The purpose of this activity is for students to give precise descriptions of translations, rotations, and reflections. In previous lessons, students have identified and sketched transformations from written directions, however they have not used this more precise language to give descriptions of the three transformations. The images in this activity are given on grids to encourage students to describe the transformation in terms of specific points, lines or angles (MP6).

As students describe their transformations and sketch their images, monitor for students using precise descriptions with their partner in terms of specific points, lines, or angles. 

Students may get stuck thinking they need to use the precise terms for the transformation in their description. Encourage these students to describe it in a way that makes sense to them and to look for things they know about the specific points, lines, or angles on their card to help them.

Display the following questions for all to see and give groups 2 minutes to discuss:

• What pieces of your partner’s description were helpful when you were sketching?
• What pieces did you find difficult to explain to your partner? Point to specific examples on your cards.
• When you were sketching, what questions would have been helpful to be able to ask the describer?

Ask selected students who were observed using precise descriptions and sketching based on those descriptions to explain why they used the information they did and how it was helpful in sketching. Focus on:

• The direction and distance of a translation
• The center and the measure of a rotation
• The line of a reflection

If time allows, ask students who were both using and not using tracing paper to explain their process.

Reinforce the term "transformation" as a term that encompasses translations, rotations, and reflections. Tell them that there are other types of transformations, but for now, we will focus on these three types.

This activity introduces the term sequence of transformations and gives students an opportunity to describe a sequence of more than one transformation using precise language.

Each time a reflection is mentioned, ask students where the line of reflection is located and when a rotation is mentioned, ask for the center of the rotation and the number of degrees. Monitor for students who apply these different transformations:

• Reflect Figure B over line to Figure C
• Rotate Figure B about point to Figure  C
• Choose a sequence of transformations from Figure A to B to C
• Choose a sequence of transformations using a different order or not going through Figure B.

The key connection is that different transformations or sequences of transformations may result in the same image. There may be more than one way to describe or perform a transformation.

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 prompt is “What is the same and what is different?”, comparing 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.