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Lesson plan

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

teaches Common Core State Standards MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards MP2 http://corestandards.org/Math/Practice/MP2
teaches Common Core State Standards 8.G.B.7 http://corestandards.org/Math/Content/8/G/B/7
teaches Common Core State Standards 8.G.B.6 http://corestandards.org/Math/Content/8/G/B/6

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

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