Using proportional reasoning

General overview

This focus is about learners operating effectively with decimals, fractions, percentages, ratios and rates, and interpreting and moving fluently between the different representations.

In early levels, learners divide quantities, using the ideas of “fair” and “the same” in developing a sense of equality, and compare the relationship between quantities for example “twice as big” and “half as much”.

As learners progress through the levels, they visualise and develop a sense of the size of fractions, decimal and percentages, and the relationship between these as well as using them to solve problems.

At upper levels, students interpret, illustrate and order relationships and solve complex problems involving fractions, decimals, percentages, ratios and rates.

Students critically evaluate claims such as those in the media, advertising and the food industry, synthesise numerical data and texts to communicate information, and support conclusions about social, economic and environmental issues. Learners must be aware that different representations are used frequently to confuse people, or to conceal the underlying size of the problem.

A critical element of using proportional reasoning is developing a firmly established sense of the “whole” and place value, which allows students to recognise and move between the different representations, for example the comparison between the fraction 2/3 and the ratio 2:3.

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