About Proportional Reasoning

The study of proportional reasoning is one of the most important areas of mathematics for everyday, workplace and scientific tasks. It underlies much of the mathematics curriculum, including work on percentages, ratio, reading and making scales, reduction and enlargement, similar triangles, construction of pie charts, linear functions, trigonometry, etc.

There are two main factors leading to growth in proportional reasoning. Firstly, students need to identify that the task does indeed involve proportional reasoning. The difficulty of this recognition varies from one type of situation to another. Secondly, students need to be able to work with the numerical ratios that are involved. When the ratios are simple, then intuitive 'building-up' methods are available (eg, Q1 or Q2 below). When the ratios are complex, more formal methods are required (eg, Q3 and Q4 below).

Eels E, F, G and H in the zoo are to be fed according to their length.

Q1. If E gets 2g of a vitamin mix, how much do F and G get?

Q2. If F gets 12g of fish food, how much does G get?

Q3. If G gets 9 g of frog mash, how much does H get?

Q4. If H gets 10g of shellfish mash, how much does F get?

Building up methods are generally used by students before full multiplicative methods. For example, in Q2 students will generally answer "12 plus half of 12" before they see this as multiplication by one and a half. "Building up" methods are very good, and should be encouraged with younger students, but cannot be used for harder problems.