## 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. Spare copies of the task may also be needed.
• 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.

## Mathematical Practices

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

## Mathematical Content Standards

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