I was teaching my third graders how to solve division problems the other day. Specifically, we were solving story problems which involved division, and the students had to figure out what to do with the remainders.
The first problem involved brownies. There were three people sharing sixteen brownies, and we figured out that each person received five whole brownies and one-third of the last one. Simple enough.
The next problem involved balloons. Again, three people had to share sixteen balloons. Balloons, of course, don’t lend themselves well to fractions; a third of a balloon is essentially worthless. For this problem, we decided the best answer was five balloons each, with one balloon left over, to be popped. For some reason, third graders always prefer to pop the leftover balloon, rather than let one of the five people have it. Maybe it’s greed; maybe it’s the thrill. Who knows.
We practiced several of each type of problem, until they got pretty good at deciding whether a problem was a brownie problem, where the remainder gets turned into a fraction, or a balloon problem, where the remainder is left alone.
Then I introduced a new problem. Sixteen people were going on a boat ride. They had to rent rowboats, and each boat held three people. How many boats would they need?
“Five and one-third!” said Ronald. He saw this as a brownie problem.
“So Ronald, you think they should rent five whole boats and then get one-third of another boat?”
“Of course!” He was adamant.
Let me explain about Ronald.