Our school district started a new alternative school this year. I went to the alternative school during our professional days. In retrospect, my visit was serendipitous to say the least.

I walked into an English teacher's classroom. After pausing momentarily, she asked, "Where are you going?" As I stepped out of the room, I replied, "I left my phone in the car. I need to get my camera." I returned and took a photograph of the classroom layout.*Exhibit A: English classroom. Note the students in the back left corner of the background. These two students will bump into each other as they pull their chairs away from the table.*

The English teacher asked me, "Is there a mathematical way I could figure out the best way to arrange my tables?" I asked her how many students does the arrangement need to seat. She said 19 students. I posed the problem to my MTPS students with only the photograph as a reference. Students began modeling the problem in several ways: drawing on graph paper, cutting out paper trapezoids and taping them to notebook paper, applying masking tape on the floor of the classroom to represent the tables, even using manipulatives.

*Exhibit B: A physical model of a possible table configuration, affectionately referred to as "Taylor's Diagram"*

Before going to the lab to model with Geogebra, I did receive some clarification on the table and classroom dimensions. I included them in a follow-up file for students.

*Exhibit C: The table photograph with dimensions listed.*

The English teacher also added there is a tenth table available should we need to use it. I will publish some of the students' modeling work later. For now, I am interested in potential solutions readers will pose.

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