How do you know? (talking math with your kids)

who: J2
where: in the car
when: this evening, driving home from a picnic

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Yep, in this part of the world it is perfect picnic weather. I would have taken a picture, but

I was driving, so I didn't hear the full conversation, but what I caught was:

J2: Yes, 384 is a multiple of 12
P (mommy): How do you know?
J2: Because 384 is 192 + 192 and 192 is a multiple of 12.
P: How do you know?
J2: Becuase 192 is 96 + 96 and 96 is a multiple of 12.
P: How do you know?
J2: Well, it is 8 x 12 . . . also, it is 48 + 48 and 48 is a multiple of 12.
P: How do you know?
J2: 48 is 24 + 24 and 24 is a multiple of 12
J0: how do you know?
J2 (exasperated): Daddy, everyone knows 24 is equal to 12 x 2!

So, I'm still not sure how he knew that 384 was a multiple of 12. Surely it wasn't really through the decomposition in this conversation . . .

While "How do you know" is probably overused in this conversation, I think it is a good question to have as a parenting habit. You can see we fall back on it when very tired. Also, the kids expect to hear it, so they are immediately ready to enter into that type of discussion.  I'm looking forward to the times when (1) they turn it around and ask us "how do you know?" and (2) when they use it on other people (each other, friends, teachers).