Subtraction by Adding On

This is also sometimes called “subtraction using a blank numberline” and I’ve even heard it called “that nonsensical modern method”. This latter is a real misnomer since it is neither nonsensical nor modern. In fact it’s a method that dates back to before I was born, in days before we had calculators and electronic tills. It’s also a really useful method involving counting forwards, which is always easier than counting backwards – even for maths geniuses!

Let’s return to those old-fashioned little shops. I buy some sweets for 24p and hand over a £5. To work out my change, the shopkeeper needs to calculate £5 – 24p. Now she could count £4.99, £4.98, £4.97 until she had subtracted 24p, but what you actually would have heard is this:

24 and 6 makes 30, and 20 makes 50 and another 50 makes £1. 2, 3, 4, £5. And while doing this they counted the change (£4.76) into your hand.

This is the method that schools have returned to. To begin with, Children use a “blank numberline” – that is, a line that they can write the numbers on themselves. They then write the lower number at one end, and see what they need to add to make the higher number. Here’s an example:

96-38

The children first of all use their knowledge of number bonds to add to the next 10 (38 + 2 = 40).
They then use their ability to add multiples of 10. In the example above the child has done 40+10 = 50 and then 50 + 40 = 90. They may have been able to see straight away 40 + 50 = 90 and done this as one step, or they may have needed to do 40 + 10 = 50, 50 + 10 = 60, 60 + 10 = 70 and so on up to 90. The method isn’t about having to complete it in a certain number of steps, it’s about each child breaking it down into the smallest number of steps that they can manage.
When they reach the multiple of 10 before the higher number, they add on whatever units are needed to make the higher number, in this case it was +6 to make 96.
Finally, they add up all the numbers they added on to find the answer: 2+10+40+6 = 58 so 96 – 38 = 58.

When they are confident with this, they move on to jotting down only the numbers they are adding on, and they keep the tally in their head, until eventually they develop their working memory enough to hold all of the numbers in their head and write down just the answer.