In this activity, students rotate images on both a rectangular grid and an isometric grid to practice rotating by a variety of angles. They will practice considering all the aspects of a rotation: center, angle, and direction of rotation.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

The purpose of this discussion is to solidify the aspects of a rotation.

“What information do you need to do a rotation?” (Center, angle, and direction of rotation.)

“Why don't you need to know the direction of rotation when the angle of rotation is 180 degrees?” (Both the clockwise and counterclockwise rotation land in the same place since 180 degrees is half a circle.)

Students practice drawing transformations by following a character's instructions. This is the first time students see the point-by-point transformations that they will use in a subsequent unit to prove that triangles are congruent. 

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

The purpose of this discussion is to emphasize that figures are congruent if there is a rigid transformation that takes one to the other. Here are some questions for discussion:

• “What is the definition of congruent?” (There is a rigid transformation that takes one figure to the other.)
• “We have a transformation that takes triangle to triangle . What does that tell us?” (Our sequence includes a translation, a reflection, and a rotation. Each of those is a rigid motion, so the measurements of triangle must match the measurements of triangle . They're the same, just in different locations.)

If students are struggling to identify the angle of rotation, ask students to find and trace the angle by connecting a point, its image, and the center of rotation. Then provide two options. They can use a protractor to measure an angle, or they can use the properties of the grid to calculate the measure of an angle.