Lesson 6 | Pythagorean Theorem and Volume | 8th Grade Mathematics

Objective

Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.

Lesson Map

Topic A: Irrational Numbers and Square Roots

Lesson

Define, evaluate, and estimate square roots.

Standards

8.EE.A.2

Lesson

Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.

Standards

8.NS.A.18.NS.A.2

Lesson

Locate irrational values approximately on a number line. Compare values of irrational numbers.

Standards

8.NS.A.2

Lesson

Represent rational numbers as decimal expansions.

Standards

8.NS.A.1

Lesson

Represent decimal expansions as rational numbers in fraction form.

Standards

8.NS.A.1

Topic B: Understanding and Applying the Pythagorean Theorem

Lesson

Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.

Standards

8.G.B.6

Lesson

Understand a proof of the Pythagorean Theorem.

Standards

8.G.B.6

Lesson

Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.

Standards

8.G.B.6

Lesson

Find missing side lengths involving right triangles and apply to area and perimeter problems.

Standards

8.G.B.7

Lesson

Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).

Standards

8.G.B.7

Lesson

Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).

Standards

8.G.B.7

Lesson

Find the distance between points in the coordinate plane using the Pythagorean Theorem.

Standards

8.G.B.8

Topic C: Volume and Cube Roots

Lesson

Define and evaluate cube roots. Solve equations in the form $${x^2=p}$$ and $${x^3=p}$$.

Standards

8.EE.A.28.NS.A.2

Lesson

Solve real-world and mathematical problems involving the volume of cylinders and cones.

Standards

8.G.C.9

Lesson

Solve real-world and mathematical problems involving the volume of spheres.

Standards

8.G.C.9

Lesson

Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.

Standards

8.G.C.9

Pythagorean Theorem and Volume

Objective

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Pythagorean Theorem and Volume

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