Unit 8
Applications of the Pythagorean Theorem
Pythagorean Theorem & Irrational Numbers
Lesson 10
8.EE.A.2: Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
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.
8.NS.A: Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations
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Warm Up
Unit 8 ● Lesson 10
1 min individual - 1 min team share - 3 mins class share
Page 167
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 8 ● Lesson 10
We will be able to use the Pythagorean Theorem so that we can solve problems involving right triangles.
Learning
Goal
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Where were we? Where are we? Where are we going?
Unit 8 ● Lesson 10
Agenda Review
You are successful today when...,
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
10.2 Activity: Cutting Corners
You can use the Pythagorean Theorem to solve problems.
100m
80m
pg 168
How can it be helpful to organize calculations when problems have multiple steps?
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
10.2 Activity: Cutting Corners
You can use the Pythagorean Theorem to solve problems.
10 mins total
6 minutes group - 4 mins class share
Tyler
80² + 100² = c²
6,400 + 10,000 = c²
16,400 = c²
√16,400 = c
√16,400/5 ≈ 25.6 seconds
pg 168
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
10.3 Activity: Internal Dimensions
You can use the Pythagorean Theorem to solve problems.
What can we do to make sense of this problem before we start? Brainstorm ideas to calculate the length of the diagonal.
pg 169
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
10.3 Activity: Internal Dimensions
You can use the Pythagorean Theorem to solve problems.
10 mins total
5-7 minutes group - 3 mins class share
pg 169
Find the diagonal of the base
16 + 25 = c²
41 = c²
√41 = c
Substitute & Solve
41 + 36 = c²
77 = c²
√77 = c
Find the diagonal of the base
25 + 25 = c²
50 = c²
√50 = c
Substitute & Solve
50 + 25 = c²
75 = c²
√75 = c
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Applications of the Pythagorean Theorem
You can use the Pythagorean Theorem to solve problems.
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Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Jib Sail
You can use the Pythagorean Theorem to solve problems.
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Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 8 ● Lesson 10
Learning
Targets
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
6.3 Activity: Meet the Pythagorean Theorem
You can explain what the Pythagorean Theorem says.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
6.3 Activity: Meet the Pythagorean Theorem
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.
All curriculum excerpts are under the following licenses:
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
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