Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 11
Math
Unit 7
8th Grade
Lesson 11 of 16
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Lesson Notes
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Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).
The core standards covered in this lesson
8.G.B.7 — Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Lessons 10 and 11 engage students in real-world and mathematical problems that can be modeled and solved using the Pythagorean Theorem. In these two lessons, students tackle problems involving a race and speed, and students will see how to apply the Pythagorean Theorem in three dimensions (MP.4). Depending on time, these two lessons can be combined into one lesson for a longer class period, or they can be kept as two separate lessons.
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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
a. Act 1: Watch the Taco Cart by Dan Meyer.
b. Act 2: Look at the information below. Note, the speeds refer to the speed of walking on the sand and the speed of walking on the concrete sidewalk. Determine who will reach the taco cart first.
c. Act 3: Watch the video answer. Was your answer reasonable? Why or why not?
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Taco Cart by Dan Meyer is licensed under the CC BY 3.0 license. Accessed March 20, 2017, 11:57 a.m..
Two rectangular prisms are shown below.
a. Which figure do you think has the longer diagonal? Note that the figures are not drawn to scale.
b. Calculate the lengths of both diagonals. Which one is actually longer?
Grade 8 Unit 8 Lesson 10 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 9, 2022, 12:10 p.m..
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
A rectangular prism is shown below. Use the given information to determine the exact length of $${\overline{DF}}$$.
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.
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Find the distance between points in the coordinate plane using 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
Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.
8.G.B.6
Understand a proof of the Pythagorean Theorem.
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).
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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