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Unit 1

Polygons

Lesson 11

Area and Surface Area

Expressions and Equations

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Let’s investigate polygons and their areas.

Unit 1 ● Lesson 11

Learning

Goal

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Bases and Heights

Unit 1 ● Lesson 11 ● Activity 1

Warm-up: Which One Doesn’t Belong?

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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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What are Polygons?

Unit 1 ● Lesson 11 ● Activity 2

Here are five polygons:

Here are six figures that are not polygons:

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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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What are Polygons?

Unit 1 ● Lesson 11 ● Activity 2

  1. Circle the figures that are polygons.
  • What do the figures you circled have in common? What characteristics helped you decide whether a figure was a polygon?

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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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Quadrilateral Strategies

Unit 1 ● Lesson 11 ● Activity 3

  • What is a quadrilateral?
  • How would you find the area of quadrilateral D? What would be your first move? Would you enclose or decompose? Can you show us?

Find the area of two other quadrilaterals of your choice. Show your reasoning.

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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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Quadrilateral Strategies

Unit 1 ● Lesson 11 ● Activity 3

  • Choose one quadrilateral your group worked on (other than D).
  • What was the first couple of moves you made for finding its area? Why did you choose those moves?
  • Encourage other group members to listen carefully, and contribute.

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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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Pinwheel

Unit 1 ● Lesson 11 ● Activity 4

  1. In your group, decide on a plan to find the area of the shaded region in square units.
  2. Then use that plan to find the area.
  3. Show your reasoning in a visual display to share with the class.

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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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Pinwheel

Unit 1 ● Lesson 11 ● Activity 4

  • Did another group arrive at the same area of the pinwheel as our group? If not, why?
  • How is their strategy like our strategy?
  • How is their strategy different than ours?

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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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Polygons

Unit 1 ● Lesson 11

  • Which of these figures is not a polygon? Why?

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  • How do we know this figure is a polygon?
  • What does it mean to find the area of this polygon?
  • How can we find the area of this polygon?

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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.

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Unit 1 ● Lesson 11

  • I can describe the characteristics of a polygon using mathematical vocabulary.
  • I can reason about the area of any polygon by decomposing and rearranging it, and by using what I know about rectangles and triangles.

Learning Targets

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Triangulation

Unit 1 ● Lesson 11 ● Activity 5

  1. Here are two five-pointed stars. A student said, “Both figures A and B are polygons. They are both composed of line segments and are two-dimensional. Neither have curves.” Do you agree with the statement? Explain your reasoning.
  • Here is a five-sided polygon. Describe or show the strategy you would use to find its area. Markup and label the diagram to show your reasoning so that it can be followed by others. (It is not necessary to actually calculate the area.)

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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.

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polygon

Unit 1 ● Lesson 11

A polygon is a closed, two-dimensional shape with straight sides that do not cross each other.

Figure is an example of a polygon.

Glossary

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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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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).

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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).

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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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