The Grid Is Symmetric
Multiplication is commutative: 7 × 8 and 8 × 7 give the same answer. That symmetry halves what there is to learn — a 12 by 12 table has 144 cells but only 78 distinct facts, and most of those are already familiar.
The diagonal holds the square numbers: 1, 4, 9, 16, 25 and so on. Learning those first gives an anchor for everything nearby, since 7 × 8 is just 49 + 7.
Patterns Worth Knowing
| Table | Pattern |
|---|---|
| 2 | Doubling; every answer is even |
| 3 | The digits of each answer sum to a multiple of 3 |
| 4 | Double, then double again |
| 5 | Answers end in 5 or 0; each is half the ten times table |
| 6 | Even multiples of 3 |
| 8 | Double three times |
| 9 | The digits always sum to 9; the tens digit counts up as the units count down |
| 10 | Add a zero |
| 11 | Repeat the digit, for 1 to 9 |
| 12 | Ten times plus two times |
The Nine Times Finger Trick
Hold up ten fingers. To find 9 × 7, fold down the seventh finger. Six fingers remain to its left and three to its right: 63. It works because the tens digit is always one less than the multiplier and the two digits always sum to nine.
The Hard Ones
Research on which facts children find hardest consistently identifies the same small set: 6×7, 6×8, 7×8, 7×9 and 8×9. They sit in the middle of the table with no obvious pattern and no easy anchor. Focused practice on that handful is far more efficient than drilling the whole grid.
7 × 8 = 56 has a mnemonic worth the trouble: the digits 5, 6, 7, 8 run in order.
Why It Still Matters
Fluent recall frees working memory for the actual problem. A student computing 7 × 8 from scratch mid-way through a long division has less capacity left for the division itself. This is the case for automaticity — not that the facts are important in themselves, but that recalling them should cost nothing.
Frequently Asked Questions
How far should the tables go?
Up to 12 is the traditional English-speaking standard, largely from pre-decimal currency and imperial measures. Up to 10 is standard in most metric countries and sufficient for almost all arithmetic.
What is the best order to learn them?
2, 10 and 5 first — they have the clearest patterns. Then 3, 4 and 9, then 6, 7 and 8, which are hardest. Learning one table at a time beats working through the grid row by row.
Does memorisation still matter with calculators?
For estimation and error-catching, yes. Someone who knows 7 × 8 immediately notices when a calculator shows 54 because of a mistyped digit.