On a more topical note, while I'm neither a fan of EM nor of the lattice method, partial products is nothing more than a paper representation of steps many people take when they solve multiplication problems mentally. I would argue that it not only simplifies many multiplication problems, but also validates the way in which many strong math students flexibly use number understanding to solve those problems.
DH and I were just talking about this over the weekend, when DS showed DH how to do the lattice method - which provided us all a good laugh as DH tried to make sense of that one
. I agree about the partial products method being something that is commonly used as a simple breakdown method.
