Times Tables: 6s through 10s

Arithmetic · Axiom Academy

LESSON Times Tables: 6s through 10s Finish the multiplication table — and see how few facts are actually left to learn. Lay the whole table out as a 10 × 10 grid: rows 1 to 10 across columns 1 to 10, one hundred products in all. Now cross out every row and column you have already learned. What is left is a small square in the corner — and half of even that is a repeat. Any product with a 1, 2, 3, 4, 5 or 10 in it is already yours. That clears 84 of the 100 squares. What is left is the 4 × 4 block where both factors come from 6, 7, 8, 9. Every square above the diagonal has a twin below it: 6 × 9 and 9 × 6 are one fact. 36, 42, 48, 54, 49, 56, 63, 64, 72, 81 — and the next three steps take most of them off the list. The 9 times table carries the strongest pattern in the whole grid. Line up ten markers — the ten fingers of the classic method — and fold down the n th one. The markers still standing to its left are the tens digit; the ones to its right are the units digit. Nothing has to be recalled; it is read off. 9 × n is one group of n short of 10 × n. Taking n away from n tens leaves (n − 1) tens and (10 − n) ones. (n − 1) + (10 − n) = 9, whatever n is. Use it to check any answer in the 9s. 9 × 7 starts with a 6; 9 × 4 starts with a 3. One less than the number you multiplied by. This one pattern handles 6 × 9, 7 × 9, 8 × 9 and 9 × 9 — four of the ten. Fold down the 7th marker. Six stand to its left, three to its right, so the answer is 63. Check it: 6 + 3 = 9.

This is the written version of the interactive lesson above. See the full Arithmetic course.