Mailbox Placement

An administrator told me about a problem from the world outside school he faced while building his home last year. He had gone to the post office to confirm the location in which he wished to place his mailbox was acceptable to the U. S. Postal Service mailbox guidelines. The administrator poured the footing and ordered the stone for the mailbox. A few days later, the mail delivery person informed the administrator the mailbox placement was incorrect. As a result of a miscommunication, the Post Office instructed the administrator to move his mailbox, causing the administrator to lose his considerable fiscal investment in the mailbox. The issue has to do with the route the mail delivery person drives each day. Below is a map of the neighborhood in question.

Mailbox_Problem_Map_Mr_S_Adj

Exhibit A: The neighborhood. Mailboxes appear as an "X." The house in question is drawn in red. Street names have been suppressed to protect the innocent. Red ovals indicate either a cul-de-sac or a potential entrance from a main road into the neighborhood.

Some background information: mail delivery personnel prefer not to get out of their vehicle. Many mail delivery vehicles have the driver's side door on the right hand side, so a person could infer the mail delivery route using the condition the mailbox must be on the right hand side of the delivery vehicle.

The administrator came to our classroom Thursday. He served as a guest speaker for twenty minutes, drawing the annotations on the Google Maps image. It reminded me of a press conference format; the students asked questions about relevant and irrelevant information in an effort to fully understand the problem.

This problem is the perfect follow-up to the "Chomp the Graph" activity on graph theory. Students can investigate routes using directed paths. Students can compute distances by coordinatizing the image and applying the scale which appears in the lower left. What the students really want to know is whether it is possible to optimize the mail route in a way that benefits the administrator. My students will work on this problem next week in the computer lab. I am eager to see where the investigation takes us.

6 thoughts on “Mailbox Placement

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  2. Looks like a great interaction and I especially like the part where students are asking questions, both relevant and irrelevant, to get a feel for the problem: that aspect of thinking and problem-solving is often sorely lacking in our textbooks.

    Perhaps an extension of this problem could be for students to take this back to their own neighborhood and answer the same problem: using Google maps at first, but perhaps actually testing out the routes by foot, car, or bikes. That way you could have the whole class present their findings and they wouldn't be presenting the same thing over and over since they live in different neighborhoods.

    Love the activity and if I ever include graph theory into Precalculus, I'll remember this activity as one to definitely include!

  3. Sounds like a great lesson, I'm also curious to see where the students investigation will go. I always liked how Graph Theory for how simple the problems can be stated and understood but how complex and deep the solutions can be.

    1. aaberg

      Post author

      I will post a sequel, George, to let everyone know how the investigation unfolds. I took a look at your new blog (mathodical.org). I would love to see some student work from the lesson plan you posted in response to MTBoS Task #1.

  4. Leslie Billings

    I like the speaker/interview concept. Students act differently when their teacher asks for questions versus when a speaker asks for questions. The authenticity of this task is what makes it so nice. Will the students report their findings to the administrator?

    1. aaberg

      Post author

      Leslie, thanks for the comment. It was an interesting dynamic in the room. The administrator had just as many questions for the students as they had for him. This particular person has great relationships with the majority of students. The kids do not want to let the administrator down, making both parties emotionally invested in the outcome of the problem.

      Our class plans to share findings with the administrator. I think the administrator desires closures on the issue. I would think the USPS uses some type of analytic software package to determine routes and mailbox placement; however, there is always the chance an error was made.

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