An accessible introduction to mathematical ideas basic to counting. Counting depends on mathematical ideas, including the pattern and structure of our number system, the magnitude of numbers, and how numbers can be decomposed and combined.
The Mathematics of Counting
There is an ordered sequence of number names. Counting involves using the same sequence each time, starting with one. Extending the counting sequence is accomplished by repeating certain aspects of the previously used numbers in a structured way (according to our base-ten number system)
Exactly one number from the counting sequence is assigned to each object in the collection
The last number assigned to an object in counting the collection indicates the total quantity of objects in the collection