Comparing strategies for proportion problems

This lesson develops the concept of direct proportion and its application to problems. The works addresses the following problems that students might have:

• Use of inappropriate additive strategies in scaling problems.
• Inefficient strategies such as not using a single multiplier for solving proportionality problems
• See multiplication as making numbers bigger, and division as making numbers smaller

The activity involves working on three situations requiring proportional reasoning:

• Scaling a recipe
• Pricing for tins of paint
• Enlarging a photograph

Students make an initial attempt at the problems. There are then examples of both correct and incorrect student work, providing opportunities for peer assessment and discussion. This work leads to developing efficient methods for working with proportional reasoning.

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.