Background

The ideas of ratio, proportion and proportional thinking/reasoning are complex.

The “unit” (one whole) to which we are referring can change during proportional problems and often this is not obvious. This is a common feature of such problems and should always be kept in mind.

Conceptual discourse is really important to engage with in these problems. This means allowing students to discuss their ideas at length and allowing them to debate their own answers, without giving them the ‘correct’ answer. Listen and ask and listen again to see inside the mind of the student.

A fundamental concept in mathematics is that when comparing we must compare the same “size” unit. This is true with ratio, subtracting and dividing. Ratios can be operated on sensibly when the total parts involve the same “one”. Understanding this idea is a major step forward.