should add also learn to add three-digit numbers using the column method, so your child is likely to encounter both of these methods.
What is bridging through 10?
‘Bridging through ten’ is a method that many people use (possibly without realising it!) to add numbers mentally.
To add these numbers mentally, we can take 1 from the 6 to take the 9 up to 10, and then add the remaining 5 to get the answer, 15:
The bridging through 10 mental maths strategy can also be used to add a one-digit number to a two-digit number, for example:
Here, we take 2 from the 4 to take the 28 up to 30, then add the other 2 to get the answer, 32:
This method relies on children knowing their number bonds to 10, therefore it is important that a teacher is confident that the whole class know their number bonds to ten off-by-heart before teaching this method. Children also need to be able to mentally add a number ending in 0 and a single-digit number (that is, they need to know, for example, that 10 + 6 = 16 and work this out without having to use their fingers).
The point of teaching the bridging through 10 method is that it will help children to add numbers mentally. It is quite possible that you (the adult) already use this method without having been taught it,because it is a quick and efficient way of adding numbers without having to count on your fingers!
Try the game below:
In history this term we will be comparing two significant people from our past. We have spent some time focusing on Florence Nightingale already and are now beginning to look at the life of Mary Seacole. Use the link above to find out some more about this special lady!