## Who is this Sequence for?

This set of lessons is designed to develop and consolidate skills and conceptual understanding of Pythagoras’ Theorem. The Year 9 lessons assume that students have been introduced to Pythagoras’ Theorem and are able to complete routine calculations to find the length of the hypotenuse or of one of the short sides. The Year 10 lesson Bent Bamboo assumes knowledge of Pythagoras’ Theorem and makes links to the algebra of binomial expansions and graphs of quadratic functions.

## Summary of learning goals

Students apply Pythagoras’ Theorem to explore practical and historical real-world problems. In the lessons Lunch Lap and Bent Bamboo they can see connections between their solutions and concepts of symmetry and algebra, and Phone Finding explores technology reliant on mathematical concepts. Each lesson involves an initial problem context that can be approached using Pythagoras’ Theorem.

## Rationale for this sequence

The concepts behind Pythagoras’ Theorem and its proofs are taught well in classrooms, and there are ample high quality resources to assist teachers. This sequence is not intended to prove or teach the theorem for this reason. However traditional applications are often shallow and uninteresting and so the focus here is on providing explorative and atypical applications.

The tasks in this sequence provide, in order:

- An imagined application of interest that produces a surprising result
- A historical look at cross-cultural appearances of the theorem
- An exploration of practical real-world technology that relies on the theorem

Lessons 1 (Lunch Lap) and 2 (Phone Finding) provide useful opportunities for fluency with Pythagoras’ Theorem and Lesson 2 in particular can serve as a useful assessment task due to its self-contained focus and emphasis on fluency exercises.