Homeschooling my daughter in math has been a very interesting experience so far. As a mathematician, I try to re-imagine the topics in our curriculum with the goal of introducing deeper concepts as soon as I can.
Recently thanks to Allen Knutson, on Google+, I found out about a great video series by Ester Dalvit on braids and knots. My daughter has made it though about half of it, which already covers quite a lot of mathematical concepts (especially from a nine-year old's perspective). So I am trying to use it as a springboard to do some algebraic concepts that most K-12 students never see, like noncommutative groups.
So far I've just made a worksheet on braids along with a reference sheet, which went over pretty well today. I'm not sure how much farther I should push it now.