As I pose various multiplication problems, student use the base 10 pieces to build & solve. This leads naturally into learning about area model and partial products (again, place value is the basis for these). We move from building multiplication problems to learning how to record our process on paper.
For homework, instead of giving a worksheet with numerous problems, I've been giving 1 problem and students solve using at least 4 different methods. They LOVE this and for me it's time-saving because it's self-checking; all four solutions should be the same answer!