This activity informally introduces reflections, which appear in addition to some translations and rotations. Students are given a 6-frame cartoon showing the change in position of a polygon. As in the previous lesson, they describe the moves, but this time there are reflections. Students identify the new moves and try to describe them. Since the focus of this activity is informal descriptions, it is not necessary to introduce the formal terms at this time.

Students may see a reflection as a translation especially since the figures are not on the same frame. Ask these students to trace Frame 2 on tracing paper. Is there any way to turn it into Frame 3 by sliding it? What do they have to do to turn it into Frame 3? (They have to flip the tracing paper over, so this is a new kind of move.) 

In describing reflections, students may confuse the terms horizontal and vertical. Consider posting the terms horizontal and vertical with examples in the room.

Before students share their thinking:
Direct students' attention to the reference created using Collect and Display. Ask students to share their descriptions of the new move. Invite students to borrow language from the display as needed and update the reference to include additional phrases as they respond.

The purpose of this discussion is an initial understanding that there is a third type of move that is fundamentally different from the moves previously encountered, because it flips over. Some possible discussion questions are:

• “How is the motion from Frame 2 to Frame 3 different from sliding or turning the shape?” (When the shape is flipped, you can't put it back without flipping it again.)
• “Is there anywhere else that happens in this set of dance moves?” (It happens twice, from 2 to 3 and from 5 to 6.)
• “What features of the image help us to see that this move is happening?” (If you put them across from each other, they look like mirror images. If you look at the sharp point on the shape, they are pointing in opposite directions.)

Display this image with the vertical dotted line.

Ask students, “What do you think this line represents for the move from 2 to 3?” (It is where the mirror is; it is the line that the shape flips over; it is a line of symmetry.)

Use a transparency or tracing paper to demonstrate flipping or mirroring the figure, then ask students how this is different from rotating the figure . Demonstrate the rotation so students can visualize the difference.
If time allows, show Frame 5 and ask students where the mirror line or line of symmetry is to go to Frame 6. (It is a horizontal line below the figure.)

In this partner activity, students take turns identifying translations, rotations, and reflections. There are 3 translations, 3 rotations, and 3 reflections. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

As students work, monitor for groups who have sorted the cards into translations, rotations, and reflections (though not necessarily using those words). Also monitor for descriptions of corresponding points, such as “these points go together” or “here are before and after points.”

Students may struggle to differentiate between the three moves, confusing reflections with either translations or rotations. After they make their best decision, encourage these students to use tracing paper to justify their response. In Card 10, students may be confused when the translated figure overlaps the original. For Card 4, students may first think that this is a rotation (much like Cards 6 and 9). Encourage these students here to use tracing paper to check their answers.