This evening Katie was entertaining herself by counting to 100 by 2s, 3s, 4s, etc. After counting by 9s, Katie exclaimed, “That was easy; but you know what’s even easier? Counting by 10s – I can count by 10s to a million!”
Me: I don’t think that you could count all the way up to a million – it would take too long.
K: No it wouldn’t.
And off she went.
When she got to one thousand, I stopped her.
Me: It took you 5 minutes to get to a thousand. A million is a thousand thousand. At this rate, how long do you think it will take you to get to a million?
K: I don’t know, how long?
I did a quick estimate in my head…
Me: It will take you about 3 and a half days.
K: I don’t believe you. I’m going to count when I get into bed and before I fall asleep.
I certainly didn’t want to dissuade her. However, when she got into bed and I asked her whether she was going to count, she said that she changed her mind. “I’m going to count by millions. One million, I’m done!” she exclaimed. But then after a moment she decided that this was cheating too much.
K: What if I count by thousands – how long will it take me then?
Me: I estimate about an hour.
K: That’s still too long. I’ll fall asleep before I finish.
So then I told her about the trick of switching what you’re counting by whenever you get to a new power of ten: i.e., you count by 1’s to 10, then by 10’s to 100, by 100’s to 1000, and so on. I had to help her with almost every transition, but when she reached a million she was very excited. And it only took about five minutes.
Musings of a Mathematical Mom 