Partitioning is used to make solving maths problems involving large numbers easier by separating them into smaller units.
What is partitioning? Subtraction, addition, multiplication technique
Partitioning is used to make solving maths problems involving large numbers easier by separating them into smaller units.
For example, 782 can be partitioned into 700 + 80 + 2. It helps kids see the actual value of each digit. So rather than seeing 782 as an intimidating number, they’ll see it as 700, 80, and 2.
Using the partitioning method helps children to understand the values of each digit. It also prepares children to complete trickier calculations and gives them a head-start on the foundation knowledge they need to apply some maths concepts, including the short division method.
It is easiest to partition numbers into units, tens, and hundreds. Children can also understand more about the different place values of each number before adding or subtracting other numbers. The method can help with rounding since they will be more confident in understanding which value is the relevant one to round to.
The partitioning method is also used to solve addition sums. Instead of using adding numbers in a column like this:
700
+82
782
Young children will be taught to partition (separate) each of these numbers into units to understand their value fully. The problem is much more manageable for younger children when they can see the sum presented like this:
700 + 80 + 2 = 782
Another example is a bit more complicated:
365 + 28
To complete this sum using partitioning, children can work it out like this:
300 + 60 + 5 + 20 + 8
The answer that they will eventually reach is 393.
This method is also known as addition by partitioning. It is a beneficial way to begin teaching children how to add more complex numbers together.
Partitioning is the opposite of recombining, where numbers are put back together.
Examples of partitioning
This example shows a simple way to partition a two-digit number. For example, 37 can be partitioned into 30 and 7.
Addition by partitioning
Children should learn to add two-digit and three-digit numbers by partitioning. Partitioning helps a child be confident adding big numbers, for example, 80 + 60, and multiples of 100, 300 + 500.
It can help combat maths anxiety by breaking big numbers into more manageable chunks. Over time, children will become more confident with adding more significant numbers together, and the addition method by partitioning will no longer be needed.
Example:
If the question to solve is 468 + 194, then partitioning can be used.
400 + 100 = 500
60 + 90 =150
8 + 4 = 12
500 + 150 + 12 = 662
The column method can also be used; children in Year 3 must be prepared to encounter this method too.
Partitioning in multiplication
The partitioning method can solve multiplication equations for two-digit numbers multiplied by one digit. It can look intimidating, but partitioning helps break down the process into smaller steps that are easier for children to handle. Once they have got to grips with partitioning, they can move on to more complicated multiplication methods.
Example:
23 x 6 =
20 x 6 = 120
3 x 6 = 18
120 + 18 = 138
So 23 x 6 = 138, which was easily solved using partitioning.
To solve multiplication equations for three-digit numbers multiplied by two-digit numbers.
725 x 24 – Partition 725 into 700 and 20, and 5 and put in a table.
Partition 24 into 20 and 4.
| x | 700 | 20 | 5 |
| 20 | 14000 | 400 | 100 |
| 4 | 2800 | 80 | 20 |
So by adding all these numbers in the table together, it is easy to solve the equation of 725 x 24 = 17400.
Partitioning: subtraction
Partitioning can also be used when children begin to learn subtraction.
Here is an example of partitioning in subtraction:
33 – 12
When you partition the sum, you get this:
(30 – 10) + (3 – 2)
When you have worked out the calculations in the brackets, you get this:
20 + 1
Finally, add the two results from the brackets to get the answer of 21.
When partitioning numbers to help with subtraction, you can check that children have got the answer right by working with column subtraction. Eventually, children will also build up to the column subtraction method. They will also have more vital mental maths skills to work out sums alone.
