Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 6
Math
Unit 7
8th Grade
Lesson 6 of 16
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Lesson Notes
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Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.
The core standards covered in this lesson
8.G.B.6 — Explain a proof of the Pythagorean Theorem and its converse.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In this lesson, students are introduced to the famous relationship that exists between the side lengths of right triangles. In the next lesson, students will investigate informal proofs of the Pythagorean Theorem, followed by lessons where students will apply the theorem in various problems.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Several right triangles are shown below (not drawn to scale). In a right triangle, the two side lengths that form the right angle are called legs, and the side length opposite the right angle is called the hypotenuse.
Use the triangles to investigate the question: What relationship do you see between the measures of the legs and the measure of the hypotenuse?
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Use the Pythagorean Theorem to show the relationship between the sides of the right triangles shown below.
A right triangle has side lengths $$6$$ units, $$4$$ units, and $${\sqrt{20}}$$ units.
Which side length represents the hypotenuse?
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Lee tried to use the Pythagorean Theorem on the triangle shown below and found that the relationship did not hold true.
Explain why the Pythagorean Theorem did not show a true relationship in Lee’s triangle.
Which three measures could be the side lengths of a right triangle? Explain or show your reasoning.
$$5$$ $$2$$ $$7$$ $$\sqrt{24}$$
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Understand a proof of the Pythagorean Theorem.
Topic A: Irrational Numbers and Square Roots
Define, evaluate, and estimate square roots.
Standards
8.EE.A.2
Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.
8.NS.A.18.NS.A.2
Locate irrational values approximately on a number line. Compare values of irrational numbers.
8.NS.A.2
Represent rational numbers as decimal expansions.
8.NS.A.1
Represent decimal expansions as rational numbers in fraction form.
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Topic B: Understanding and Applying the Pythagorean Theorem
8.G.B.6
Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
Find missing side lengths involving right triangles and apply to area and perimeter problems.
8.G.B.7
Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).
Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).
Find the distance between points in the coordinate plane using the Pythagorean Theorem.
8.G.B.8
Topic C: Volume and Cube Roots
Define and evaluate cube roots. Solve equations in the form $${x^2=p}$$ and $${x^3=p}$$.
8.EE.A.28.NS.A.2
Solve real-world and mathematical problems involving the volume of cylinders and cones.
8.G.C.9
Solve real-world and mathematical problems involving the volume of spheres.
Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.
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