Classifying proportional and non-proportional situations

This lesson develops the concept of identifying when two quantities vary in direct proportion to each other. Students enhance their ability to:

• Distinguish between direct proportion and other functional relationships
• Solve proportionality problems using efficient methods

The lesson begins with students answering questions set in the following contexts:

• An exchange rate transaction
• A mobile phone bill
• A car journey at constant speed
• Painting a room

Having worked on the questions, students must then classify each as either proportional or having a constant ratio.

There is then a collaborative activity in which students must classify a situation as showing either direct proportion or not. There is a mixture of practical and mathematical contexts, drawing together a wide range of topics.

There is a collaborative activity that represents mixing orange with soda using picture cards. There are also instruction cards for mixing the two ingredients. The cards must be placed in order so that the resulting drinks go from the weakest to strongest taste of orange.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.