Counting numbers

Counting numbers are the numbers 1, 2, 3, 4, 5, and so on. They go on without end. Negative numbers, 0, fractions, and decimals are not included as part of the counting numbers.

Counting numbers are the basis of early arithmetic. In order to learn operations such as addition and subtraction, we first need to have a firm grasp of counting. Counting numbers helps build the concept of counting, as they are used to name the number in a set of objects. They allow us to quantitatively specify how many cars there are in a parking lot, the number of oranges in the refrigerator, etc. It therefore makes sense that negative numbers, fractions, and decimals are not included, since counting numbers assume that the objects being counted are whole (cannot be divided into smaller parts). We also can't count objects that don't exist, so it makes sense that 0 is also typically not included in the counting numbers.

Below is a number line that represents the counting numbers. Only the numbers 1-11 are explicitly shown, but the arrow at the end of the number line indicates that the numbers continue following the same pattern through infinity. On the left, the dot indicates that the number line does not continue to the left.

Counting numbers are also referred to as natural numbers, but can more specifically be defined as the non-negative integers, not including 0. When 0 is included, the set of numbers is referred to as the whole numbers.

The terms whole number, natural number, and counting number are generally vague. They can be helpful when first learning about the various sets of numbers, but once we learn the concept of integers, it is often more efficient and clearer to describe sets of numbers in terms of integers.

Counting methods

There are two commonly used methods of teaching/learning counting: finger counting and counting tangible objects.

Finger counting

In finger counting, each finger represents one digit. Depending on the region, the thumb or the index finger may be used to represent the number 1. Use whichever is more comfortable.

In cases where the thumb represents 1, the index finger is 2, the middle finger is 3, the ring finger is 4, and the pinky is 5. The second hand is then used with the thumb starting as 6, and the pinky being 10.

In cases where the index finger represents 1, the middle finger is 2, the ring finger is 3, the pinky is 4, and the thumb is 5. The second hand is then used, with the index finger starting as 6, and the thumb being 10.

Other systems may be used as well, but the above two are the most common. In either case, a person who is counting to 10 would start on one hand with a closed fist then raise each finger based on the preferred system as they count up to 10. Once they reach 10, they can start over to count 11 onwards, continuing in the same manner every 10 numbers.

Counting objects

Another more visual method for counting involves counting and moving physical objects. Start with a given number of objects on one side, say 3, then move 1 object at a time while counting it until all 3 objects are moved to the other side, as shown in the figure below. This can help with conceptualizing numbers and seeing that 3 single objects make up a total of 3 objects.

Counting objects can also be used as an introduction to addition and subtraction where addition is counting up and subtraction is counting down. Like the above example, start with a given number of objects and designate some space (such as your right side) as the reference space that we either place objects into or remove objects from. Counting objects into the chosen space symbolizes addition, while counting objects out of the space symbolizes subtraction.