# Pythagoras' Theorem: Lunch Lap

Australian curriculum number (ACMMG222)

Students apply Pythagoras’ Theorem to explore a practical real-world problem. They use spreadsheets and dynamic modelling techniques to model and solve the problem, then use geometric reasoning to justify their findings.

This sequence is designed to develop and consolidate skills and conceptual understanding of Pythagoras’ Theorem. It is for students who:

• have been introduced to Pythagoras’ Theorem.
• are able to complete routine calculations to find the length of the hypotenuse or of one of the short sides.

### Lesson 1: Modelling a Lunch Lap

Students participate in an investigation to find the length of a path that touches three sides of a rectangle, starting and finishing at the same point on the fourth side. They model the problem, use Pythagoras’ Theorem to calculate the length of the path, then work with spreadsheets and GeoGebra models to find the shortest possible path.

### Lesson 2: Understanding a Lunch Lap

This task builds on the first lesson in the sequence. Having established that the length of the shortest path remains unchanged regardless of the position of the gate, and that it forms a parallelogram, students use geometric reasoning to find the positions of the carts and justify that the parallelogram is the shortest path.

Last updated October 8 2018.