# Finding the Shortest Route: A Schoolyard Problem

## Mathematical goals

This lesson unit is intended to help students to:

- Select appropriate mathematics to solve a problem.
- Compare and evaluate different methods for solving a problem and make generalizations about the appropriateness of different approaches.
- Understand the Pythagorean Theorem and how it can be used to solve problems in the real world.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt
*The Schoolyard Problem*individually. You review these initial attempts, formulating questions that will help students to improve their work. - After a brief lesson introduction, students respond individually to the questions on their work.
- Then, in groups of 2 or 3, students compare their different approaches and examine and comment on some sample student responses. They identify features of these responses that may help them with their own work.
- In the same small groups, students now work together to produce a collaborative solution in the form of a poster.
- In a whole-class discussion, students explain and compare the strategies they have seen and used.
- Finally, students reflect on their work and their learning.

## Materials required

- Each student will need a copy of the task
*The Schoolyard Problem*. - Each small group of students will need a sheet of poster paper, a marker, and copies of the
*Sample Responses to Discuss*. - Provide calculators, rulers, and squared/graph paper for students who choose to use them.
- There is a projector resource to support whole-class discussion.

## Time needed

20 minutes before the lesson, a 100-minute lesson (or split into two shorter lessons) and 10 minutes in a follow-up lesson (or for homework). Timings given are approximate. Exact timings will depend on the needs of your 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

## Mathematical Content Standards

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