Learning the Times Tables

The idea in one sentence

The 144 facts in a times table grid collapse to about twenty you actually have to memorise, because most of them can be reached from one you already know.

Why the grid is smaller than it looks

Start with 12 × 12 = 144 facts. Then:

• Order doesn’t matter. 7 × 3 and 3 × 7 are the same array turned sideways, so every fact off the diagonal is learned twice. That halves the grid immediately.
• The 1s, 2s, 5s and 10s come almost free — they’re counting, doubling, and the patterns of our number system.
• The 9s have a trick of their own, below.

What’s left is a small stubborn core: 3×4, 3×6, 3×7, 3×8, 4×6, 4×7, 4×8, 6×7, 6×8, 7×8, and the squares. Roughly twenty facts. That’s a manageable list, and naming it that way takes most of the dread out.

Build from what you know

Recall should be the goal, but a fact you can rebuild in two seconds is worth far more than a blank.

• 8 × 6: double 6 to get 12, double to 24, double to 48. Three doublings, because 8 = 2 × 2 × 2.
• 7 × 6: it’s 6 × 6 plus one more 6, so 36 + 6 = 42. Squares make good landmarks.
• 6 × 4: halve the 6 and double the 4 — 3 × 8 = 24. Halving and doubling keeps the product fixed, and often lands on an easier pair.
• 12 × 7: split the 12 into 10 and 2, giving 70 + 14 = 84.

Every one of these is the distributive property in disguise, which is why time spent here pays off again in algebra.

The nine trick

So 9 × 7 is 70 − 7 = 63. Every answer’s digits sum to 9, and the tens digit is always one less than the number you multiplied by — 9 × 7 starts with 6. Both facts follow from the subtraction, and either one catches a slip.

Squares are worth knowing outright

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. They anchor the grid, they’re the neighbours of the hardest facts, and they come back for square roots, area, and the Pythagorean theorem. Knowing 7 × 7 = 49 puts 7 × 8 = 56 within one step.

Practice that works

Short and often beats long and rare. Mix the facts up rather than chanting a single table in order, because chanting trains the sequence, not the fact — a child who can only get to 7 × 8 by running through the whole 7s has not learned it yet. And practise the division alongside it: 56 ÷ 7 should come from the same place as 7 × 8.

Common mix-ups

• Confusing near neighbours, like 6 × 8 = 48 and 7 × 8 = 56.
• Learning tables in order only, which hides whether the fact is known.
• Counting on fingers past 5 × something, which is slow and error-prone rather than wrong — the fix is a strategy, not more speed.
• Forgetting that × 0 gives 0, not the number you started with.

Check yourself

Work out 8 × 6 by doubling, and 7 × 9 with the subtraction trick.

Doubling 6 three times: 12, 24, 48. For the nine: 7 × 10 = 70, minus 7, is 63 — and the digits 6 and 3 add to 9, which is the check.