Kaleidoscopes, Hubcaps, and Mirrors

Symmetry and Transformations

The explorations in Kaleidoscopes, Hubcaps, and Mirrors help students to refine their knowledge of symmetry and use it to make mathematical arguments. Students explore transformations (reflections, rotations, and translations) that preserve angle and side length relationships of figures in the plane.





Goals of the Unit
• Understand important properties of symmetry
• Recognize and describe symmetries of figures
• Use tools to examine symmetries and
transformations
• Make figures with specified symmetries
• Identify a basic design element that can be used
with a transformation to replicate a given design
• Perform symmetry transformations of figures,
including reflections, translations, and rotations
• Examine and describe the symmetries of a
design made from a figure and its image(s)
under a symmetry transformation
• Give precise mathematical directions for
performing reflections, rotations, and translations
in terms of the effect of the transformation on
points of the original figure
• Draw conclusions about a figure in terms of the
effect of the transformation on points of the
original figure based on what symmetry or
symmetries the figure has
• Understand that figures with the same shape
and size are congruent
• Use symmetry transformations to explore
whether two figures are congruent
• Give examples of minimum sets of measures of
angles and sides that will guarantee that two
triangles are congruent
• Use congruence of triangles to explore
congruence of two quadrilaterals
• Use symmetry and congruence to deduce
properties of figures
• Write coordinate rules for specifying the image
of a point under particular transformations
• Appreciate the power of transformational
geometry in the real world

Kaleidoscopes, Hubcaps, and Mirrors