There is a blog Math Notations that covers various topics about math. This weeks topic is titled "Counting, Multiplication Principle, Pigeonhole Principle and Reasoning for Middle Schoolers and Beyond."
I know I have a different perspective on this subject that many of you have been forced to see in Fundamentals, but one of the reasons I like it is that this idea comes up in almost every one of my classes at some point.
No matter what I teach, at some point I find myself arguing that the number of something is the product of two values and the reason is the multiplication principle. In number theory, this simple idea allows us to derive very deep results from drawing a few pictures.
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