Chapter 3 is at the heart of what many consider to be elementary school mathematics: addition, subtraction, multiplication and division. There is also a great deal of research which describes how children think about these four basic operations. As a result, this chapter is longer than all the others and is rich with descriptions of children’s mathematical thinking. The first section describes some manipulative models of our number system. Section two describes how addition and subtraction are counting activities for children. Section three describes how children come to know multiplication and division. Section four describes how children understand the basic properties of numbers such as commutative and associative. Section five gives many examples of how children may develop their own self-generated algorithms as well as describing ways to help children understand the standard algorithms. The last section describes how children estimate and use mental math. One perspective of computation instruction is that it should focus on “the ability to apply meaningfully learned procedures flexibly and creatively” (Hatano, 2003) rather than rote memorization.