"Look, Mama, I've been discovering things about circles while you were gone."
"Oh really? What did you discover?"
(It looks like she discovered an old pad of graph paper and was exploring a drawing of concentric circles made by me a while back - she drew in the divisions -- and then moved on to make one of her own with a compass.)
"Well, I discovered that there are lots of ways to divide a circle...and I discovered that no matter how big or small a circle is you can still divide it the same way."
"Well, that's very interesting! But what's this?"
"This is a cylinder and these are circles."
"Cool! And what's this one?"
"These are ovals. They're squooshed (sic) circles. This one has one triangle with a curve and the others are rectangles."
"Hmmm...I don't think I agree with that. Remember that a rectangle has to have four right angles. That's why they call it a rec-tANGLE..."
I really think that using geometry and shapes to explore number concepts is a strong combination. I've been working on a new idea that's sort of algebraic, geometric and numeric all at once. Since the kid seems to be experiencing a post-holiday renaissance I might just be able to finish up the activity with her some time soon. Stay tuned!