Probability and Percentages

Probability reared its random head in the 3-4s today. We investigated vocabulary such as impossible, unlikely, equally likely, likely, and certain, in addition, of course, to random, defined by one third grader as "not moving your hand around and around and around trying to find exactly the right one." We also introduced various ways of using numbers to write probabilities. If there is just one red card in a group of 5, then the chances of getting a red card (at random, of course), are "1 out of 5," or "1 in 5," or "1/5."

Or "20%." Percentages can be tricky and often require some serious numbercrunching to carry out. At the same time, they can be extremely useful in comparing two probabilities (it's hard to tell by looking whether 3 out of 7 is better or worse than 12 out of 29) and in getting a rough idea of how likely an event actually is (a percentage is easier to interpret than a fraction like 57/243). So we did some fairly straightforward percentages, using what students already know about fractions and division. If the probability of drawing a red card is 1/5, that's also 20%, because 20 is one fifth of 100. And if there were two red cards out of 5, the probability would be 40%--double the previous one. We also looked at more complicated situations such as 1/7, dividing 100 by 7 to get an approximate equivalent of 14%. Not good odds, the classes agreed.

Later, on their own, they found the probabilities of various events, expressing them in both fraction form and as a percentage. Conversion was easy enough when the denominator of the fraction was 10; most students recognized right away that 7 out of 10, say, was 70%. Other denominators were a bit more complicated. Still, the students persevered, and in the end 110% of them thoroughly understood percentages...wait...