# 3. Use an area proof of the Pythagorean Theorem to design a park (A)

## About this lesson

Lesson objective: Apply the method for a Pythagorean Theorem area model proof to a real-life situation.

This lesson provides an opportunity for students to apply their knowledge and understanding of geometric representations of the Pythagorean Theorem to a real-life situation. Students are asked to design a configuaration for a park where the square on the hypotenuse of a right triangle is decomposed into two squares that fit the squares on the legs of that right triangle.

Key Concept students will use:

- Area models can be used to demonstrate the relationship showing the sum of the squared lengths of two legs of a right triangle is the same as the square of the measure of the hypotenuse.

Skills students will use:

- decompose area into smaller areas (Grade 6, Unit 10)
- write the algebraic representation of the Pythagorean Theorem
- classify geometric shapes by their attributes (Grade 5, Unit 11)

Students engage in Mathematical Practice 4 (model with mathematics) as they use representations of of the Pythagorean Theorem to explain how to decompose the area of a park.

**Key vocabulary: **

- hypotenuse
- legs
- Pythagorean Theorem
- sides of a right triangle

**Special materials needed (not required.) Students may draw park designs or use the manipulative template:**

- worksheet , access in For This Lesson or download here
- glue
- scissors