| Realistically, how long does it really take to master the multiplication tables? Realistically, one needs only the tables for 2 through 9, since 0 and 1 are so trivial, and 11 and 12 are not necessary to be able to multiply. That's 8x8 products. But identifying a x b with b x a leaves only 36 things to memorize. I don't think anyone, at home or in school, ever used a picture of a rectangle of dots to illustrate multiplication (and enabling one glance to explain why a x b = b x a). Or a rectangle of anything! But that should certainly be part of teaching multiplication!!! How many of us have, many times, met someone at a party or on an airplane who said: "Math? I always *hated* math!" Shouldn't we try to do something about this? --Dan