In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it deeper meaning. Opinions may vary as to how one should slice up mathematical ideas in order to form a teaching methodology, but the underlying picture that unites all such opinions must be the same. Gibson presents a pictorial view of the number system, using colored counters to represent numbers. His introduction to this system is a board game called "The Wizard's Web"--an animated video of the game is available on "YouTube."