Reflections on the Fire Hydrant

It is hard to know where to start after my “sabbatical” from blogging. I have been absolutely overwhelmed with writing this CCSS geometry course. I barely have the lessons written in time for class, and so I have not had time to process the lessons out loud, although I have been mulling over them in my head.

I am just getting home from the Texas Instruments T^3 International Conference in Philadelphia where I had to take the time to reflect on what I have been doing this school year. Since this week is Spring Break, I am determined to write a few thoughts that I have been mulling over for a while.

Early in the course we asked students to determine the location for a fire hydrant that was equidistant from three buildings (vertices of a triangle). As I was preparing some stories to tell for my sessions at the conference, it occurred to me how much technology added to this problem.

The students started with pencil and paper to determine the location for the fire hydrant. 

Some students folded their paper, others used a ruler, and others “eyed” where the point equidistant from the vertices was located. We talked together about answering a simpler problem (where would we locate a fire hydrant equidistant from two buildings?). Then we moved the problem to our dynamic geometry environment. Eventually, students found the location of the circumcenter, which is the point of concurrency of the perpendicular bisectors. But as we changed the location of the buildings by moving the vertices of the triangle, the students began to ask a different question. Is the circumcenter always the best location of a fire hydrant to service three buildings? And then we began to ask under what conditions the circumcenter would be the best location of a fire hydrant to service three buildings.

On the summative assessment for the unit, I asked students to extend their thinking to placing a fire hydrant to service four buildings. Does every quadrilateral have a circumcenter? What method could we use to determine whether a quadrilateral has a circumcenter? And where should we put the fire hydrant when a quadrilateral doesn’t have a fire hydrant? We have so much more to explore with this task. I look forward to revisiting some of these questions with my students as our journey continues ….

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