Today I was thinking about a method of adding and subtraction using your fingers. I saw a classroom of children do this on television years ago. They were so fast, much faster than the adults sitting there with calculators. The method is called Chisenbop. The following videos explain it well, but don't really show the speed that one can attain.
The first video is of a teacher explaining Chisenbop. The second video is of a five-year-old boy using it to add. It really is pretty amazing.