Rotational Symmetry Lesson Plan

Instructor: Christopher Sailus

Chris has an M.A. in history and taught university and high school history.

In this lesson plan, students learn about rotational symmetry. They'll learn the mathematical representation for rotational symmetry, verify it through rotating objects that exhibit rotational symmetry, then draw their own objects and recognize them in real-life situations.

Learning Objectives

After this lesson, students will be able to:

  • Identify rotational symmetry in geometric objects and real-life examples
  • Create objects and symbols with rotational symmetry


1 hour


  • Index cards
  • Colored pencils or markers
  • Pictures of everyday objects that exhibit different orders of rotational symmetry. Examples of what you could find and print include:
    • For n=2, a rectangular piece of word
    • For n=3, a triangular traffic sign
    • For n=4, a blank pizza box
    • For n=5, a generic clipart star
    • For n=6, the Star of David
    • For n=8, a typical stop sign

Key Vocabulary

At the conclusion of this lesson, students should be able to identify and define the following vocabulary terms:

  • Rotational symmetry

Curriculum Standards

  • CCSS.Math.Content.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations.

  • CCSS.Math.Content.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.


  • Prior to class, display 'Cn' on the board. Next to it, write 'n=2,'n=3,' 'n=4,'n=5,' 'n=6,' and 'n=8.' Write these horizontally so that each is a heading.
  • Beneath each heading, draw a generic geometric object that exhibits that type of rotational symmetry.
    • For n=2, draw a rectangle
    • For n=3, draw an equilateral triangle
    • For n=4, draw a square
    • For n=5, draw a star
    • For n=6, draw a hexagon
    • For n=8, draw an octagon
  • Beneath these geometric drawings, place the corresponding printed pictures of real-life objects with each type of rotational symmetry.
  • Once the class arrives, explain to your students that rotational symmetry describes an object that can be turned and at some point exhibits the exact same shape as when you began turning the object.
  • Explain that this is represented mathematically as 'Cn', where C represents the object and the subscript n represents the amount of times an object exhibits the same shape during one full rotation.
  • To exemplify this, use the photos of real-life objects to demonstrate the rotational symmetry, stopping at each point where it exhibits the same shape. If your students are having trouble grasping the concept, rotate the shape until it reaches the proper point, stop, and ask students if it is the same shape. If it is, put a tally mark on the board. Then your class can count the tally marks after each full rotation.

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