1. Verify experimentally the properties of rotations, reflections, and translations.
Have you ever seen a baby looking at herself in a mirror? For starters, she has no idea that the little person staring at her is her! This other person thinks almost exactly the same way she does—she raises her hand, and so does the other kid! She jumps, and the other kid does, too.
Of course, what she doesn't realize is that when she raises her left hand, the reflection is raising her right hand. (Honest! If you don't believe us, try it yourself.)
Reflections are just one of the three main types of transformationsthat shapes (and babies) can undergo, and we're not talking about an extreme makeover. A transformation is a fancy term for a movement on the coordinate plane.
Even if your students aren't doing too well in Spanish, they can still translate, or shift, shapes to their hearts' content. A reflection can be thought of as "flipping" a shape across an axis of symmetry, while rotation is the same as turning a shape around a central point.
Students should be aware of these different transformations and understand how to perform them. In order to explore the different properties (ahem, congruence) of these different transformations, students can experiment with them on the coordinate plane. With these concepts, hands-on activities are the way to go.