## Fawn Nguyen and Bridges

This weekend Fawn Nguyen was speaking at a conference and posted the following problem that she was using as an icebreaker:

I use so much of Fawn’s stuff with my kids that we may as well move to California and have her teach them directly.  This problem seemed like one the boys would love, so we tried it out right away:

I definitely enjoyed the discussion and it was a nice surprise to see how this problem engaged my younger son  In fact, so much so that my older son actually complained after the video that he couldn’t get a word in.  Ha!

After we finished up the video yesterday we went out to join a little neighborhood dog walking group that meets every morning.  One of the people who joins that walk on the weekends is the principal of one of the local high schools.  He and I spend a lot of time talking about fun math activities for kids and I mentioned this problem to him.  He joked (in a good-natured way) that there wasn’t much real world connection to this problem.   Connecting math problems to the “real world” isn’t something that I spend a lot of time worrying about  – we do plenty of problems with real world connections and plenty that are more theoretical.  The reason that Fawn’s problem was attractive to me is the problem solving techniques required to solve it.  The unusual circumstances described in the problem do not bother me at all.

But . . . I couldn’t get the comment out of my head and it occurred to me that there are a few other neat math problems related to bridges that do have “real world” connections.   Two of those problems made for great discussion topics this morning.    The first is a short explanation of why bridges have expansion joints.  The answer to the math problem in the example is really surprising – almost no one guesses right when they see the problem for the first time:

This one turned out to be such a neat problem that my younger son joined in about half way through because he was so interested in what we were doing.

The next problem is the Königsberg Bridge puzzle which is a famous puzzle that was solved by Euler in the early 1700s.  Unfortunately I stated the problem slightly incorrectly – you just have to go over every bridge once, you don’t have to return to where you started.   Since I wasn’t planning on going into any theory here, I decided not to go back and correct the mistake.  The boys really liked playing around with this and spent 10 minutes after the video trying to solve a modified version of the problem (add two bridges – one to each land side – to the island that started with three bridges).  Definitely a fun example for kids:

Finally, I could do a post about bridges without mentioning the book that Mr. Waterman gave to me my sophomore year of high school that was my first introduction to abstract mathematics:

So, thanks to Fawn Nguyen for inspiring one more fun weekend of math!

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