But really, teaching the 5 cases version is also not quite right. Maybe even numbers are "a bunch of 2s added up" and odd numbers are "a bunch of 2s and a lefto

But really, teaching the 5 cases version is also not quite right. Maybe even numbers are "a bunch of 2s added up" and odd numbers are "a bunch of 2s and a leftover one". Then you just deal with the cases... two bunches of 2s is still a bunch of twos, if you have two of the leftover ones you get another two... The point is, both lines of reasoning are fine. The value comes from having the students struggle through any of many, many ways of explaining it, comparing their answers, and thinking about the aesthetics of the models, and getting a tangible feel on their isomorphism. All of which you can do before needing to even have memorized your multiplication tables. That said, 100 addition problems can be useful: jamming the addition and multiplication tables into your memory so you can do the needed symbol manipulation later. But similarly massive problem sheets for, say, remainders or algebra is just silly.