Counting

Counting is a way of finding how many objects there are by matching each object with a number in a fixed order. When we count a group of toys, for example, we say 1, 2, 3, 4, and so on, giving each toy one number. The last number we say tells us how many objects are in the group. This idea is called the cardinal principle of counting.

The order in which the objects are counted does not change the total, as long as every object is counted once and none is counted twice. Counting can also be used without physical objects. We count days on a calendar, steps on a journey, points in a game, or items in a list. The numbers used for ordinary counting are called natural numbers; depending on the mathematical convention, this sequence begins with 0 or with 1.

Learning to count helps children understand that numbers represent quantities, not simply a sequence of words to memorize. Number words can be connected to written symbols, such as 5, and to groups containing five objects. As counting skills develop, children learn to count forward and backward, compare quantities, recognize which number comes before or after another, and eventually use counting to solve simple problems.

Counting by twos, fives, or tens is also useful for finding totals more efficiently. The ability to count accurately is an important foundation for later work with addition, subtraction, measurement, patterns, and other areas of mathematics. Although counting seems simple, it involves understanding both the order of numbers and the relationship between numbers and quantities.