Probability and Math Games

We continue playing daily and reading our living math books, Life of Fred and Childcraft: Mathemagic - Volume 13 specially. Last week we watched a chapter of Cyber Chase that dealt with fair games, if they were the same chances to win for the participants and the one offering it, and they also talked about probability. I check here all the episodes and what they are about, and at youtube I type Cyberchase, and, for example, 103, or the third episode of the first season, and I get the one I'm looking for.  In this one called R-Fair City, Hacker had a fixed game in which he told the children to get two from these four numbers, 1, 2, 3, and 4, and if when multiplied they resulted in an even number, he'd win, if the number was odd, the children would win.

At the end of the episode, one of the Cyberchase youngsters talks about heads and tails, why when we do that 10 times we don't get 5 and 5, or rarely, and why if we do that over 700 times we'll be getting closer to half of the time heads and half of the time tails.

I thought about throwing three dice 50 times, and I asked Blue Heart if she wanted even or odd numbers, she picked odd, every time the dice were 1, 3, or 5, she'd put a tally by those numbers, and I'd do the same with 2, 4, and 6. We practiced tally marks, counting by fives, and finally we had to add the scores of each of our three numbers. Here I realized that she only knew to pick the strategy of writing marks for the three scores, and erase and count. She lost count like this. Meanwhile, I got these toothpick bundles inspired by Algoritmos ABN, and I represented each of my three numbers and grouped them to count. Even though she knew that 30 and 20 is 50, she did not think about looking at 29 and 26 and borrow one from 26 to make 30. I realized that my daughter looks at worksheets and not always understands what they are asking her to do. Games show me much better what strategies she has, and where she is when it comes to her understanding of tens and ones, grouping, regrouping, and adding, and she truly loves playing these games as well as reading our math books.

Lastly we analyze the data, which number came up most, and saw they were all between the 20's and 30's. Throwing 3 dice 50 times is like throwing one dice 150 times, and the chances start to even out. There was not a huge difference between her score and mine, or between odd and even, but it was considerable, 65 versus 76.

We are also back doing Xtramath. Sometimes, after many months, coming back to something has a better reception.

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