Here's something cool (and free
)!
http://nlvm.usu.edu/When I explain "borrowing" to kids I say that we take a 10 and break it apart into 1's or we take a 100 and break it apart into 10's, etc. Legos are a great way to demonstrate this.
When I teach subtraction I say things like, "You can make a 10 out of a 3 and a 7. If I take away the 7 part the 3 part is left." So many kids get stuck in counting backwards mode or drawing ten dots and crossing out 7 one at a time mode. They don't think of numbers as chunks. They are only thinking of them in terms of counting.
Kriston, sorry if I freaked you out with the wikipedia stuff. And remember, it's just notation! There are beautiful books about fractals and the Mandelbrot set. Kids love to study the pictures and look for patterns. And, guess what--that's what mathematicians do, too!
Today, with my math class I had them do some experiments on Mobius strips, cutting them in different ways. We also generated a distribution graph by rolling two dice and graphing the results. I try to use math vocabulary when I talk about these things. I say things like "surface" and "topology" and "distribution" and "probability". And I read to them from Penrose the Mathematical Cat.
