If you aren’t familiar with Robert Kaplisnky’s Ms. Pacman, you may want to take a moment to read through the lesson.

Before we began our math discussions about transformations, I had students work in their table groups at their vertical whiteboards to describe Ms. Pacman’s movements in the initial video. All but one group used terms such as slow or “in different directions” or right angles. When I inquired about their descriptions by asking, “how would you describe her movements other than slow” or 90 degree angles (to which I contributed our previous discussions about angles), only a few could produce directional movements.

I was at a lost of how students would get from here to describing transformations which was the goal of the lesson. I was bailed out by this group’s description:

As they looked around at other groups descriptions, they erased what they had and wrote slow and in different directions. I quickly asked them to rerecord their original thinking and proceeded to ask about Ms. Pacman’s movement on each pathway drawn. To which they responded up, down, left or right.

I called the rest of the class’ attention to this group’s thinking. Other groups imitated the pathway requesting to see the video again to ensure they were accurately drawing the path. This group described her horizontal movement as east and west and her vertical movement as north and south. After seeing the thinking of surrounding groups, they added more explanations to their board (pictured above).

This group identified the right angles as places Ms. Pacman turned.

We came back together as a whole group to discuss our layers of thinking.

Layer 1: Identifying the movement. During a running of the video, a student (without my prompting) came to the board and traced the path used by Ms. Pacman. I called on the group who I first identified to label her movements by sliding right, left, up and down. We labeled the path with the initials of the direction she moved. I asked the group who used cardinal directions to share their thinking of the path. I asked the class if we could say right or east, left or west, up or north, down or south. They agreed so I labeled the path using the initials of the cardinal directions. We used this video to determine if we correctly identified her slides.

Layer 2: identifying turns. I asked group 1 why they circled all of the right angles on their path. They explained the right angles are the places where she changed position. One of the group members asked if that was called a rotation, as she had learned about transformation in her Connections class. Someone else blurted out she was turning. We replayed the original video and students shouted turn each time she rounded a right angle. One student asked if she flipped instead of turned.

Enter layer 3: We briefly discussed what it would look like if she had flipped instead of turned. One student offered the synonym mirrored. We replayed the video and concluded she flipped or mirrored once at the very beginning.

Layer 4: Summarizing. We summarized our lesson by putting our conclusions on an anchor chart.

We discussed the moves or transformations made in order. I began by using the language the students stated in their explanations. Then I attached the formalize math language to each. For example, in recording the example of reflection, I drew a representation of Ms. Pacman flipped or mirrored and stated, “this is what we call a reflection”. Although dilation was not a part of this lessons, we extended our discussions by briefly connecting Pixels, an Adam Sandler movie where Pacman is enlarged or dilated. This anchor chart was hung in the room as a reference for math language and understanding of the four transformations based on this context.