Only ten new facts
Multiplication works both ways round, so if a child knows 4 x 7 they know 7 x 4. Cross off every fact in the 6, 7, 8 and 9 tables that already appears in the 1 to 5 and 10 tables, and what is left is the facts where both numbers are 6, 7, 8 or 9. There are sixteen of those, and six are repeats (6 x 7 and 7 x 6, and so on), leaving ten unique products.
| Fact | Answer | Trick or pattern |
|---|---|---|
| 6 x 6 | 36 | A square number; the digits of 36 are 3 and 6, half of 6 and 6 itself |
| 6 x 7 | 42 | Double 3 x 7, which is 21 |
| 6 x 8 | 48 | Even x 6: the answer ends in the same digit (8) and starts with half of it (4) |
| 6 x 9 | 54 | Nines: tens digit is one less than 6, and 5 + 4 = 9 |
| 7 x 7 | 49 | A square number; one less than 50 |
| 7 x 8 | 56 | Say the digits in order: 5, 6, 7, 8 |
| 7 x 9 | 63 | Nines: tens digit is one less than 7, and 6 + 3 = 9 |
| 8 x 8 | 64 | A square number; double 32, or 8 more than 56 |
| 8 x 9 | 72 | Nines: tens digit is one less than 8, and 7 + 2 = 9 |
| 9 x 9 | 81 | Nines: tens digit is one less than 9, and 8 + 1 = 9 |
The ten facts that are genuinely new once the 1 to 5 and 10 tables are known. Learn these and the 6, 7, 8 and 9 tables are done.
The 9 times table: three tricks, pick one
The 9s are the easiest of the four once a child sees the pattern. The tens digit of the answer is always one less than the number being multiplied, and the two digits of the answer always add up to 9. So 9 x 7: tens digit is 6, and 6 plus what makes 9? Three. 63.
The finger trick works for children who prefer something physical. Hold up both hands and fold down the finger for the number you are multiplying, counting from the left. Fingers to the left of the folded one are tens, fingers to the right are ones. For 9 x 4, fold the fourth finger: three fingers on the left and six on the right, 36.
The third trick is subtraction: 9 times a number is 10 times it minus the number. 9 x 8 is 80 minus 8, which is 72. This is the one to keep, because it still works past 12 and it is how adults actually do it.
The 8 times table: double, double, double
Eight is 2 x 2 x 2, so 8 times any number is that number doubled three times. 8 x 7: 14, 28, 56. Children who know their doubles can do the 8s from scratch without memorising anything, and the answers get memorised anyway through use.
There is also a pattern in the ones digits: 8, 6, 4, 2, 0, then 8, 6, 4, 2, 0 again. Write the 8 times table down the page and children spot it themselves, which makes 8 x 6 = 48 and 8 x 9 = 72 easier to check.
The 6 times table: double the 3s, and the even-number pattern
Six is double three, so 6 x 7 is double 3 x 7: 21 doubled is 42. That handles the whole table for a child who knows the 3s.
For even numbers there is a neater pattern. When you multiply an even number by 6, the answer ends in that same number and starts with half of it. 6 x 4 = 24 (ends in 4, starts with 2), 6 x 6 = 36, 6 x 8 = 48. It only works for even numbers, but those are half the table.
The 7 times table: the one with no trick
Seven is prime, so there is no doubling shortcut and no digit pattern. That is why 7 x 8 is the most-missed fact in every survey of children's tables. The honest approach is to point out how little is actually new. In the 7 times table, 7 x 1 to 7 x 5 and 7 x 10 come from other tables, 7 x 6 and 7 x 8 and 7 x 9 have tricks from the 6s, 8s and 9s, and only 7 x 7 = 49 stands alone.
For 7 x 8, the sequence 5, 6, 7, 8 (56 = 7 x 8) is the one most children remember. For 7 x 7, one less than 50. For anything else, build from a known fact: 7 x 6 is 7 x 5 plus one more 7, which is 35 plus 7, 42.
A two-week order that works
Five minutes a day is enough. Say the fact and the answer out loud, write it, and come back to the specific facts missed rather than re-drilling the whole table. Most children have the four hard tables in two to three weeks, and the ten new facts are the only ones they will need to keep revisiting.
- Days 1 to 3: the 9 times table with one trick, until 9 x anything is instant.
- Days 4 to 6: the 8 times table by doubling three times, then the ones-digit pattern to check.
- Days 7 to 9: the 6 times table by doubling the 3s, plus the even-number pattern.
- Days 10 to 12: the ten new facts from the table above, as flashcards, mixed with the easy ones so the session does not feel like a wall of hard questions.
- Days 13 and 14: mixed practice across all tables, timed if a tables check is coming, and a note of any fact still missed for another week of attention.
Common mistakes
- Learning all four hard tables at once. Take them one at a time, 9s first.
- Chanting in order only. A child who can only reach 7 x 8 by starting at 7 x 1 has not learned the fact; mix the order early.
- Dropping the easy tables while the hard ones are learned. Keep 2s, 5s and 10s in every practice session as quick wins.
- Treating the finger trick for 9s as the end point. It is a bridge; the goal is instant recall without hands.