# 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.

## Introduction

- 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*,*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.

## 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:*

- 8.EE: Understand the connections between proportional relationships, lines, and linear equations.
- 8.F: Define, evaluate, and compare functions.
- 8.F: Use functions to model relationships between quantities.