Unit and non-unit fractions

The first comparison tasks usually encountered by students involve unit fractions. An example of a comparison task is

Which is larger, \(\frac{1}{4}\) or \(\frac{1}{8}\) of this tart?

A suitable student response might be "One quarter because cutting 4 makes bigger pieces than cutting 8."

Part of the early development of good fraction sense is realising that 'the larger the denominator, the smaller the parts'. This understanding forms the basis of a sensible strategy for comparing the relative size of a pair of unit fractions.

Unfortunately, unless students are well supported in developing another strategy when later asked to compare non-unit fractions, they often continue to apply the unit fraction rule. If asked,

Which is larger, \(\frac{2}{4}\) or \(\frac{5}{8}\) of this tart?

applying 'the larger the denominator, the smaller the parts' strategy is inappropriate and leads to an incorrect answer.

An incorrect student response might be, "Two quarters because quarters are bigger than eighths."