This Math Talk focuses on describing rigid motions without a grid. It encourages students to think about the labeled points and to rely on the structure of the figures to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students will need to be able to put together rigid transformations that take one polygon to another without making reference to a grid.

In describing the transformations, students need to be precise in their word choice and use of language (MP6). 

To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”

• “Did anyone use the same strategy but would explain it differently?”

• “Did anyone solve the problem in a different way?”

• “Does anyone want to add on to ’s strategy?”

• “Do you agree or disagree? Why?”

• “What connections to previous problems do you see?”

If no student brings it up, ask students how a rotation may be used to take to .

Math Community

After the Warm-up, display the revisions to the class Math Community Chart that were made from student suggestions in an earlier exercise. Tell students that over the next few exercises, this chart will help the class decide on community norms—how they as a class hope to work and interact together over the year. To get ready for making those decisions, students are invited at the end of today’s lesson to share which “Doing Math” action on the chart is most important to them personally.

The purpose of this activity is to activate students’ prior knowledge about rigid and nonrigid transformations. This is the first Card Sort activity of the course. An important aspect of this routine is to allow students time at the start to sort the cards into categories of their choosing. This step gives students the opportunity to familiarize themselves with the content of the cards without the additional pressure of organizing them in a specific fashion. It also provides insight into the aspects of each card students attend to and the language they have to describe their observations.

Students also begin to practice the skill of defining a rigid transformation that takes one figure onto the other without using a grid to estimate or define centers, angles, lines of reflection, or directed line segments. If students struggle to define rigid motions precisely, they may benefit from doing the optional lesson on point-by-point transformations.

Students may struggle to describe the location of the line of reflection. There is no need to address this during this activity as it will be covered in a subsequent activity.

Monitor for students who first translate to line up one pair of corresponding vertices and then rotate for the card with triangle .

In this activity, students determine whether a reflection can take one figure to another and how to find the precise line of reflection for disjoint figures.

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