Mandalas, Polygons, and Symmetry

Merging mathematics, culture, and art by creating a geometric pattern


Key Staff

This lesson can be taught by a mathematics teacher. No additional instruction required.

Key Skills

Making Art: Composing and Planning
Global Connections: Connecting to History and Culture


Students will explore the mathematics behind mandalas, including but not limited to shapes and symmetry. After examining mandalas that are both natural and man-made, students will create their own mandalas using mathematical concepts and skills. They will then analyze other students’ creative work for style and message.

Learning Objectives

Students will:

  • Review elements and basic vocabulary of geometry
  • Apply geometry skills to increase understanding of polygons
  • Learn about the history and cultural background of mandalas
  • Combine their knowledge of polygons and understanding of mandalas to design their own mandalas
  • Correctly incorporate polygons, symmetry, and color scheme in the design of their mandalas

Teaching Approach

Arts Integration

Teaching Methods

  • Discussion
  • Hands-On Learning
  • Self-Paced Learning
  • Reflection
  • Group or Individual Instruction

Assessment Type

Self Assessment


What You'll Need

Required Technology
  • 1 Computer per Classroom
  • Internet Access
  • Projector
Lesson Setup

Teacher Background

  • Mandala Video
  • Free Mandala
  • Review Mandalas and Polygons Vocabulary
  • Explore the website: The Mandala Project
  • Find photographs of flowers that show the petal arrangement

Prior Student Knowledge

Students should have a working knowledge of geometry, including shapes of polygons and compass (technical drawing) skills.

Physical Space



Individualized Instruction


Test web links and computer/projection equipment

Gather art supplies

Accessibility Notes

This lesson may be difficult for students with fine motor skills issues. It may be easier for these students to work with limited, larger shapes, perhaps using a template or shapes to trace. Large grid paper may also be helpful.

Students with vision problems may find it easier to work on a larger scale or use solid (pre-cut) shapes.

Some students may require one-to-one aide assistance.


Resources in Reach

Here are the resources you'll need for each activity, in order of instruction.

Build Knowledge


1. Introduce class to student-created mandalas by showing the video.

2. Encourage students to share their observation of the creative process. Guide them to use mathematical terms, such as circle, shapes, polygons, and symmetry. (After viewing the entire video, you can pause the video at a frame that shows a good image of the final product for the discussion.) Ask them what they noticed about the environment in which the mandala was created. (The creation of a mandala can be both meditative and reflective and is often used as part of a religious or spiritual experience.) Ask students to share words that describe the mandala to them. (These words can indicate color, emotion, feeling, movement, etc. Explain that there is no right or wrong answer for this part of the experience.)

Build Knowledge

1. Dissect a mandala using mathematical terms. Distribute a pre-selected, non-colored mandala, the Mandala and Polygons Vocabulary handout located within the Resource Carousel, and a ruler and a compass to each student. Discuss the following with the students:

  • The circle as the starting point for a mandala (The word mandala originates in the Sanskrit language and loosely translates to circle or magic circle. Identify the center of the circle and the circle itself, either shown or implied in the design. Using the compass, have students re-create the circle by locating the center point and tracing the circle.)
    NOTE: Some mandalas are square shaped. For the purpose of this lesson, do not select a non-circular mandala.
  • The use of concentric circles to show movement into and out from the center of the circle.
  • The use of shapes to create a pattern. (Using a pencil, shade or cross hatch repetitive shapes within the mandala. Use the correct terminology for the various shapes.)
  • The use of symmetry to show reflection within the circle. (The symmetry can be vertical, horizontal, or radial. Using a ruler and pencil, draw lines of symmetry on the mandala.)

2. Show photographs of flowers. Ask students to note what is similar in both flowers and man-made mandalas. Explain that nature is the inspiration for man-made mandalas. Explain that in some religions and cultures, the mandala is used as a tool for reflection. (The Mandala Project web site is an excellent resource for background information.)


1. Students will merge their mathematics knowledge and understanding of basic mandala structure to create their own mandalas. Distribute white paper and copies of the mandala Directions handout located within the Resource Carousel to each student. Have students follow the directions and work independently to create their own mandalas.


