This lesson is designed to help students develop strategies for solving optimization problems. Such problems typically involve using limited resources to greatest effect, as in, for example, the allocation of time and materials to maximize profit.

Before the lesson, students attempt the problem individually. You then review their work and formulate questions for students to answer in order to improve their solutions.At the start of the lesson, students work alone answering your questions.Students are then grouped and engage in a collaborative discussion of the same task. In the same small groups, students are given sample solutions to comment on and evaluate.In a whole-class discussion, students explain and compare solution strategies seen and used.Finally, students revise their individual solutions and comment on what they have learned.

Materials required

Each individual student will need a copy of the task, some plain paper, a calculator, and a copy of the How Did You Work? questionnaire.Each small group of students will need copies of the Sample Responses to Discuss.Graph paper should be kept in reserve and used only when necessary or requested.

Time needed

Approximately 15 minutes before the lesson, a 1-hour lesson, and 10 minutes in a follow-up lesson.