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The Game of 21

March 2, 2008

Inspired by Dave’s recent post at MathNotations, I recently introduced the game of “21” to my intermediate group (approx. 3rd – 5th grade levels). (See the post linked above for rules.) I introduced it in the 2nd half of a class before our February break. I told them to come challenge me when they thought they could beat me. (I went ahead and told the kids that once they figured out all the tricks to the game, whoever went first could guarantee a win, and so when I played against them, I offered to let them go first. ) Usually, after beating their partner a few times in a row, they would conclude that they could beat me, but they couldn’t. 😉 Most of them had started recognizing a few winning (or losing) positions near the end of the game, but only a couple were making methodical notes. By the end of that period, no one had really “solved” the game, though a few (particularly those making notes) were getting there.

We played again Friday. One by one, they started solving it. By the end of the period, about half of them could win consistently if they went first. The others are on their way.

The nice thing about this game is that when someone “solves it” you can just change the game on them, and keep them busy. I sent one pair off with the rule “whoever says 21 wins” and another pair wanted to play to “23” instead. Neither of them made an immediate leap to how to change their strategy for those new conditions. But when they get good at that, we can change the number of numbers they are allowed to play in a turn, etc.

Incidentally, I also taught the game to a pair of 9- and 11-year-old brothers who were driving their mother crazy in the waiting room at Honda’s service department. The 11-year-old was catching on faster than his brother, but still didn’t have the whole thing figured out, so I offered the younger brother that I would beat the older brother on his behalf. 😉 In any case it kept them busy until their car was ready.

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12 Comments leave one →
  1. March 2, 2008 1:37 pm

    Your last few posts have made me so SAD that I didn’t have someone like you to teach me math! You make it all so fun and interesting!

  2. March 2, 2008 1:44 pm

    Thanks, YogaMum! I do try to make it fun and interesting, though sometimes it does devolve into “frustrating” when I overestimate the kids too much (mainly the middle schoolers). This is my 6th year doing this, and I am getting better. 😉 Still, I often get to teach the little ones with a “real” (i.e. trained) teacher as backup, and I always learn a lot from her.

  3. MathDad permalink
    March 5, 2008 10:50 am

    That sounds like fun and will try with my kids. I picked up a couple games at a home school conference by a company called Cutting Edge Education. Real simple dice games but the dice are interesting/fun and they keep my two children engaged.

  4. August 21, 2014 3:52 am

    Howdy! I could have sworn I’ve been to this website before but
    after reading through some of the post I realized it’s
    new to me. Anyways, I’m definitely delighted I found it and
    I’ll be bookmarking and checking back frequently!

  5. September 4, 2014 8:05 pm

    free! free! free! the game is boring and the math formula and ugly numbers are complex. never play the game of 21.(math) But play basketball’s game of 21.=(

  6. September 4, 2014 8:07 pm

    blah blah =( game play game of 21 hoops baby

  7. September 4, 2014 8:08 pm

    Giau Pham is a lover of this game

  8. September 4, 2014 8:09 pm

    he craxx the egg

  9. September 4, 2014 8:10 pm

    My name is Zulu?

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