A counting number is any of the numbers you use when you count things: 1, 2, 3, 4, 5, and so on forever. These are the first numbers you learned as a small child, probably by counting toys or crackers or your fingers.

Counting numbers are also called natural numbers or positive integers in many school settings. They start at 1 and continue infinitely, with no largest counting number. Notice what's missing: zero usually isn't a counting number (you don't say “zero, one, two” when you start counting), and neither are fractions, decimals, or negative numbers. You can't have 2.5 apples in a basket when you're counting them, you have either 2 or 3.

Mathematicians sometimes debate whether zero should be included as a counting number, and some definitions of natural numbers do include zero. But in most elementary contexts, counting numbers begin at 1. The term helps mathematicians be precise about which numbers they're discussing, since there are many different types of numbers: whole numbers (which add zero to the counting numbers), integers (which include negative numbers), rational numbers (fractions and decimals), and more.

When your teacher asks you to “name three counting numbers greater than 10,” they want answers like 11, 12, and 13, not 10.5 or -12.