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UNIT 9

Tessellating Polygons

Putting It All Together

Lesson 3

Expressions and Equations

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Let’s make tessellations with different polygons.

Unit 9 ● Lesson 3

Learning

Goal

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Triangle Tessellations

Unit 9 ● Lesson 3 ● Activity 1

Your teacher will assign you one of the three triangles. You can use the picture to draw copies of the triangle on tracing paper. Your goal is to find a tessellation of the plane with copies of the triangle.

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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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Triangle Tessellations

Unit 9 ● Lesson 3 ● Activity 1

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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Triangle Tessellations

Unit 9 ● Lesson 3 ● Activity 1

  • Were you able to make a tessellation with copies of your triangle?
  • How did you know that you could continue your pattern indefinitely to make a tessellation?

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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Quadrilateral Tessellations

Unit 9 ● Lesson 3 ● Activity 2

  1. Can you make a tessellation of the plane with copies of the trapezoid? Explain.
  2. Choose and trace a copy of one of the other two quadrilaterals. Next, trace images of the quadrilateral rotated 180 degrees around the midpoint of each side. What do you notice?
  3. Can you make a tessellation of the plane with copies of the quadrilateral from the previous problem? Explain 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 Tessellations

Unit 9 ● Lesson 3 ● Activity 2

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 Tessellations

Unit 9 ● Lesson 3 ● Activity 2

  • Were you able to tessellate the plane with copies of the trapezoid?
  • What did you notice about the quadrilateral and the 180-degree rotations?
  • How do you know that there are no overlaps?

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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Pentagonal Tessellations

Unit 9 ● Lesson 3 ● Activity 3

  • Can you tessellate the plane with regular pentagons?
  • Can you think of a type of pentagon that could be used to tessellate the plane?

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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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Pentagonal Tessellations

Unit 9 ● Lesson 3 ● Activity 3

  1. Can you tessellate the plane with copies of the pentagon? Explain. Note that the two sides making angle A are congruent.

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Pause your work here.

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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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Pentagonal Tessellations

Unit 9 ● Lesson 3 ● Activity 3

  1. Take one pentagon and rotate it 120 degrees clockwise about the vertex at angle , and trace the new pentagon. Next, rotate the pentagon 240 degrees clockwise about the vertex at angle , and trace the new pentagon.
  2. Explain why the three pentagons make a full circle at the central vertex.
  3. Explain why the shape that the three pentagons make is a hexagon (that is, the sides that look like they are straight really are straight).

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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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Pentagonal Tessellations

Unit 9 ● Lesson 3 ● Activity 3

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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Pentagonal Tessellations

Unit 9 ● Lesson 3 ● Activity 3

  • Does the hexagon made by three copies of the pentagon tessellate the plane?
  • How do you know?
  • Why was it important that the two sides of the pentagons making the 120 angles are congruent?
  • What is special about this pentagon?

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 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®.