The Broken Pipe

A teacher from another school across the state emailed me last week. She described a terrible facilities issue she has dealt with for days.

I don't have all the details and may not be able to get them... a pipe in my room burst on Monday and caused water damage in the hallway end and a total of 6 classrooms in full or in part... I have been told varying amounts as to how high the water was in my room and mere estimation by our custodial staff on how much water they themselves eliminated... the plumber said that the little copper pipe was spewing 12 gal per min...

We had been working on a different project during MTPS (Math Theory Problem Solving) class that I didn't want students working on without me being present... I had a sub coming in last Friday and decided this would be a great opportunity for students to do some modeling work in the computer lab.

Take a moment to consider how elaborate this situation is. Water accumulates within a room. Many places exist where the water could escape. Some places are obvious, like underneath the door. Other places are not as obvious, such as through electrical outlets or through the cracks in the drywall where the tile meets the wall. There are many potential sources for error. Modeling simple cases is easy, flow in is positive, flow out negative. But this is definitely a problem from the world outside school (I've never been a fan of the term 'real world'... that would imply high school isn't real... and I remember sitting through some interminable classes with a very real feeling of when will this class ever end...)

I worked to write a worksheet that would help students identify some of the potential complications in modeling how water would accumulate in various rooms. I thought about using theoretical "bathtubs" to simplify the computations and help the kids understand some of the complexities they would encounter in modeling a real room.

The students have spent one 46 minute period and one 90 minute period in the computer lab working on modeling the situation. The source worksheet appears below.

The Broken Pipe Problem-1

Students will have another 90 minute period in the computer lab Wednesday, then 30 minutes on Friday before each student gives a 3 minute presentation on Friday about their lab work and findings. I will share some of the students' work on this dilemma later.

P. S. On the worksheet, I use Google images to retrieve pictures of each of the bathtubs. The copy did not turn out as nicely as I had hoped, so I traced over the images and scanned the resulting worksheet. I told the students the half-cylinder tub should be oriented in a way where the curved side is tangent to the floor. (The 3D image on the worksheet makes it look like the tub is tilted, but I did not intend for the half cylinder tub to be tilted). The values for the time in minutes were arbitrary. All of my students have chosen to set up tables of values in Excel so they can address some of the interesting questions (like how many minutes will it take to fill the rectangular prism bathtub?)

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