Multiplication and division structures

The repeated aggregation structure - other contexts

Apart from ‘so many sets of so many,’ are there other contexts in which pupils will meet multiplication in the repeated aggregation structure? Any situation in which we aggregate a certain number of portions of a given quantity, such as mass, liquid volume, length and time, provides an application to this multiplication structure. For example, finding the total mileage for 42 journeys of 38 miles each (42 x 38); finding the total volume of drink required to fill 32 glasses if each holds 225 ml (32 x 225); finding the total time required for 12 events each lasting 25 minutes (12 x 25).

But, not surprisingly, the most important context will be shopping, particularly where we have to find the cost of a number of items given the unit cost. Two important words here are each and per. For example, we might need to find the cost of 25 cans of drink at 39 cent each (25 x 39). Or we might purchase 25 tickets at 3 euro 50 cent per ticket (25 x 3.50). In both cases we have to associate the language and the structure of the example with the operation of multiplication.

Remember to give special attention to helping pupils to use the word per with confidence and to associate the practical problems about unit cost and cost per unit of measurement with the corresponding multiplications.

Then there are important situations where we encounter repeated aggregation in the context of cost per unit of measurement. For example, if we purchase 28 litres of petrol at 89 cent per litre, we should recognise that a multiplication (25 x 0.89) is required to determine the total cost, although, of course, in practice the petrol pump will do it for us. Likewise, we should connect multiplication with situations such as finding the cost of so many metres of material given the cost per metre, or someone’s earnings for so many hours of work given the rate of pay per hour, and so on.