I focus on understanding 6x5 is six fives, or five sixes, and often refer to it this way, vs. a "math fact." Then I focus on learning "landmark" facts that they can leap to if they can't recall individual facts. These are the perfect squares, doubles, fours fives and tens. Every other fact can be quickly gotten to from these with just one more step.
Upper squares can be difficult, and I find some sort of way they can remember. 7x7 is "almost 50" - 49. 8x8 is remembered by a silly rhyme my kids learned from a book: "8 times 8 walked in the door to play Nintendo 64." It never fails to stick. 6x6 rhymes with 36.
So 7 times 5 is five fives plus two fives (25 + 10) or six fives and one (30 + 5) whichever is easier. Four times a number is to double it twice. 7 times 6 is either (7x5) 35 plus 7, or (7x7) 49 minus 7, whichever way their mind works best.
8 x 7 is more difficult to leap to, so I work on this one from memory. I think, 8, 7, 6, 5 and reverse the last two digits. It seems to work.
Some kids don't seem to remember facts though unless they are using them. I am working with an 11 year old now who is increasing her recall dramatically as she practices prime factoring, which she enjoys doing. Breaking down a number into factors is much easier for her than building it up with factors. By practicing the one skill, it is improving the other. She has been particularly difficult to wean off of skip-counting, but this is working.
Some kids are helped by seeing visual patterns, some are not. Using the facts in ways that make sense seems to be the best way for long term recall.
-----Original Message----- I do one on one tutoring and one of the most common problem I run across is students (grades 6-8) who do not know the basic multiplication tables. (They rely on counting.) Other than just doing drills, what would you suggest to help them learn the basic math facts?