Discovering The Pythagorean Theorem

Cluster: Understand And Apply The Pythagorean Theorem

Task Overview: Students will discover the proof of the Pythagorean Theorem through a series of tasks that leads them to the theorem. Students find the area of the squares attached to the sides of the right triangle and then conclude that the area of the sides of the legs add to the area of the side of the hypotenuse. Though formal mathematical language is not used, students may refer to the legs as sides a or b and the hypotenuse as c.

8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse.

This focus of this standard is on examining different models of the Pythagorean Theorem and its converse and showing understanding of how the models support the theorem.

Objectives

Students should be to explain the Pythagorean Theorem.
Students should be able to use the Pythagorean Theorem to find the hypotenuse of a right triangle.

• Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (7.G.B.6)
• Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. (8.EE.A.2)