Why Are Rows and Columns Useful?

Step 1 of 5

Scattered things are slow to count.

A pile of twenty-four counters takes twenty-four steps and it is easy to double-count or miss one.

Step 2 of 5

A grid makes the structure visible.

Line them into four rows of six. Now you can see the shape of the number, and count six four times instead of one twenty-four times.

Step 3 of 5

An array shows why order does not matter.

Turn the grid a quarter turn and four rows of six become six rows of four. Same counters, so 4 × 6 must equal 6 × 4.

Step 4 of 5

It makes division obvious too.

Twenty-four shared between four is asking how long each row is. The same grid answers both multiplication and division questions.

Step 5 of 5

Grids are everywhere.

Egg boxes, chocolate bars, seats in a cinema, pixels on a screen, tiles on a floor. We arrange things in grids because it makes counting them easy.

This is exactly why children are shown times tables as grids — the picture makes the fact make sense.