Transformations Lab

by Sue Plisch and Craig Russell, University of Illinois Laboratory High School

Purpose:  Students practice using reflections, glide reflections, and translations, and preview rotations.

NCTM Standards:

·        Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.

·        Use various representations to help understand the effects of simple transformations and their compositions.

File:  http://www.uni.uiuc.edu/~hcrussel/TransformationsLab.gsp

The first tab in the Geometer's Sketchpad file challenges students to use reflections to make a path from the tee to a hole on a mini-golf course (three bounces required).

The second tab refers students to a java applet to explore the effects of two successive reflections.

The third tab investigates translation vectors tied to coordinate systems and independent of coordinate systems.

The fourth tab prompts students to discover that any glide and reflection may be written as a glide reflection with the glide parallel to a line of reflection.

The final tab encourages students to discover a center of rotation based only on the locations of the pre-image and image.