Mathematical goals

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

• Choose appropriate mathematics to solve a non-routine problem.
• Generate useful data by systematically controlling variables.
• Develop experimental and analytical models of a physical situation.

Introduction

• Before the lesson, students watch a video of Rolling Cups. They then work on a related task designed to assess their current approaches to modeling. You collect and review students’ work and write questions to help improve their models.
• During the lesson, students first work individually to review their initial work. They then work in pairs to compare their approaches to the task, choosing a strategy that will produce an improved model and together implement that strategy. Students next review some sample work before discussing as a class the strengths and weaknesses of different approaches to the modeling task.
• In a follow-up lesson, students review their work on the task.

Materials required

• Each student will need a copy of the task sheet: Modeling Rolling Cups.
• Each pair of students will need a fresh copy of the task sheet, Modeling Rolling Cups, copies of each of the Sample Responses to Discuss, a large sheet of paper, and a felt-tipped pen.
• It is desirable that each pair of students has access to a computer with the applet Modeling with Geometry: Rolling Cups. If this is not possible the lesson can still be conducted with one class computer and a data projector.
• Supply paper and plastic cups, rules, scrap paper, graph paper, protractors, string, chalk, glue, scissors, and calculators for students who choose to use them.
• For the whole-class discussions, you will need a computer with data projector and two plastic/paper cups that have different base diameters and heights.

Time needed

30 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons), and 20 minutes in a follow-up lesson. All timings are approximate and will depend on the needs of your students.