Finding the Shortest Route: A Schoolyard Problem
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.
- 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.
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.
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: