Teaching Math: Translations, Rotations and Reflections

Students in elementary and middle school generally enjoy geometry-it's a little different from other aspects of math. As part of the geometry unit, the boys and girls learn about transformations. A transformation occurs when we slide, flip, or turn a figure. In math these are known as translations, reflections and rotations, respectively. Begin by teaching the necessary terminology and then quickly move to hands-on activities in order to increase interest and understanding.

Introduce students to vocabulary.
It's important to use visual aids as you teach these terms:

Translation (slide): Every point in the figure slides the same distance in the same direction. It's like taking a step or steps forward, backward or sideways.

Rotation (turn): Rotating a figure means turning it around a point. The point can be on the figure or some other point. Go over the terms clockwise and counterclockwise. Don't assume that middle-school students understand the terms. Discuss turns of different degrees, such as 90 and 180 degree turns.

Reflection (flip): This is a reverse image. Think of what you see when you look in a mirror. Reflections are flips over a line. The points on the reflection image are the same distance from the line as the original image points.

Transformation Image: This is what we call the second image, after it has been transformed. If triangle XYZ is flipped over a line, the transformation image is named X'Y'Z', read as "X prime, Y prime, Z prime."

Provide transformed figures for students to identify.

First place this sheet of shapes on the overhead. As a class, decide whether each transformation is a translation, rotation or reflection. Discuss why the decisions are correct. Next, distribute this second worksheet of shapes to each student. Allow them to work in partners to identify the various shapes as slides, flips or turns.

Ask students to draw translations, rotations and reflections.

Copy these three shapes onto cardstock. Distribute them to the students. They will also need blank paper. Instruct them to cut out and trace each shape onto the blank paper. Next to each image, draw its translation, reflection and 90-degree clockwise rotation. For more practice and to move closer to the abstract, ask students to draw the required shapes in this transformation worksheet.

Review the concepts by showing how transformations are used in real life.

Students invariably ask the question, "When are we ever going to have to use this?" Show them this You Tube video of how transformations are used in computer animations. It is a great culmination to the lesson. Students will enjoy seeing life-like dinosaurs and dragons being created through translations, reflections and rotations. The video lasts about 6 and ½ minutes.

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