Looking at addition

The aggregation structure of addition

The term aggregation is used to refer to a situation in which two or more quantities are combined into a single quantity and the operation of addition is used to determine the total. For example there are 15 marbles in one circle and 17 marbles in another: how many marbles are there altogether? The idea of ‘how many (or how much) altogether is the central notion in the aggregation structure. Notice in this example the two sets do not overlap. They are thus called discrete sets. When two sets are combined into one set they form what is called the union of two sets. So another way of describing this addition structure is ‘the union of two discrete sets’.

Firstly, the aggregation structure is encountered whenever pupils are putting together two sets of object into a single set, to find the total number i.e. combining two separate piles of counters e.g. 48 blue and 26 red, how many altogether? Secondly, and in terms of relevance, most importantly, pupils will encounter the aggregation structure in the context of money. This might be, for example, finding the total cost of two or more purchases or the total bill for a number of services. The question will be, ‘How much altogether?’ Then they also have to recognise addition in situations of aggregation in the contexts of measurement such as length and distance, mass, capacity and time.

Important: ensure that pupils experience the two addition structures in a range of relevant contexts including money (shopping, bills, wages and salaries) and in various aspects of measurement.