Evaluating statements about enlargements

This lesson develops the concepts of:

• Finding perimeters, areas, and volumes using formulas.
• Finding relationships between perimeters, areas, and volumes of shapes after scaling.

There are three initial questions to consider that deal with:

• The perimeter of a circle and scaling
• The area of a circle and scaling
• The volume of a cone and scaling

As an example, two circular candy bracelets are shown, one having double the radius of the other. Students must test the statement that two smaller bracelets have the same total perimeter as the larger bracelet.

There are then statements to evaluate relating to scaling both 2D and 3D shapes. For example, students must find out if the following statement is true or false:

‘If you double the radius of a sphere then you double its surface area.’

There are sufficient questions relating to 2D shapes to allow for the lesson to be differentiated for students who have not moved on to working with 3D shapes.

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.