Times Table Grid — 12×12 — free printable diagram

How to read a 12×12 times table grid

This grid holds every multiplication fact from 1 × 1 = 1 up to 12 × 12 = 144. To find a product, follow the row for one number across and the column for the other down; the square where they meet is the answer. There are 144 products in the body of the grid.

Size

12 × 12

Products in the grid body

144

Smallest product

1 × 1 = 1

Largest product

12 × 12 = 144

The diagonal

the square numbers — 1, 4, 9, 16 … 144

Why it is symmetric

a × b = b × a, so the halves either side of the diagonal match

• Reading the grid is a two-step move, not a search: go along the row of the first number until you are under the column of the second. 7 × 8 and 8 × 7 land on different squares but hold the same number, 56, because multiplication can be done in either order.
• The squares running corner to corner are the square numbers — 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144 — because those are the cells where a number meets itself.
• The grid is a mirror image of itself across that diagonal. That halves what there is to learn: 144 products, but only 78 different facts.
• Each row is one times table on its own. Read across the 6 row and you have the 6 times table; read down the 6 column and you have the same numbers again.
• Patterns in the columns are worth pointing out: every product in the 5 column ends in 0 or 5, every product in the 10 column ends in 0, and the digits of each product in the 9 column add up to a multiple of 9 — 27 gives 9, and 99 gives 18, whose digits add to 9 in turn.