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