Big numbers and BIG NUMBERS (emulating classic TMWYK)

During a recent chat with J3, 3.5 years old, I decided to test some ideas about her number sense. She was playing with 3 and had just counted them.

me: How many fingers do you have?
J3: 10, here's five (shows one hand) and here's five (shows the other hand)
me: Let's count them?
J3: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
me: I'll try mine. 1, 2, 3, 4, 5, 7, 8, 9, 10, 11
J3: (laughs) That's silly. You skipped ... you don't have 11. Let me show you. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
me: Oh, thanks for helping! I have something else to show you. (I write down the numbers below). Do you know which is bigger?

Why is it so dark? Oh, yeah: winter

J3: this one (points to 306).
me: what number is that?
J3: 3-zero-(pauses) 9.
me: what about this one?
J3: 3-(pauses) 8

I  realized that I had drawn the 306 a bit larger than the 36. Maybe that was why she pointed to 306? I drew two more.

me: Hmm, what about these two numbers?
J3: (points to the 2). That is a really big number (stretches her arms wide)

we then drew faces for each other.

A J2 project and challenge

J2 was arranging the pieces from a checkers set. He wanted me to pose this challenge to all of you:
what are your favorite ways to arrange 24 checkers, split equally into two colors? here is one of his designs, to get you started:

We are working on imitating JJ Abrams lens flares, but only have gotten lens glare