Probability with Two Colors (a variation of coin flipping)
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| For these activities, you could use any sort of pouch, or even a paper lunch bag or a cup. (It did seem exciting to my student, however, to use this colorful bag with such a colorful name; "Probability Pouch." Using the name also reinforces the word "probability" each time we used talked about the pouch.) |
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| I wanted to start with a two chance probability, most often called coin flipping as coins are the most readily available two-sided math manipulative to use. There are two-color math manipulatives you can buy, as well, but I decided to use our game pieces from our Othello game (another great math game) since they have two different color sides. |
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| I started by asking him what the possible combinations could be and he easily told me two blacks, two whites and one black and one white. We then made three columns of a piece of paper and labeled them WW, BB and BW. He then began pulling them out of the Probability Pouch in pairs and then putting a check under the appropriate column. |
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| These two-sided pieces effectively mislead students into thinking they have only three outcomes to consider. Some students might figure our that BW occurs more times because it is a composite of the two possibilities BW and WB but it is more likely at this age (1st grade) that they will not be able to provide an explanation of why this column has more checks. I asked him to suppose why this was to give him an opportunity to think about it, to focus his attention on the possibility that since something seems to be happening, there may be a reason for it. This develops mathematical thinking. We will spent more time exploring probability, which may solve or only deepen the mystery for him. |
