I was teaching a math lesson about factor trees. I told Noah that every composite number has a unique set of factors that no other number has, like its fingerprint. He didn't believe me. He tested me with several composite numbers. Then he said, "But what about the really big numbers? There are only a certain number of prime numbers, right?" I said, "No. Prime numbers march on into infinity." I made little marching motions with my hands. He got that look that I LOVE. The one that is realization dawning, learning occurring, the beginnings of an awestruck smile. My favorite part of teaching. It's very rare, but it's worth the wait every time. He gets it. But he's not done discussing it quite yet.
N: The factors for 35 are only 5 and 7. Is that right?
N: I mean, is that good enough?
M: 5 and 7 are the factors of 35. There's no value judgment of good or bad. It's just a fact. That's one of the reasons I love math.
N: But all the other numbers I've done have at least 4 prime factors...
M: That doesn't make them better, you factor racist. [He understood and laughed, which is another reason it's a joy to be with him.] Just as each person has different characteristics that make him unique, he's not better than another person with different characteristics.