Mr. T and I have been playing with probability lately. The other day he made a spinner.
We got the idea from Math By All Means: Probability, Grades 1-2. I really like these books by Math Solutions, particularly the Math By All Means series and the Teaching Arithmetic series. I used them back when I was teaching (and was even one of the test teachers for the first Math By All Means book, on multiplication.) Each book is a series of activities on a single math topic, geared for a certain age group. The emphasis is on presenting interesting activities, and letting kids figure out their own ways of making sense of the problems. The books aren’t for everyone: each activity has many pages of explanation, with word-for-word dialogues of how a teacher introduced the idea to her classroom, what the kids said, and examples of their work. For some that’s overkill, but if you’d like to get a better sense of how to let your kids use their own smarts and learning style in math, the books are fantastic. The math philosophy behind all Math Solutions books is sound: it’s always about comprehension, rather than rote learning.
It’s also nice to have the work of other kids to share with your own child–hard to do in a homeschool setting. And when activities require looking at larger pools of results than you’d have with one or two kids, you can always look at the classroom results reproduced in the book.
And no, I am not a rep for this company–I just think these might be books that homeschoolers might not come across on their own. We’ve never used math texts until my kids were close to their teen years; we use a variety of activities, games and books. These Math Solutions books are a backbone we return to often. But even with them, we don’t do all the activities. We just pick and choose, depending on the kids’ interests and what they already know. And we adapt them, as you’ll see.
Anyway, Mr. T made a spinner. The book instructed kids to make a spinner that was one-quarter red and three-quarters blue. Well, I know Mr. T, so I told him he could make any categories he wanted on the spinner. When I said, “Even characters, if you want to,” little fireworks practically shot out from his eyes.
He drew an alien in each of the two spinner sections, and named them 2-MO and Z-31. Actually, he didn’t use dashes; he drew sort of a flattened T symbol for one alien, and an upside-down version of the same for the other. When I asked what the symbols meant, he just rolled his eyes and said, “They’re aliens.”
The book’s design for these spinners is pretty brilliant. You basically use some 4-by-5 index cards (I used cut-up manila folders ’cause that’s what we had). You draw a line from one corner of the bottom card to the center of it, which indicates which part of the spinner “wins”. Then you poke the bent spoke of a paperclip through the bottom card and the round spinner, and tape the rest of the clip flat to the bottom of the card; a little flag of tape will keep the spinner from flying off the card. But the secret mechanism is a one-quarter inch cylinder, cut from a drinking straw, which goes between the bottom card and the circular piece. That makes the spinner really spin, in an obsessively fun way. Like a record, baby, round, round, right round.
The fact that the spinner featured aliens made testing it all the more fun. Filling out the results graph became a race between aliens. Of course, Mr. T didn’t want to just color in or put an X in the graph paper squares–he wanted to draw each alien’s personal planet in his square whenever the spinner landed on his spot. Which was fine by me; graphic graphs are more fun to look at anyway.
Poor Z-31 was pretty much doomed from the start, getting only one-quarter of the space on the spinner and all. Plus, luck wasn’t on his side: out of 22 spins, the spinner landed on 2-MO eighteen times, and Z-31 four times. Which led to a conversation about how chance factors into probability.
We’ve been talking about probability in terms of game design. Mr. T is still making his own Pokemon-style card game called Dinkers; until now he’s planned for players to use dice on their turns. But he’s starting to see how spinners give the game designer more control. If he wants a rare outcome, he can allot it a very slender slice of the spinner’s pie. Plus, you can make a spinner have words and pictures and personality.
But mostly, spinning a spinner is just dang fun.