Unit 5 - Geometric Applications of Exponents (8th Grade)

# Unit 5

Students will extend their work with irrational numbers by applying the Pythagorean Theorem to situations involving right triangles, including finding distance. Proof of the Pythagorean Theorem and its converse allow students to demonstrate an understanding of the theorem. Real-world problems are solved involving volume of cylinders, cones, and spheres.

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### Understand and apply the Pythagorean Theorem. Solve real‐world and mathematical problems involving volume of cylinders, cones, and spheres. Work with radicals and integer exponents.

MGSE8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

MGSE8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

MGSE8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

MGSE8.G.9 Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

MGSE8.EE.2 Use square root and cube root symbols to represent solutions to equations. Recognize that x2 = p (where p is a positive rational number and lxl < 25) has 2 solutions and x3 = p (where p is a negative or positive rational number and lxl < 10) has one solution. Evaluate square roots of perfect squares < 625 and cube roots of perfect cubes > -1000 and < 1000.