Today Katie and I had a conversation about BIG numbers. However, I told her that in order to get a sense of big numbers, we first needed to start with some smaller ones. For this purpose, I brought out the abacus. Katie has played with it much before and so she already knew, without counting, that there were 10 beads on each rod. I then told her to count the rods and tell me how many beads there were total. She quickly counted by 10’s and came up with 100.
We then proceeded to count by 100’s to 1000.
Me: So if we had 10 abacuses (or is it abaci?), then there would be 1000 beads total. Do you think that’s a lot?
Katie: Not really.
We then talked about why 10, 100, and 1000 are written the way they are. We had a few discussions about 2-digit numbers in the past, so this wasn’t completely new to her.
Katie: How do you write down 1 million?
Me: A 1 followed by 6 zeroes.
Katie: What if you have a 1 followed by 100 zeroes?
Me: That’s called a googol.
Katie: Is that the biggest number?
Me: No, because there is also a googol and one. In fact, there is no biggest number. Lets play a game. You say any number and I will say a bigger one.
Katie was very amused by this. At first she would say things like googol million and googol googol, but then she started stringing together meaningless combinations of words like “googol hundred thousand googol googol fifty hundred.”
However, the question of a biggest number still bothered her. “What if you added up all the numbers in the universe, would you get the biggest number?” she would ask. Or, “What if you counted everything on earth, and then the moon, and then all the other planets, would you get the biggest number then?”
I tried to tell her that there is no biggest number because to any number you can add one and get a bigger one. I don’t think that she believed me though, and I didn’t press it very hard. I do think that she got a sense that there are really big numbers out there, and that’s good enough for now.
Musings of a Mathematical Mom 
I had a conversation like that with one of my students a few years ago. He would name any number and then I would point out that you could add 1 to it and get an even bigger number. This got him so overwhelmed that he said he had to stop talking to me!
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Katie, on the contrary, wanted to continue talking about it. I think that different kids have different ways of dealing with things they don’t understand – some want to keep asking questions about it while other prefer to stop thinking about it altogether.
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I had a similar conversation with my cousin Alik a couple days ago. He asked me what I’m doing (I was doing algebra) and I told him I’m studying a different kind of numbers, that you can’t count to, and when he asked for an example I said not everyone agrees what these numbers are named, but some people call one of them “x”. “So you’re studying numbers even bigger than a trillion?” We then had a conversation about the biggest number, where I told him there’s always a bigger number, and he was very excited about naming numbers up to a nonillion. I told him the numbers I was writing down are still a different kind. He came away very happy, saying that Mitka is studying numbers even bigger than a nonillion.
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It’s great to see when math makes kids happy :-). How old is your cousin?
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