The Welding of Metal Tech and Math

An early morning text from my brother prompted this tweet:

We estimated a little, but the Slinky didn’t yield much discussion until someone shared: I wonder how much wire is in one of those Mig welder spools!

If you are like me and have no idea what a mig welder is, here’s a photo:mig_welder

These things hold massive spools of 1 mm thick wire.


Luckily, the welding instructor was willing to part with one of these for the hour.  Unluckily, the only information we had was the  1 mm thickness of the wire and the spool’s weight of 44 pounds.

Our initial thought was to weigh a snippet of wire and then scale it to the entire spool, but I was sure that the welding teacher wouldn’t have appreciated the rogue math teacher messing with his supplies.   I praised them for the interesting method anyway.  They then began measuring:  height, diameter of the spool, diameter of the inner circle, diameter of the wired portion, number of wires going up the spool.  It was math-magical.

Here are their calculations:


Now, I realize that these are a little off because we needed to take into account that the circumference of the spool is getting smaller as we move inward.  But I was very pleased with their work thus far and their vigor in posing this problem and then working to solve it.  I’m excited about where we can go with this type of problem posing.  There are only eight students in this class, all boys that have metal in their bloodstream.  I am hoping that with these sorts of ideas, I can engage them in math that excites them more often.  Maybe I can even get them excited about my Slinky question.

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