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Rotate and Tessellate

Lesson 17

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2019 Open Up Resources |

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Let’s make complex

patterns using

transformations!

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Today’s Goals

  • I can use properties of angle sums to reason about how figures will fit together.
  • I can repeatedly use rigid transformations to make interesting repeating patterns of figures.

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Deducing Angle Measures

Warm Up

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  • How many copies of the equilateral triangle can you fit together around a single vertex, so that the triangles’ edges have no gaps or overlaps? What is the measure of each angle in these triangles?
  • What are the measures of �the angles in the…
    • square?
    • hexagon?
    • parallelogram?
    • right triangle?
    • octagon?
    • pentagon?�

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Tessellate This

Activity 1

  • Group Presentations
  • Stronger and Clearer Each Time
  • Collect and Display

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What’s a tessellation?

a regular repeating pattern of one or more shapes that covers the entire plane

The pattern continues forever in all directions.

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  • Design your own tessellation. You will need to decide which shapes you want to use and make copies. Remember that a tessellation is a repeating pattern that does on forever to fill up the entire plane.
  • Find a partner and trade pictures. Describe a transformation of your partner’s picture that takes the pattern to itself. How many different transformations can you find that take the pattern to itself? Consider translations, reflections, and rotations.
  • If there’s time, color and decorate your tessellation.

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Share your designs.

Describe a transformation that takes the design to itself.

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Rotate That

Activity 2

  • Group Presentations
  • Collect and Display

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What transformation could you perform on the figure so that it matches up with its original position?

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  • Make a design with rotational symmetry.
  • Find a partner who has also made a design. Exchange designs and find a transformation of your partner’s design that takes it to itself. Consider rotations, reflections, and translations.
  • If there’s time, color and decorate your design.

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Share your designs.

Describe a transformation that takes the design to itself.

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Today’s Goals

  • I can use properties of angle sums to reason about how figures will fit together.
  • I can repeatedly use rigid transformations to make interesting repeating patterns of figures.