The digits always add to nine
18, 27, 36, 45, 54, 63, 72, 81. One and eight is nine. Seven and two is nine. Every answer, all the way up. A child who answers 9 × 6 with 56 can see that 5 + 6 is eleven and that the answer must be wrong, without anybody marking it.
Ten of them, take one away
Nine sevens is ten sevens with one seven removed: 70 − 7 = 63. This is the method worth teaching, because it survives. Nine twenty-threes is two hundred and thirty take away twenty-three, and no finger trick reaches that far.
The fingers
Hold up ten fingers and fold down the sixth: five fingers stand to the left, four to the right, and 9 × 6 = 54. It works for one to ten and children love it. It is also a dead end — it does not extend past ten and it hides the reason — so use it to get a child moving and teach the tens method behind it.
The tens go up while the units go down
09, 18, 27, 36, 45 — the first digit climbs by one each time and the second falls by one. Written out as a column it is the most orderly thing in the whole grid, and it is worth writing out once for a child who thinks the tables are chaos.