# Mandala

## Curriculum Goal

#### Junior: Patterning and Algebra

• Create and translate repeating, growing, and shrinking patterns using various representations, including tables of values, graphs, and, for linear growing patterns, algebraic expressions and equations.

#### Junior: Geometry and Spatial Sense

• Describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations.

#### Junior: Visual Arts

• Apply the creative process to produce art works in a variety of traditional two- and three-dimensional forms, as well as multimedia art works, that communicate feelings, ideas, and understandings, using elements, principles, and techniques of visual arts as well as current media technologies.
• Demonstrate an understanding of a variety of art forms, styles, and techniques from the past and present, and their sociocultural and historical contexts.

## Context

• Whole-class discussion followed by individual activity at desks.

## Materials

• Background information on mandalas (Appendix A)
• 2 sample mandalas (Appendix B): 1 completed and 1 incomplete
• Pattern worksheet (Appendix C)
• Circle cut-outs, divided into 4 quadrants (Appendix D)
• Dice
• Pencil
• Eraser
• Pencil crayons
• Calculator

## Lesson

• Show students pictures of mandala tapestries and ask questions such as: Do you know what this is? What do you see? Do you know what mandala means? What language is it?
• Provide background information on mandalas (Appendix A) and discuss what math is involved.
• Pattern terminology: terms, pattern rule, term number, growing/shrinking/repetitive patterns.
• Why are mandalas a growing pattern?
• Provide an example of a growing pattern (e.g., 2, 4, 6, 8, 10).
• Types of symmetry: reflection, radial, translational, and transflection.
• What kind of symmetry do mandalas have?
• Optional: congruency and transformational geometry.
• Show the completed sample mandala (Appendix B) and explain to students that they will make their own.
• Have students decide on their growing pattern rule and record the algebraic expression on the pattern worksheet (Appendix C).
• Invite students to roll the dice to determine the first term and apply the pattern rule to find the other terms.
• Provide students with circle cut-outs (Appendix D). Tell them that each quadrant will contain the number of shapes as described by the term (e.g., if the first term is 3 and the shape chosen was circles, the innermost pattern of the mandala is 12 circles, or 3 per quadrant).
• Demonstrate making the mandala using the incomplete mandala (Appendix B).
• Allow students to work individually to create their mandala, helping if necessary.

## Look Fors

• Do students understand the concept of a growing pattern?
• Can students identify different kinds of symmetry in the mandala?
• Are students using the grid to assist them in creating the mandala?

## Extension

• Students can solidify their understanding of radial symmetry by creating mandalas using the symmetry tool on Autodesk Sketchbook (available free here for Windows/Mac computers and mobile devices).