Extending patterns

Fiona and I were waiting for Sophie's Aikido class to finish. We were hanging out in the van. She had brought along her math but after a couple of minutes decided she didn't want to do any more of that, but would like to do some "different math." On a paper I drew pictures:

square, triangle, circle, triangle, square, _____

She easily drew a triangle to continue the pattern. We used to play games like this with pattern blocks. No big deal. I decided to up the ante. I gave her:

5, 7, 9, 11, ___

which she got easily. Told me it was too easy, it was just odd numbers, and could she please have something harder. Next came:

102, 213, 324, 435, ___

and she got that one too. I was sure of stumping her with:

1/2, 1, 2, 4, ___

but she examined it for a minute, said "I can't explain it, but it's 8." I had failed to outwit her again, and she thought this was hilarious. So in a final attempt to challenge her I wrote out:

0, 1, 3, 6, 10, ___

and she looked at it for about 5 seconds and said "oh! it just steps up and up!" and laughed and told me the next one was 15. I put my face in my hands and wailed aloud about my inability to fool her. She laughed and laughed until she was giddy.

I just love it when kids can take a rudimentary understanding of something, and extend and extend their learning, moving from what they know into what they don't know with enthusiasm, pushing the envelope bigger and wider with every new challenge.