# Representing: Road Race

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to model a real-world situation and compare and critique sample models. In particular this lesson aims to identify and help students who have difficulty recognizing and using proportional relationships.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt the
*A Race*task individually. You then assess their responses and formulate questions that will prompt students to review their work. - At the start of the lesson, students think individually about their responses to the questions set.
- Next, students work in pairs or threes to combine their thinking and work together to produce a collaborative solution to the task, in the form of a poster.
- Working in the same small groups, students evaluate, comment on, and complete some sample responses.
- In a whole-class discussion students compare and evaluate the methods they have seen and used.
- Finally, in a follow-up lesson, students reflect on their work and what they have learned.

## Materials required

- Each student will need a copy of the
*A Race*task, some paper to work on, a mini-whiteboard, pen, and eraser, and a copy of the*How Did You Work?*questionnaire. - Each small group of students will need a large sheet of paper, copies of the
*Sample Responses to Discuss*and one or two post-it notes. - Calculators and graph paper should be made available upon request.
- There is a projector resource to support whole-class discussions.

## Time needed

20 minutes before the lesson, a 100-minute lesson (or two 50-minute lessons), and 15 minutes in a follow-up lesson. 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
- 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:*

- 7.RP: Analyze proportional relationships and use them to solve real-world and mathematical problems.