Proportional Reasoning - Introduction

Understanding proportionality provides the key to much of the secondary mathematics curriculum. In number, proportionality occurs in work with fractions, decimals, percentages, ratios and rates. In algebra, proportional relationships (y = mx) are a subset of linear relationships (y = mx + c). In geometry, proportionality occurs in ideas of scale and enlargement and in statistics, it underpins many statistical measures, graphical representations and probability.

Proportional thinking is essential in the solution of many problems. This may not be immediately apparent and may not be accessible through a single technique such as the unitary method. The underlying ideas need to be developed systematically.

Use the Proportional reasoning summary table to gain an overview of the teaching and learning support available in the four related sections:

As you work through the four sections re-visit this collection of problem resources:

Each of the four sections includes aspects of proportional reasoning which pupils find hard to understand and which are often overlooked in text books. Here is the structure of each section:
  • an overview of concepts and relationships
  • an outline of associated language and notation, supported by teacher notes for short mental activities
  • suggestions for making connections through supporting images, along with teacher notes and resources. Use Images for fraction, scaling and proportion to gain an overview of the images which are developed in the related materials.

For a fuller discussion about some of the concepts and relationships within proportional reasoning see the short booklet, What is a fraction?.