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UNIT 8

When Is the Same Size Not the Same Size?

Pythagorean Theorem and Irrational Numbers

Lesson 13

Expressions and Equations

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Let’s figure out how aspect ratio affects screen area.

Unit 8 ● Lesson 13

Learning

Goal

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Three Figures

Unit 8 ● Lesson 13 ● Activity 1

How are these shapes the same? How are they different?

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Warm-up

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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A 4 : 3 Rectangle

Unit 8 ● Lesson 13 ● Activity 2

A typical aspect ratio for photos is 4 : 3. Here’s a rectangle with a 4 : 3 aspect ratio.

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  1. What does it mean that the aspect ratio is 4 : 3? Mark up the diagram to show what that means.
  2. If the shorter side of the rectangle measures 15 inches:
    1. What is the length of the longer side?
    2. What is the length of the rectangle’s diagonal?
  3. If the diagonal of the rectangle measures 10 inches, how long are its sides?
  4. If the diagonal of the rectangle measures 6 inches, how long are its sides?

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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The Screen Is the Same Size . . . Or Is It?

Unit 8 ● Lesson 13 ● Activity 3

Before 2017, a smart phone manufacturer’s phones had a diagonal length of 5.8 inches and an aspect ratio of 16 : 9. In 2017, they released a new phone that also had a 5.8-inch diagonal length, but an aspect ratio of 18.5 : 9. Some customers complained that the new phones had a smaller screen. Were they correct? If so, how much smaller was the new screen compared to the old screen?

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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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Unit 8 ● Lesson 13

  • I can apply what I have learned about the Pythagorean Theorem to solve a more complicated problem.
  • I can decide what information I need to know to be able to solve a real-world problem using the Pythagorean Theorem.

Learning

Targets

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This slide deck is copyright 2021 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).

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-NC 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).

Adaptations and additions to create IM 6–8 Math Accelerated are copyright 2020 by Illustrative Mathematics®, www.illustrativemathematics.org, 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®.