I always find myself repeating that math starts with play and proceeds to questions; these are the seeds from which the trees grows. A new, beautiful example of this just emailed to me by a parent of some students I work with is this Doodling in Math Class video. In addition to the irreverence, the pacing, and the smooth development from play to question to more play to further questions, I happen to love the topic of the videos: star polygons. A question she doesn’t ask (but which I’ve spent a huge amount of time on with students of mine) is: what is the sum of the interior angles of a given star polygon?
In any case, it’s a lovely video, and fun to watch. She has another on binary trees that is equally enjoyable.