Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

• Interpret a situation and represent the constraints and variables mathematically.
• Select appropriate mathematical methods to use.
• Make sensible estimates and assumptions.
• Investigate an exponentially increasing sequence.
• Communicate their reasoning clearly.

Introduction

This lesson is designed to help students develop strategies for modeling. Note that a video of this lesson is available in the professional development materials.

• Before the lesson, students attempt the problem individually. You then review their work and write questions to help students improve their solutions.
• At the start of the lesson, students work individually answering your questions. Then, in small groups, students work collaboratively on the task before evaluating some sample solutions. In a whole-class discussion, students explain and compare the alternative solution strategies they have seen and used.
• In a follow-up lesson, students review what they have learned.

Materials required

• Each individual student will need a calculator, a copy of the Having Kittens task and the How Did You Work? questionnaire, a mini-whiteboard, pen, and eraser.
• Each small group will need the Sample Responses to Discuss, a large sheet of poster paper, and a felt-tipped pen. Graph paper should be kept in reserve and used only when requested.
• There is a projector resource to help you with whole-class discussions. Spreadsheet software might also be helpful if available.

Time needed

20 minutes before the lesson, a 100-minute lesson (or two 55-minute lessons), and 15 minutes in a follow-up lesson. Timings are approximate. Exact timings will depend on the needs of your class.