# Modeling Motion: Rolling Cups

## 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
- 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.

## Lesson Type

## Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

- H.A-CED: Create equations that describe numbers or relationships
- H.F-BF: Build a function that models a relationship between two quantities
- H.G-GMD: Visualize relationships between two-dimensional and three- dimensional objects
- H.G-MG: Apply geometric concepts in modeling situations
- H.G-SRT: Prove theorems involving similarity