Mandala

Junior (Age 9 – 12)

Curriculum Goal

Junior: 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: 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.
Mandala divided into quadrants

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).

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