Click here to see the original "Mailbox Placement" post. You will want to see the details before reading below.
My students have spent some time trying to model the mailbox problem. Let's examine the similarities and differences across the various models students built with Geogebra.
A photo collage of students in action. I used Fotor to make this.
Similar actions among students
- Tying the source image to three points to preserve scale
- Using vertices to represent mailboxes
- Using edges, segments, and curves to represent driving routes
- Using arrow heads on segments to indicate directed paths
- Using color to mark different paths and different directions
- Breaking the entire graph into smaller sub-graphs in an effort to solve the smaller sub-graphs
Different actions among students
- Measuring distances on the graph and applying scale factors to determine true driving distance (this information will help the student find an optimal path with respect to distance)
Using check boxes to give the user the ability to remove layers of the graph (for example, the background photo) to help the user keep information organized
-Offering the user the ability to hide the mailboxes (I thought this was a great feature because it allows the user to focus on the neighborhood layout without the clutter)
- Solving smaller sub-graphs and then taking the union of these solutions to solve the larger problem
- Seeking alternative maps that offer more or fewer details
The administrator came to class Thursday to monitor work for a short time and offer additional background information to assist students with modeling. Our class has learned the actual mail route may have been assigned arbitrarily - that is, without the aid of software. The administrator is working to determine the mail route the delivery person takes. If we are able to acquire this information, we could work to find a path which contains the administrator's preferred mailbox placement that also shortens the total driving distance - a win for everyone.
Our class will spend two 90 minute class periods this week finishing up modeling work and coming to a class consensus on the optimal path. I will post the findings as they become available.