Multiplication and division structures

Situations using the ratio division structure

Remember that primary pupils can be introduced to the idea of using division to find the ratio between two quantities in order to compare them, but the results are difficult to interpret if they are not whole numbers.

Many primary-school pupils can learn to recognize the need to use division to compare two quantities by ratio. Situations where comparisons could be made between numbers in sets, between amounts of money or between measurements of various kinds are readily available. The problem is, however, that in practice, unless the questions are contrived carefully, the answers tend to be quite difficult to interpret.

It’s easy enough to deal with, say, comparing two children’s journeys to school of 10 minutes and 30 minutes, and, using division (30 + 10), making the statement that one pupil’s journey is three times longer than the other. But it’s a huge step from interpreting a statement like that with whole numbers to making sense of, say, comparing the heights of two pupils, 125 cm and 145 cm, using a calculator to do the division (145 divided by 125 = 1.16), and concluding that one pupil is 1.16 times taller than the other.