Following a problem in the CME Project’s Alg1 book, I’ve been teaching the distributive property via mental multiplication. Kids see how quickly they can do this multiplication, and the fastest way to do a lot of these is to split the factors into two summands. This provides a great context for the distributive property, which we then work hard to express clearly without variables (which will come later).
Another version of this problem that I’m throwing in to the opening set today: “Sam is doing mental math. One of his steps in his calculation is (100 x 7) + (15 x 7). What was his original problem?”
I think that this will help everyone focus in on a clearer expression of the distributive property.