Fairy Tale Math Circle #3

What a perfect day for the fairy tale circle #3! Today is the summer solstice. And it so happens, that this week’s fairy tale, Снегурочка (The Snow Maiden), takes place at the summer solstice celebration. If you’re not familiar with the plot, it goes something like this. An elderly childless couple make a little girl out of snow. The girl comes to life and all. But come spring, she is in danger of melting. So she stays inside the house except that one time when friends invite her to the solstice celebration. While there, she jumps over a bonfire and melts.

P1000740The story is not a happy one. But we started off by talking about how the Snow Maiden could’ve been saved from the hot weather. I showed them a little “refrigerator” I put together with two clay pots, wet sand and a towel (never leave home without a towel!). We tried to figure out how it worked. And how the process was similar to what we experience on a hot day.

P1000737By the way, today was a very hot day. We switched parks again (I kind of like this park-hopping). This time we hit the jackpot – a screened porch with ceiling fans, breezes from the lake, access to an open shady area with rocking chairs, and all this glorious space was very close to the restrooms and drinking fountains!

P1000741After the refrigerator, we moved on to the math problems. First, we did a couple of algebra problems of the kind “if I pick a number, add it to itself, and take out five, I will be left with 11. What number did I pick?” Just like last time, two strategies emerged – guessing and checking and working backwards. Interestingly, the kids made more mistakes when working backwards (such as forgetting to divide by two at the end or subtracting 5 from 11 and getting 7).

P1000742From that we moved to a magic trick that I came across here. The kids seemed to be really impressed, except for L. Everyone wanted to continue picking numbers and me do this magic trick. But noone seemed to be eager to find out how it worked… except for L. At this point, as unimpressed as he seemed with the trick, he was working hard on figuring the magic. He was also the one who found a mistake on the cards. Actually, he found a number that couldn’t be guessed correctly (I made a mistake typing the numbers onto the cards the night before).

P1000743After a few rounds of guessing, L announced that he figured out how the trick worked. He then proceeded to correctly guess several numbers. The awesome thing was that he used a very different approach from the one that I used (and that’s described in the Math Mom Puzzles post). It longer and was more difficult, but it worked and it was entirely L’s own discovery!

While L was explaining his approach, V (who is the youngest of the group) made a discovery of his own – the numbers in the top left corners of the cards formed a doubling sequence! Such a key discovery for this magic trick!

P1000745The time was running short and everyone was really curious about a pack of disposable diapers I brought with me. L and V have younger siblings who are still in diapers. So all sorts of theories started flying. I asked the kids if they ever thought of what’s inside a clean disposable diaper. Even though I emphasized the word “clean” the first two answers I got were… well, you can imagine. So everyone got a clean diaper and a pair of scissors and we got to work taking the diapers apart.

Once we carefully shook out the white fluffy particles from the diapers, I asked the kids if they ever thought about how come diapers could hold so much liquid. Nope, of course they didn’t think about it. Who would want to think about dirty diapers! So I told them that we were about to make some snow and added a bit of water to the sodium polyacrylate powder we so carefully collected.

P1000744From then on, the rest of the circle was spent on adding more water to the powder, making more and more snow, thinking up all sorts of pranks that could be played with it, and discussing why it should never be ingested. At the end, when I thought nothing could surprising the boys any more, I let them pour an entire package of salt into the “snow”. Boy, were they amazed when it released all that absorbed water! (We promptly thought of a few more pranks).


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