I had previously mentioned that my children are very picky and slow eaters. This creates much frustration for me, but at the same time has been on multiple occasions inspiration for interesting math conversations.
Yesterday, Katie was eating a cutlet for dinner, and I, as usual, was trying to make her hurry up a bit.
K: I’m almost done with it.
I look at the cutlet and notice that there is still almost half of it left.
Me: What fraction of the cutlet do you think must be remaining for you to be “almost done with it”?
K: I think a third.
Me: Why a third?
K: Because a third feels so much smaller than a half.
Me: Well, you definitely have more than a third left.
K: (taking a big bite) Not any more.
She went back to chewing, very slowly of course, and I thought the conversation was over. But about 5 minutes later, when she was still not finished with the cutlet, Katie suddenly decided to resume the conversation.
K: Mom, if someone could eat the whole cutlet in just one bite, could they say that they’re almost done with it before they take the bite?
Me: I don’t know. Can you be almost done with something before you even start?
K: Because if they can’t say it before they take the bite, they can never say it, because after taking the bite they will be fully done with the cutlet!
I couldn’t argue with her there.
So what do you think, does “being almost done with a task” depend on how quickly you do it or just on what fraction of it you have already done?