# Modeling Relationships: Car Skid Marks

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to use an approximate mathematical model of a real-world situation and use data to test, critique, and compare models. In particular this unit aims to identify and help students who have difficulty using variables to represent quantities and analyze the relationship between these variables using tables, graphs, and equations.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt the
*Car Skid Marks*task individually. You then assess their responses and formulate questions that will prompt them to review their work. - At the start of the lesson, students think individually about their responses to the questions set. They then work in small groups to combine their thinking to produce a collaborative solution to the
*Car Skid Marks*task, in the form of a poster. - Working in the same small groups, students evaluate and comment on sample responses, identifying strengths and weaknesses in each approach and comparing them with their own work. In a whole-class discussion, students compare and evaluate the methods they have seen and used.
- 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
*Car Skid Marks*task, the*How Did You Work?*questionnaire, a mini-whiteboard and eraser, and some plain or squared paper to work on. Calculators and graph paper should be available on request. - Each small group of students will need a large sheet of paper and enlarged copies of the
*Sample Responses to Discuss*.

## Time needed

20 minutes before the lesson, a 100-minute lesson (or two 55-minute lessons), and 15 minutes in a follow-up lesson (or for homework). 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:*