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.


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:

Mathematical Content Standards

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