Make Your Own Paint Chart: a Realistic Context for Developing Proportional Reasoning with Ratios

Proportional reasoning has been recognised as a crucial focus of mathematics in the middle years and also as a frequent source of difficulty for students (Lamon, 2007). Proportional reasoning concerns the equivalence of pairs of quantities that are related multiplicatively; that is, equivalent ratios including those expressed as fractions and percents. Students who do not learn to reason proportionally are unequipped to learn mathematics topics such as similarity, scaling, and trigonometry. Proportional reasoning is also essential to understanding rates and hence many science concepts such as speed, density and molarity.