Looking at subtraction

The partitioning structure

The Partitioning Structure refers to a situation where a quantity is partitioned off in some way or other and subtraction is required to calculate how many or how much remains. For example, there are 17 marbles in the box, 5 are removed, how many are left?

Partitioning is the structure that teachers (and consequently their pupils) most frequently connect with the subtraction symbol. It cannot be stressed too strongly that subtraction is not just ‘take away’. As we shall see, partitioning is only one of a number of subtraction structures. So teachers should not overemphasise the language of ‘take away, how many left’ at the expense of all other important language identified below that has to be associated with subtraction.

The partitioning structure is encountered whenever we start with a given number of things in a set and a subset is taken away (removed, destroyed, eaten, killed, lost, blown up or whatever). In each case the question being asked is: ‘how many are left?’