In Hubcaps, Kaleidoscopes and Mirrors students investigate symmetries and transformations. This unit will help them to:
- Understand important properties of symmetry
- Recognize and describe symmetries of figures
- Use tools to examine symmetries and transformations
- Create figures with specified symmetries
- Identify basic design elements that can be used to replicate a given design
- Perform symmetry transformations of figures, including reflections, translations, and rotations
- Examine and describe the symmetries of a design created from a figure and its image(s) under a symmetry transformation
- Give precise mathematical directions for performing reflections, rotations, and translations
- Draw conclusions about a figure, such as measures of sides and angles, lengths of diagonals, or intersection points of diagonals, 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 general point (x, y) under particular transformations
- Learn to appreciate the power of transformational geometry to describe motions, patterns, designs and properties of shapes in the real world
