Make-Over Monday ~ Postage

Dan Meyer's Make-Over Monday task for this week is about an example of a piecewise function.  It relates to the cost of postage since 1995.  The original problem gives the students a table, labeled with years and cost in $ (presumably per ounce) to ship a letter to a domestic destination.  (I tried pasting the picture into the blog, but the scale was all wrong...so here's a link instead)

http://blog.mrmeyer.com/wp-content/uploads/130715_4hi.jpg

I submitted a suggestion on twitter on how to improve this question.  First off by posing the question, without taking the fun of finding out the information from the students. I know that doing this would help avoid a pitfall my students seem to always fall into, how to deal with the independent variable. (should you look at 1995, 1999, 2001, 2002, etc OR should you consider years since 1995?)

Secondly, I suggested that the students could also look at how costs for postage have changed in other countries (Canada, the European Union, or its member-states).  Lastly, I suggested that the students could also look at how shipping costs using UPS and FedEx have changed in that same time-frame.

I think this question has another good extension which could be done.  Looking at how the postage costs have changed (since 1995) could be compared to either the inflation rate (another piecewise function) OR the costs of various different products (during that same timeframe).  The natural extension for each of these explorations would be to predict when the next price increase would occur, or how much that next increase would be.  

Of course, the best case scenario would be if you could introduce the original problem (but not how the original problem was given) to the students and if they were able to come up with the extension activities out of their own curiosity on their own.