There is an interesting little puzzle called the Monty Hall problem that is a great way to introduce statistics for kids. There are different ways to present the problem (one requires goats), but for our kids, we used three cups and M&Ms. The kids (and Lily’s doll) took turns hiding one M&M under one of the three cups. We asked Mama to pick one of the cups. Before lifting the cup, we pick up one of the other cups and reveal that it does not have an M&M underneath. Is it to Mama’s advantage to switch her original choice?
MaryAnne’s intuition (as well as most people’s intuition) is that it doesn’t matter—that there is just a 50% chance of being right or wrong—so we decided to play a game to test her hypothesis. If MaryAnne’s original guess is right, she gets to keep the M&M; otherwise the kids get to keep whatever is under the other cup. To keep track of our data, we collected the M&Ms on a piece of paper with an area for “Mama” and an area for “Kids”. The kids loved getting high-fives and adding the M&Ms to their pile as the experiment progressed, but it was a little difficult to keep the kids from eating our data.
Much to Mama’s disbelief (and to the kids’ great excitement) the kids got a little over twice as many M&Ms!
I didn’t go over the mathematical proof that you are expected to do twice as well if you switch, but it did get the kids excited about counting!
By the way, interested readers can play a version of the game with goats here.
MaryAnne lives is a craft loving educator, musician, photographer, and writer who lives in Silicon Valley with her husband Mike and their four children.
This is crazy!!!! Whoa!
Love the M&Ms! Definitely a math motivator… goats, not so much. I had a goat as a kid. They are a headache :) Thanks for sharing this one. My son loves games and he is getting to be a good little counter!
What a fantastic way to get kids into counting!
M & M’s make anything fun and worth learning about:-). Both you and Mike are so smart and are raising some super intelligent children! I am always impressed with what you teach them and the ways you go about it.
I hope you left some the bag for you to eat later. What fun!
We did this in our statistics class in college, I’ve done the proof, but I STILL don’t “Believe” it! Clearly I need to do the M&M experiment to get my hind-brain to buy in.
I”ve seen that before, but never quite understood exactly how the math worked.
I just checked out the goat version. It’s not nearly as fun as the M&M version!
@Catherine: Yeah, it drives nearly everyone crazy. Apparently, when the problem appeared in a magazine a while back, approximately 10,000 readers (including those with PhDs), wrote in claiming the switch strategy was wrong. It was reassuring to have the M&Ms validate the mathematics since it is so counterintuitive. :-)
This drives me crazy even after reading the proof.
@Catherine – I’m with you!
Sounds interesting.
What a great hands-on game! I bet all of you will remember what you learned (to switch!).
I love seeing the kids’ posters on the wall behind them as well! :)
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What a fun game! Especially since M&M’s are involved! :)
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OK, I am tempted to read through the proof when I have more than 3 minutes of available time. I would agree with Emma that the choice of cups shouldn’t matter.
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I was just going to say that it would have been a lot more fun with the goats! ;-)
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That is so cool! I’m going to go up the street to a local farm and see if I can round up some goats! Or, maybe we will just stick to m&ms!!!
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