I spent the last year tutoring math full time (approximately 28 fourth grade students per day in small groups). At one point we did an exercise with a blank 12

I spent the last year tutoring math full time (approximately 28 fourth grade students per day in small groups). At one point we did an exercise with a blank 12x12 multiplication table. I had students fill in what they already knew. Ones, fives, tens, elevens up to 11x10, and twos were easiest. Most of them could figure out threes and fours pretty quickly. I taught them the finger trick for nines (9x6... hold up your fingers, drop the 6th finger, you have 5 on the left and 4 on the right for 54.) Most of them also had 6x6, 7x7, and 8x8 memorized. This left 6x8, 7x8, 12x6 through 12x9, 11x11, 11x12, and 12x12. Not surprisingly, these are also the products adults tend to have the most trouble with. I had students select some problems they didn't have memorized, and commit to memorize them over the coming week. Lest you think it was all about memorization, I also taught a number of techniques for quick computation -- often taking the form of number splitting (6x8 = 5x8 + 1x8) or quick drawings (draw 6 horizontal lines, cross them with 8 vertical lines, count the intersections for 6x8 -- this can be combined with the previous technique by counting by 5s and then counting the remaining intersections.) Those students who gained proficiency in multiplication also improved quickly in division, fractions, and various other parts of the curriculum.