The Talking Stick Blog

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The Ants Go Marching

Math Circle 5.6.2014

(May 6, 2014)  Today I have a quickie report and lots of photos.

We started with Smuyllan’s Inspector Craig puzzle #72.  Today our variables A, B, and C represented Able, Beatrice, and Cable.  I asked the kids if they realized that these are different people from the A, B, and C last week.  “Of course,” came the reply.  Then the kids discussed it with each other (not me – woo hoo!) and solved it handily. Next week I’ll raise the thinking-requirement ante significantly on these puzzles, at least IMHO.

I then gave everyone 12 blocks and asked them to model “the ants go marching one by one.”  Boy did we have fun with this.  Everyone was singing, the kids were lining up blocks, we were laughing, the ants lined up 2 by 2, then 3 by 3, then 4 by 4,… uh oh.  Five didn’t work.  We couldn’t line them up in arrays of 5.  Easily solved.  Each student, independently, grabbed 3 more blocks.  (My instinct was to put 3 back – interesting how their solution different from mine but was totally valid.)

When the ants went marching 6 by 6, they grabbed more.  Then different strategies emerged:  N and F both destroyed their arrays each time and rebuilt from scratch;  A took a huge stash of spare blocks and added what he needed;  M noticed that each time the row size increased by one unit, she needed 3 more blocks because she had 3 rows.  All of them were engaging in the foundations of multiplying and factoring.  We got up to 10, often arguing about what the ants did for each formation.  By then, though, the kids all argued for “the ants go marching ten by ten, the little one stopped to say The End!”  To be continued next week.

We then tackled parts 1 and 2 of a logic puzzle that I first learned as “The Princess and the Tiger.”  (Now I see in my research for this report that this is another Smullyan puzzle!  It’s about a prisoner choosing which door to open, another matter of life or death.)  The kids collaborated again to solve them.

At this point we only had 5 minutes left.  I decided to present a problem that I expect they’ll think about for a long time to come, probably beyond the duration of this course.  One of my goals here with kids is to expose them to problems that cannot be handily solved in one session, one week, or even one month.  In other words, to foster perseverance, something much needed in real-world mathematics.  The problem is another from math folklore called the Wolf, the Goat, and the Cabbage.  Click here to see the problem – this site doesn’t give a spoiler:  Of course, you can google it to find the solution, but you’ll have more fun if you think about it yourself for a looooooooong time.  BTW, if you have older kids who’ve been in my math circles before, or if you’ve been following these reports over the years, you may (as J did) recognize this problem as isomorphic to the Dark Bridge (Unicorn) problem that a group of our kids struggled over for 6 weeks three years ago.  Both of these problems are of a genre called River Crossing Problems.

The kids here today spent time acting it out with puppets, and discovered the challenge of the problem, but not its traditional solution.

That’s all for now.  Thanks to Asha for coming and taking lots of great photos.  Click here or scroll down to see them.


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