Lesson 17Rotate and Tessellate

Learning Goal

Let’s make complex patterns using transformations.

Learning Targets

  • I can repeatedly use rigid transformations to make interesting repeating patterns of figures.

  • I can use properties of angle sums to reason about how figures will fit together.

Lesson Terms

  • tessellation

Warm Up: Deducing Angle Measures

Problem 1

Your teacher will give you some shapes.

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?

Problem 2

What are the measures of the angles in the

  1. square?

  2. hexagon?

  3. parallelogram?

  4. right triangle?

  5. octagon?

  6. pentagon?

Activity 1: Tessellate This

Problem 1

  1. 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 goes on forever to fill up the entire plane.

  2. 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.

Activity 2: Rotate That

Problem 1

  1. Make a design with rotational symmetry.

  2. 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.