Tuesday, January 17, 2012

Three remainder one

The kids and I went down to their grandparents’ house for the afternoon yesterday. We did this for several reasons. First, we love them, and hadn’t been to their house since Christmas. Second, Jack and Andrew were sick this weekend, leaving us housebound for two straight days, and if we had had to spend another day of family “quality” time, we might have killed each other. The third reason is that their grandparents live an hour away, so that’s two hours in the car that I don’t have to think of something to do. (The third reason is linked strongly to the second reason.)

At any rate, Jack watched an episode of Peep and the Big Wide World while there, which was a refreshing treat for me, because I love Peep. We never seem to watch it here anymore; it’s usually not on during the times I let them watch TV. In this episode, Peep, Chirp, and Quack were trying to fairly divide two crackers among themselves. They started by breaking each cracker in half, so everyone got a piece with one piece leftover. They broke that into four, and I think you can see where this is going. They went through several iterations until Peep finally said, “Will there always be one piece leftover?” but then an ocean wave came and whisked away the last piece.

I thought it was weird that they didn’t solve the problem; usually they do. I had expected Quack or someone to accidentally break the last bit of cracker into three pieces. My mother-in-law must have had a similar thought, so she asked Jack how he would divide two crackers among three people. She gave him some paper and a pencil to work it out. He scribbled away for several minutes, and this is what he came up with:

Photobucket

See, he would divide both crackers in half, then break the last piece into four, and break THAT last piece into four, and so forth, and he’d do this seven times according to his drawing. And THEN, he’d take the last final piece, and throw it away.

Well, it’s fair!

(My favorite part is the level of detail on the trash can.)

2 comments:

KarenAZ said...

I love Peep! I thought I was the only adult who liked The Big World. The solutions they come up with are great.

Anonymous said...

The kids do sets of problems like this in school - what do you do with the remainder? The actual division problem is the same for all of the problems, but the answer to the question is different depending on what is being divided up - balloons, cookies, money, kids, etc.

Hannah