Adding numbers – adding on and adding all together

There are basically two different ways that numbers can be added together. One way to add numbers is to ‘add on’. That is, you start counting upwards from the largest number and count on the smallest number, one at a time, to get the total. This is often the most efficient way to add, certainly if you are adding mentally.

The written addition algorithm that is required in Indian schools uses the ‘count all together’ way of thinking about addition. This means that you take, say, seven items – stones or sweets or whatever – and then take five more. When you put them all together and count them, you get 12.

Figure 1 ‘Take seven sweets, then take five more …'

Pause for thought

When Rizwana was teaching her Class II students she noticed that Satish had written out his working for adding 23 to 37 like this:

multiline equation line 1 23 line 2 plus plus 37 low line line 3 510

What is wrong with this answer? Why did Satish write his answer in this way? How could you resolve this misconception? What other misconceptions do you commonly encounter when teaching addition?

2 Using concrete representations to develop students’ understanding