How Many In All

When you count a group of things, something special happens at the end: the very last number you say tells you how many there are altogether. That last number names the size of the whole group.

So if you count five frogs — “one, two, three, four, five” — you don't just stop at 5. The 5 means there are 5 frogs in all. The grown-up name for this idea is cardinality.

Watch: things pop in one at a time and the count climbs with them. When the last one appears, look at the final number — it lights up to show how many in all. Replay it and a different amount appears each time.

The number you land on at the end is the answer to “how many?”. Counting the same group again, even in a different order, always ends on the same last number — that's the amount of the whole group.

Khan Academy counts small groups and says how many here: