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.
Whole-class discussion followed by individual activity at desks.
Circle cut-outs, divided into 4 quadrants (Appendix D)
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.
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?
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).