Pythagorean Theorem and Volume

Lesson 11

Math

Unit 7

8th Grade

Lesson 11 of 16

Objective


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

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.
  3. Find missing measures in three-dimensional prisms using the Pythagorean Theorem. 

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.  

Lesson Materials

  • Calculators (1 per student)
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Anchor Problems


Problem 1

a.   Act 1: Watch the Taco Cart by Dan Meyer.

  1. What do you notice? What do you wonder? 
  2. Who will reach the taco cart first? Make a guess.

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?

Guiding Questions

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References

Dan Meyer's Three-Act Math Taco Cart

Taco Cart by Dan Meyer is licensed under the CC BY 3.0 license. Accessed March 20, 2017, 11:57 a.m..

Modified by Fishtank Learning, Inc.

Problem 2

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?

Guiding Questions

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References

Open Up Resources Grade 8 Unit 8 Lesson 10Lesson 10.3: Internal Dimensions

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..

Problem Set

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Target Task


A rectangular prism is shown below. Use the given information to determine the exact length of $${\overline{DF}}$$.

  • $${\overline{AB}=8}$$ units
  • $${\overline{BF}=6}$$ units
  • $${\overline{FG}=12}$$ units

 

 

 

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.

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Lesson 10

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Lesson 12

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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