Multiplication chart

A multiplication table is the multiplication operation laid out as a grid: the cell at row a, column b holds a × b.

It is symmetric, which halves the work

Multiplication is commutative, so the table mirrors along the diagonal — 7 × 8 and 8 × 7 are the same cell reflected. A learner memorising the 12 × 12 table has 144 cells but only 78 distinct facts, and rather fewer once the easy rows are accounted for.

The rows worth learning first

• 1 and 10 are free.
• 2, 4, 8 are repeated doubling.
• 5 ends in 0 or 5, and is half of the 10 row.
• 9 has the digit trick: the digits of each answer sum to 9, and the tens digit is one less than the multiplier.
• 11 up to 9 is just the digit repeated.

That leaves a genuinely small set of hard facts — 6×7, 6×8, 7×8, 7×9 and a handful of others. Naming them explicitly is more effective than drilling the whole grid.

The diagonal

The highlighted diagonal is the perfect squares: 1, 4, 9, 16, 25. The gaps between consecutive squares are the odd numbers — 3, 5, 7, 9 — which is a neat visual proof that the sum of the first n odd numbers is n².