Pythagorean Theorem and Volume

Lesson 10

Math

Unit 7

8th Grade

Lesson 10 of 16

Objective


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

Common Core Standards


Core Standards

  • 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.

Criteria for Success


  1. Identify situations in which the Pythagorean Theorem can be used to reveal new information.
  2. Solve real-world problems involving the Pythagorean Theorem, missing measures, and speeds. 

Tips for Teachers


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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Anchor Problems


Problem 1

You have a ladder that is 13 feet long. In order to make it sturdy enough to climb, you place the ladder 5 feet from the wall of a building, as shown in the diagram below. 

You need to post a banner on the wall 10 feet above the ground. Is the ladder long enough for you to reach the location you need to post the banner? Explain your answer.

Guiding Questions

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References

EngageNY Mathematics Grade 8 Mathematics > Module 2 > Topic D > Lesson 16Example 2

Grade 8 Mathematics > Module 2 > Topic D > Lesson 16 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are $${{1\over16}}$$ mile apart and arranged in a square grid. They are both standing at the intersection of 6th Ave and L Street. Doug can run at an average speed of 30 mi/hr through the streets of Salt Lake City, and Bert can fly at an average speed of 20 mi/hr. They are about to race to the intersection of 10th Ave and E Street.

a.   Who do you predict will win, and why?

b.   Draw the likely paths that Doug and Bert will travel.

c.   Who will win the race? Justify your response.

Guiding Questions

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References

Illustrative Mathematics Bird and Dog Race

Bird and Dog Race, accessed on March 20, 2017, 12:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

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Target Task


Kendrick is interested in purchasing a new television. He has picked out a specific space on a wall on which to mount the television. The wall space is rectangular in shape and measures $$1 \frac{2}{3}$$ feet tall and $$3$$ feet wide. 

Sizes of televisions are given in inches and describe the diagonal length from the top corner of the television to the opposite bottom corner. 

Can Kendrick fit a 42-inch television on the space that he has picked out? Explain your reasoning.

Student Response

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Additional Practice


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.

  • Include additional practice problems from previous lessons as needed.
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Lesson 9

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Lesson 11

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Irrational Numbers and Square Roots

Topic B: Understanding and Applying the Pythagorean Theorem

Topic C: Volume and Cube Roots

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