Yesterday I learned about the Arctic Circle theorem and used it for a fun talk with the kids:
This morning we had a fun little coincidence as one of the problems that my son was working on was the proof that 
Part 1 is a short discussion of the sum:
Part 2 is looking at the tilings of the Aztec Diamond – counting the number of tilings of the level 2 diamond is a pretty good challenge for kids.
So, a lucky second project with the Aztec Diamond. I definitely want to think more about how to share the ideas in the Arctic circle theorem with kids. I think the ideas here are something that kids will really love.
Mike's Math Page 
There are other fun problems about counting tilings. The first one I’d give them is counting domino tilings of a 2-by-n rectangle. Then rhombus tilings of an equiangular hexagon with sides of length a,b,1,a,b,1. If the kids like these, let me know; I can suggest some fun follow-ups.
On the T heading back home from Cambridge. the 2 by n tiling just made me smile. Hope to try it out this weekend. Thanks.