Exercise 1: I printed this image (created with Google Sheets) and showed it to Benny. I pointed to each pie chart and identified which fraction it represents.
Results: Good. Benny was able to name some of the fractions and seemed to understand that the words "third" and "fourth" meant less than a whole.
Exercise 2: I printed this image, took out some crayons and filled in a couple circles, copying the color image above. Then, I encouraged Benny to do the same for the rest of the circles.
Results: Poor. He filled in a couple by copying the image and then got bored. He didn't seem to learn anything.
Excercise 3: I asked Benny if he wanted a half, a third, or a fourth of a cookie.
Results: So-so. He said a whole cookie. I repeated the question and he chose a fourth. Then I showed him a fourth and he changed his mind to a half.
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Interesting! I wonder if his confusion resulted not from a misunderstanding of fractions, but instead around the language we use for fractions. I wonder if you would have asked if he wants "one-fourth" of a cookie or "a quarter" if he would have been more likely to choose correctly. Increasing numbers typically indicate an increase in quantity, and adding the "th" at the end of the word seems like such a narrow distinction for a little tiny guy. Sounds like he's got it now, though, and no one will ever be able to trick him with fourths again!
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