How to Teach Transformations for Math

In geometry, translation means moving without rotating, re-sizing or any other changes. Students may benefit from describing a translation as sliding a shape. To translate a shape, every point on the shape must move the same distance in the same direction.

Teach students about translations by showing them a shape on a graph, and drawing a translation, such as x+2, y+3. Have students trace the distance each point moved horizontally and vertically and ask if they noticed a pattern. Students should notice that all the points moved two spaces right and three spaces up.

Define reflection as a flip over a line. In reflections, the shape remains the same size, and every point on the transformation remains the same distance away from the center line – or line of reflection.

Describe the line of reflection as a mirror that portrays a replica of the original shape, just in the opposite direction. Also point out that the line of reflection can go in any direction.

Teach students about reflections by drawing a triangle on a graph, and drawing a line of reflection. Have students measure the distance of each point from the line of reflection, and replicate this distance going in the opposite direction to form the points for the reflected shape.

Explain that a rotation is turning a figure around a fixed point. For a rotation, you need to know the point that the figure is rotating around, the amount of degrees of the rotation, as well as the direction of the rotation. A positive number of degrees indicates a counterclockwise rotation.

Have students draw a figure in the first quadrant on graph paper then have students flip their paper 180 degrees and draw the same figure, as if the third quadrant were the first quadrant.

Ask students to name each coordinate on the pre-image and the transformed image to determine a pattern or rule for 180-degree rotations about the origin. Repeat this exercise with 90 degree, and 270-degree rotations about the origin.

Describe dilation as a change in a figure’s size. After a dilation, the figure will not be congruent to the pre-image, but it will still be similar. To determine the magnitude of the change in size, dilation transformations have a scale factor. For example, a scale factor of two would double the size of a figure, whereas if the scale factor was less than one, the transformation will reduce in size.

Practice dilations with a scale factor of two with students by drawing an object, then measuring each side length. Have students double each length to create the dilated image.