Using Ms. Pacman to Introduce Transformations


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. 

Teaching Math Through Projects


As I reflected upon this post, I thought, well this is project based learning.  Now I do not proclaim to know much about project based learning.  My understanding is students work to complete an ultimate project that connects to the betterment of their community all the while learning components of concepts which are in turned applied to completing the project.

What I have observed within an 8th grade classroom over the past two weeks slightly mirrors this.  The teacher introduced The Bunny Project by conducting a mini-lesson on plotting points on a coordinate grid.  Once the mini-lesson was complete, students were able to begin working on the project.  The first part of the project calls for students to plot points in order to create the image of a rabbit.  With each component of the project, the teacher strategically scheduled mini-lessons to discuss the concepts students would need to apply within the project.


In her 15-20 minutes mini-lesson (of a 70 minute class) the teacher implemented short activities requiring students to derive the rules for translation, reflection, dilation and rotation.  Most activities were adapted from those within the Navigating Through Geometry 6-8 book.  Immediately following the mini-lesson, students were able to work on their projects.

Here’s an example of the teacher’s weekly lesson plan.  Monday, she conducted a mini-lesson on translation and students worked on part 2 sliding or translating the rabbit along the coordinate plane. Tuesday, the mini-lesson covered reflection allowing students, who were ready, to move on to part 3 of the project and those who needed to finish up parts 1 and/or 2 had the freedom to do so.

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On Friday, they summed up the four transformations with a dance: Dance video

Students were engaged, received immediate feedback and had an opportunity to immediately apply concepts taught.  IMG_4640

Which made be ask, what if we taught all math concepts like this?  I know there would need to be opportunities for additional practice built in.  Wouldn’t this cut down on the number of Kunta software worksheets or even numbered problems assigned out of the textbook?  Wouldn’t this require conceptual teaching in order for students to apply it within the project?

Or is it just me?