1. Display the students’ mandalas around the classroom. Place a small paper cup by each piece of artwork,.

2. Capture the message of each mandala. Start by having the artist stand in front of his or her mandala, facing it. On a 1” x 1” piece of paper, write the first word that comes to the student’s mind as he or she views the artwork. (This word could reflect the shapes, colors, emotions, or message. Encourage descriptive words, such as angry or flowing, and not general words, such as nice or pretty.) Place the piece of paper in the cup.

3. Rotate students through the artwork to capture first thoughts. Move the students through the artwork, allowing ten seconds to view and write one word for each piece. Place the papers in the corresponding cups. When the rotation is completed, each artist should collect his or her cup with a set of words provided by classmates.

4. Each student composes a short essay about the mandala-creation experience. The essay should include three paragraphs:

  • The artist’s intention with his or her choice of shapes, colors, design
  • The message received by the viewers
  • How the artist might approach the mandala-creation experience differently if he or she were to do it again


Throughout the nation, standards of learning are being revised, published and adopted. During this time of transition, ARTSEDGE will continually add connections to the Common Core, Next Generation Science standards and other standards to our existing lessons, in addition to the previous versions of the National Standards across the subject areas.

The Arts Standards used in ARTSEDGE Lessons are the 1994 voluntary national arts standards. The Arts learning standards were revised in 2014; please visit the National Core Arts Standards (http://nationalartsstandards.org) for more. The Kennedy Center is working on developing new lessons to connect to these standards, while maintaining the existing lesson library aligned to the Common Core, other state standards, and the 1994 National Standards for Arts Education.

ArtsEdge Lessons connect to the National Standards for Arts Education, the Common Core Standards, and a range of other subject area standards.

Common Core/State Standards

Select state and grade(s) below, then click "Find" to display Common Core and state standards.

National Standards For Arts Education
Visual Art

Grade 5-8 Visual Arts Standard 1: Understanding and applying media, techniques, and processes

Grade 5-8 Visual Arts Standard 6: Making connections between visual arts and other disciplines

National Standards in Other Subjects

Math Standard 3: Uses basic and advanced procedures while performing the processes of computation

Math Standard 4: Understands and applies basic and advanced properties of the concepts of measurement

Math Standard 5: Understands and applies basic and advanced properties of the concepts of geometry



Kim Guzzetti
Original Writer

Carol Parenzan Smalley

Email Print Share


- +
Email a link to this page
Share This Page


Related Resources


Tagged As


Use this collection of resources and articles to devise an approach for supporting individual needs in the classroom: from English Language Learners or students with disabilities, to conflict resolution and giving feedback.



© 1996-2019 John F. Kennedy Center for the Performing Arts  

ArtsEdge is an education program of

The Kennedy Center 

with the support of

The US Department of Education 

ARTSEDGE, part of the Rubenstein Arts Access Program, is generously funded by David Rubenstein.

Additional support is provided by the U.S. Department of Education.

Kennedy Center education and related artistic programming is made possible through the generosity of the National Committee
for the Performing Arts and the President’s Advisory Committee on the Arts.

The contents of this Web site were developed under a grant from the U.S. Department of Education. However, those contents do not
necessarily represent the policy of the U.S. Department of Education, and you should not assume endorsement by the Federal government.
Unless otherwise stated, ArtsEdge materials may be copied, modified and otherwise utilized for non-commercial educational purposes
provided that ArtsEdge and any authors listed in the materials are credited and provided that you permit others to use them in the same manner.

Change Background:

Connect with us!    EMAIL US | YouTube | Facebook | iTunes | MORE!

© 1996-2019 John F. Kennedy Center for the Performing Arts  
    Privacy Policy
| Terms and Conditions


You are now leaving the ArtsEdge website. Thank you for visiting!

If you are not automatically transferred, please click the link below:

ArtsEdge and The Kennedy Center are in no way responsible for the content of the destination site, its ongoing availability, links to other site or the legality or accuracy of information on the site or its resources.