Secondary Mathematics
Material Type:
Activity/Lab, Assessment, Diagram/Illustration, Homework/Assignment, Lesson Plan
High School
  • IPad
  • Keynote
  • Lesson Plan
  • Polygons
  • Reflection
  • Reflectional Symmetry
  • Rotation
  • Rotational Symmetry
  • Symmetry
  • Transformation
    Creative Commons Attribution Non-Commercial
    Media Formats:
    Downloadable docs, Text/HTML, Other

    Education Standards

    Rotational and Reflectional Symmetry of Polygons with Keynote Project

    Rotational and Reflectional Symmetry of Polygons with Keynote Project


    This is a lesson plan that introduces rotational and reflectional symmetry with geometric shapes, focusing on regular polygons. Notes (two copies: a student version and also an answer key, both as a Word doc and a PDF), assignment, and cut-out shapes are provided. There is a final project, with both instructions and an example included. Cover image: Christensen, K., 2022. Reflectional Symmetry of an Atom [screenshot] (Keynote presentation, Rotational and Reflectional Symmetry Assignment).


    The following lesson is on rotational and reflectional symmetries of various regular polygons, including squares, rectangles, triangles, parallelograms, rhombi, hexagons, trapezoids and other shapes. Students will explore various reflections and rotations and determine if the image is congruent to the pre-image.


    There are 2 pages of cut-out shapes to be used for a more visual representation of the rotations and reflections. These can be printed and cut out prior to class, or the students can cut them out themselves.

    Brads may be used to allow for easier exploration of rotational symmetry if needed for demonstration purposes, or for students' individual exploration, especially for diverse learners.

    String or popsicle sticks may be used to attach to the shapes for easier exploration of reflectional symmetry if needed for demonstration purposes, or for students' individual exploration, especially for diverse learners.

    Students will need a straight edge to draw the line of reflection.

    Calculators may be needed to calculate the angle of rotational symmetry.

    iPads will be needed for the end project.


    Time Frame

    2-3, 45 minute sessions.

    Background for Teachers

    To teach this lesson, you will need an understanding of geometric transformations, specifically rotations and reflections. For example:

    • Squares have both rotational (90o, 180o, 270o) and reflectional symmetries (vertical, horizontal, and diagonal).

    Here are some helpful YouTube videos:

    How to Identify and Calculate Rotational Symmetry

    Symmetry in Geometry

    Here is an interactive webpage that rotates various shapes to set degrees (please note: the rotations here are counterclockwise, where the rotations in the notes and assignment are clockwise).

    There are also two copies of the notes and assignment. One is a student version, and the other is the teacher version which includes the answers.

    For the end project, you will need to be familiar with the iPad Keynote app as well as the Magic Move transition feature. Here is a YouTube video to get you started. Please note: in this lesson, I have the rotations set up as \(90^\circ\) meaning one quarter turn clockwise. When you rotate an object in Keynote, it will rotate it \(90^\circ\) counter-clockwise. Also, the Magic Move feature in Keynote will show rotations, but not reflections. If you flip an object, the animation will show the original shape disappear and the reflected shape re-appear.

    Magic Move YouTube Video

    You will also need to know how to insert an equation in a text box in the Keynote app. This can be found by clicking the "+" located in the top right corner in the app, and then scrolling to the very bottom and selecting "Equation." Instruction for the LaTeX to type into the equation editor for this project, see project instructions.

    Step 1 - Goals and Outcomes

    Step 1 Goals and Outcomes

    Learning Intentions:

    • Students will be able to understand rotational and reflectional translations of regular polygons.
    • Students will be able to understand rotational and reflectional symmetries of regular polygons.

    Success Criteria:

    • Students will describe various rotational and reflectional symmetries of given regular polygons.
    • Students will describe properties of the regular polygons based on these symmetries.


    Step 2 - Planning Instruction

    Step 2 Planning Instruction

    Student Background Knowledge

    Prior to this lesson, students will need to have an understading of

    • Regular polygons and some basic properties
    • Translations of lines and shapes
    • Defintion of congruent geometric figures
    • Linear equations
    • Basic understanding of degrees and rotation
    • Basic understanding of how to use an iPad
    • Basic understanding of the Keynote app, as well as the Magic Move feature (this may also be briefly taught before assigning the project).


    Strategies for Diverse Learners

    Several pages are included in the lesson to assist in creating a more hands-on experience.

    Different reflections can be drawn on the shapes with a dashed line. Or a popcicle stick or piece of string may be used as the line of reflection. Glue the popcicle stick or tape the string onto the back of the shape and use that to reflect the shape.

    For rotations, connect two congruent images in the center with a brad. The students can then rotate the top image until it matches the bottome image to understand rotational symmetries.


    Strategies and Process

    Consider having the students work in groups of at least two, which will allow students to check their answers more easily. This is especially helpful for students who may not as easily identify symmetries (as opposed to similarities), as it is easy to think that some shapes have certain symmetries when they actually don't.

    This would also work as a virtual lesson, as the student version of the notes includes the assignment and cutout shapes.

    Depending on the number of available classroom iPads, you may consider also having the students work in groups for the final project.

    Step 3 - Instruction

    Step 3 Instruction

    Step 4 - Assessments/Projects

    Step 4 Assessments

    Assessment for this lesson will include a final project.

    The students will create a Keynote presentation to accurately portray rotational and reflectional symmetries of at least one shape. They will use the Magic Move feature as a visual aid in demonstrating rotations.

    Here are images of the instructions. Please note, I have included a word doc of the instructions as well as an example project. I have included the example project as both a PowerPoint presentation and also a Keynote presentation. The PowerPoint format does not include the magic move transition feature.