Overview

Summary

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

Preparation

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

Classroom

Grouping

Individualized Instruction

Staging

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.

Instruction

Engage

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.)

Apply

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.

Reflect

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

Standards

The 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

Mathematics

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