Comparing Fuel Consumption: Buying Cars

Mathematical goals

This lesson unit is intended to help you assess how well students are able to solve a real-world problem that involves rates of change. In particular, it will help you assess how well students are able to create, compare, and evaluate different representations of functions.


  • Before the lesson students tackle the problem individually. You then review their work and write questions to help students improve their solutions.
  • At the beginning of the lesson students respond to your questions. Students are then grouped into pairs and work collaboratively to produce better solutions to the same task.
  • There is a whole-class discussion to compare and evaluate different approaches.
  • A second collaborative activity follows where students work in small groups to evaluate and comment on sample solutions, followed by a second whole-class discussion about the work.
  • Finally, students review and evaluate their work on the problem.

Materials required

  • Each student will need a copy of the assessment task: Buying Cars, two or three sheets of paper, and a copy of the review questionnaire How Did You Work?
  • Each small group of students will need a large sheet of paper for making a poster, felt tip pens, and copies of the Sample Responses to Discuss.
  • You will need a supply of graph paper and rulers. There is a projector resource to support whole-class discussions.

Time needed

Approximately 20 minutes before the lesson, a 90-minute lesson (or two shorter lessons) and 10 minutes in a follow-up lesson. These timings are approximate.