graphs, digraphs, vertex, edges, weighted graph, critical path, earliest start time, task table
This opportunity of expansion into other fields can lead to some difficulty. As far as this activity goes, it appears that unless the task is narrowed down substantially, there are too many areas for discussion which are tangential to the final goal of project scheduling. Unless a list of tasks, their specific times and prerequisites are given to the students at the beginning of the activity, there is too much opportunity for discussion about how a construction project can be accomplished. Topics such as whether different underground lines can be run simultaneously (water, sewer, cable, etc.) or how to actually route the cables can derail the discussion, and shift the focus away from actually scheduling the tasks. Although this may be desirable if an open-ended discussion is acceptable, it makes the time required for the activity increase drastically.
The tangents that come up because this is a real-world situation, while possibly being too overwhelming for a short activity, make this problem that much more attractive to a student. Since there is a clear connection to a easily understandable problem, the students may find it something interesting to explore.
Note that this basic idea of designing a city has been implemented in varying degrees as a large framework for many topics. See the article "Design Your Own City: A Discrete Mathematics Project for High School Students", by Carol A Bouma, in the 1991 NCTM yearbook.
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Kenney, M. J., & Hirsch, C. R. (Eds.). (1991). Discrete Mathematics Across the Curriculum, K-12. Reston. VA: National Council of Teachers of Mathematics.
Tucker, A., (1984). Applied Combinatorics. New York: John Wiley & Sons.
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Dossey, J., Otto, A., Spence, E., & Vanden Eynden, C. (1993). Discrete Mathematics. Harper Collins College.
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