Q&A #19209

Schoolwide math activity

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From: Claire (for Teacher2Teacher Service)
Date: Jan 05, 2008 at 17:16:23
Subject: Re: Schoolwide math activity

Hi, Gina --

Thanks for writing to T2T. This sounds like a good opportunity to develop the
concept of experimental probability vs theoretical, and the idea that the
greater the number of trials, the more closely experimental results
approximate  theoretical expectations. Also an opportunity to introduce some
of your older students to spreadsheets and their graphic capability.

Here's one idea. Investigate the probability of the sums of two dice. Set up
a station with two dice and some kind of recording system. Could be
individual pieces of paper on which children record their own results, or a
large graph on which they record group data as they generate it, depending on
how labor intensive you want to get, and how independently the children will
be working. Kids could work in pairs, one rolling and one recording. If you
go the individual recording route, you or (better yet) students you have
trained can add each day's data gathered to a master spreadsheet which graphs
the accumulated totals and can be added to the display at the station to
illustrate how, over time, the shape of the date grows more toward the
theoretical curve you would expect.

For younger children, just the practice of adding and recording the sums of
the dice will be a worthwhile experience. Older children can delve into why
some sums have a greater chance of being rolled.

This is a variation of a project I've used many times with small groups of
third graders. I believe I got my initial inspiration from a Marilyn Burns
activity. I begin with a game format (sort of a pre-test) in which they place
11 chips above any of the numbers 2-12, which are listed across the bottom of
1-in graph paper. In essence they predict (or bet on, although we don't say
that) the distribution of sums. We roll a pair of dice and call out the sum.
Anyone with a chip above that sum removes it. The first person to remove all
their chips is the winner. The first time they play, nearly all young
children spread their chips equally, one above each of the possible sums.
After a few rounds they begin to notice that some sums occur more than
others. We begin keeping a record of results. They wonder why it works that
way, and we then list the possible ways to roll each sum. I purposely use two
different colored dice to emphasize that a red 6 and a green 3 is a different
outcome than a red 3 and a green 6.

You could do a little "pre-testing" before they begin recording the results
of the rolls, and then revisit the game after the activity. Seeing them
distribute their chips in something resembling the expected outcome tells you
they understand. Some children take longer to let go of the more "magical"
notions they have about probability. "Six will come up more because it's my
favorite number."

Probability is a difficult thing for kids (and adults!) to understand. An
experience like this can take some of the hocus-pocus out of it.

I hope this is helpful, if long-winded. Please write again if you have more

 -Claire, for the T2T service

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