This activity is designed to remind students how to describe transformations. They may begin with informal language, such as “flip” instead of “reflection” or “shift” instead of “translation.” Since students will have opportunities to review formal language later in the lesson, there is no need to spend extra time on it during this activity.

The purpose of this discussion is to determine what students remember about transformations. Tell students that the proofs in upcoming lessons require some transformations, so it’s important that we review this topic now.

Ask students, “What do you know about the labels A and A'?” (Figure A' is the image after Figure A is transformed. Figure A is called the “preimage.”)

Then ask students, “What information do we need to clearly describe the following rigid transformations?”

• Translation (distance and direction)
• Reflection (line of reflection)
• Rotation (center and angle)

The goal of this task is for students to review what transformations look like and use transformation language. In this partner activity, students take turns matching the description of a transformation with an image. As students trade roles sharing their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

The purpose of this activity is for students to practice drawing transformed shapes in preparation for the next lesson, where they use transformations to prove theorems about angles formed by parallel lines and a transversal. Now that students have practiced properly describing transformations, they will perform transformations. Making geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

Monitor for students who use the following tools:

• Tracing paper
• Tools such as a compass and straightedge
• Geometry software

Each of these tools allows students to accurately draw the transformation, but each requires precision in a different step of the process. Tracing paper requires students to perform the transformation on their traced shape precisely. A compass and a straightedge can be used to measure the transformation and apply it to each vertex of a figure. In both of these methods, the final image is easier to draw. Geometry software will perform the transformation for the student, but precision is required when students input the preimage.

This is the first time Math Language Routine 7: Compare and Connect is suggested in this course. In this routine, students are given a problem that can be approached using multiple strategies or representations, and they record their method for all to see. They then compare and identify correspondences across strategies by means of a teacher-led gallery walk with commentary or teacher think-aloud (such as “I notice . I wonder ”). A typical discussion question is “What is the same and what is different?” prompting students to compare their own strategy to the others. The purpose of this routine is to allow students to make sense of mathematical strategies and, through constructive conversations, develop awareness of the language used as they compare, contrast, and connect other ways of thinking to their own.