# Sharing Costs Equitably: Traveling to School

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to solve a real-world modeling problem. There are several correct approaches to the problem, including some that involve proportional relationships.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task designed to reveal their current understanding and difficulties. You then review their work and create questions for them to answer in order to improve their solutions.
- At the start of the lesson students work alone, answering your questions about the same problem. They 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 the alternative solution strategies they have seen and used.
- Finally, students reflect on their work.

## Materials required

- Each student will need two copies of the assessment task
*Sharing Gasoline Costs*, the review questionnaire*How Did You Work?*, a mini-whiteboard, a pen, and an eraser. - Each small group of students will need copies of all three
*Sample Responses to Discuss*, a large sheet of paper for making a poster, and a marker pen. - There is a projector resource to support whole-class discussions.
- Graph paper should be available for students who require it.

## Time needed

20 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons), and 20 minutes in a follow-up lesson. Timings given are only approximate. Exact timings will depend on the needs of the class.

## 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
- MP6: Attend to precision

## Mathematical Content Standards

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