At the risk of offending (which is not my intention), I would like to make a gentle suggestion that we use a word other than "retarded". This has come up in more than one post now and while I'm sure that no one here is intending to denigrate people with disabilities, calling something retarded implicitly carries the idea that people with cognitive disabilities are somehow..."less".
Although I realize that it has not been used here in that way, it is a word that is still closely associated with its original meaning.
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.
