Proportional Sets - short mental activities

Use these short mental activities to develop pupils’ confidence in using the language of proportional sets to describe and generate sets of numbers and to explain proportional relationships, in application, where appropriate. This will support understanding of links between other aspects of proportional reasoning such as ratios and rates.

Why use these mental activities?
To provide frequent, regular opportunities refreshing and refining pupils’ mental skills in using proportional sets as part of proportional reasoning.

There are five sets of teaching activities, accessible from the following links:

1. Sweet ratio
Use the context of types of sweets in a selection to provide application of part-to-part and part-to-whole ratios, as well as an opportunity to make the connection between proportional sets, multiplying factors, and ratios.

2. Generating proportional sets
Generate two sets of multiples simultaneously, illustrating on a counting stick. Use this context to support pupils to develop fluency and confidence in generating proportional sets of numbers.

3. Webs
Use this activity to make the link between proportional sets of numbers and a range of conversions. Develop pupils’ skills in generating proportional sets of numbers linked by a conversion fact.

4. Proportion or not?
Use the given sets of data to raise the following question with pupils: Are these data sets in direct proportion? Encourage them to generalise conditions for direct proportionality.

5. Proportions and proportionality
As with many short mental activities the range and variety of examples here will be best visited regularly over time. Use the activities to make connections between proportional sets, expressing proportions, and comparing quantities.