1The finger trick (9 × 1 to 9 × 10)
Hold up all ten fingers. To find 9 × 4, fold down the 4th finger from the left. Count the fingers to the left of the folded one (3) and to the right (6): the answer is 36. For 9 × 7, fold the 7th finger: 6 on the left, 3 on the right, so 63. It works for every fact from 9 × 1 to 9 × 10, and kids love that it is "built into their hands".
2The digits add up to 9
For 9 × 1 to 9 × 10, the digits of the answer always add to 9: 18 (1 + 8), 27, 36, 45, 54, 63, 72, 81, 90. It is a fast way to check an answer. If your child says 9 × 6 = 56, the digits add to 11, so it cannot be right.
3The tens digit is one less
For 9 × 2 through 9 × 10, the tens digit of the answer is one less than the number you are multiplying by. 9 × 8: one less than 8 is 7, so the answer is in the 70s. Then use the digit-sum rule: 7 + ? = 9, so 72.
4Ten groups minus one group
Nine of something is ten of it minus one. 9 × 7 = 70 − 7 = 63. This version works beyond 10 too: 9 × 12 = 120 − 12 = 108, and 9 × 11 = 110 − 11 = 99.