Multiplication starts with equal groups

Three bowls, two pieces of fruit in each

Imagine 3 bowls. Put 2 clementines in every bowl. Each bowl has the same amount: that is what “equal groups” means.

1. The first bowl gives you two clementines.
2. The second bowl adds two more. You now have four.
3. The third bowl adds another two. You now have six.

You could write this as 2 + 2 + 2 = 6. Multiplication gives us a shorter way to describe those equal groups.

Build your own groups

Draw three circles and put two dots in each. Count the dots or add one group at a time: two, four, six.

Keep the three circles but put four dots in each. Now you have twelve. More dots in every group means more dots altogether.

A shorter way to write equal groups

The sign × means “times”. In this lesson, 3 × 2 means “three groups of two”. We counted six clementines, so 3 × 2 = 6.

The answer to a multiplication is called the product. Here, the product is six. You may see an asterisk, *, used for multiplication on a computer.

The arrangement changes, but the total stays six. You can check this by moving six real counters into those groups.

The groups must really be equal

Suppose one bowl has 2 clementines and another has 3. That is not two groups of two. The bowls hold different amounts.

Add the actual amounts instead: two and three make five. The equal-groups shortcut only fits when every group has the same size.

What about three empty bowls? Each holds zero clementines. Altogether there are still none: 3 × 0 = 0.

Try four pairs

There are four pairs of socks. A pair means two socks. How many socks are there?

You have now met adding, taking away and equal groups. If a sum feels slippery, sketch the groups before counting them.

For a later challenge, try counting ten groups and one more. For now, understanding the small groups is enough.

For the full picture, explore seven friendly starting points for basic arithmetic.