Last night during Colin's bath he was telling me about his day at school. We were talking about math. He began talking about something called a "fact family."

At first I thought he might be talking about factorials. But that wasn't it. It was something different.

He gave me some examples. The concept and term was new to me. In my day, we didn't have fact families. After a bit he explained that "8 7 15" is a fact family of four, whereas "8 8 16" is a fact family of two.

Interesting, because he was talking about different ways to arrange things (numbers) and thats also what factorials are about. So I said to him:

"At first I thought you were talking about factorials."

"Oh. What's a factorial?"

(slight pause). "It helps you calculate how many ways you can arrange things." (I reach for three colored cups and set them on the bathtub.) "For example, if you have three cups, how many different ways can you arrange them?"

After a few seconds, as I'm preparing to explain further, he says, "six."

(another slight pause) "How... what.... how did you know that!? Has your teacher been talking about factorials??"

(all smiles) "I just.... thought about it."

(further silent amazement from me)

Then he reaches over and proceeds to show me his thought process of all the ways that the cups could be rearranged. I'm still a little flabbergasted.

Then I explained how when you know that 3-factorial equals six, you can calculate 4-factorial by multiplying 6 times 4 (24). More smiles and giggles. 24 times 5 (120). times 6 (720). times 7 (5040). And that was as far I could go.

BTW, here is a good explanation of fact families.