K-2
3-5
Number pervades all areas of mathematics. Students with number sense naturally decompose numbers, use particular numbers as referents, solve problems using the relationships among operations and knowledge about the base-ten system, estimate a reasonable result for a problem, and have a disposition to make sense of numbers, problems, and results. For example, children in the lower elementary grades can learn that numbers can be decomposed and thought about in many different ways--that 24 is 2 tens and 4 ones and also two sets of 12.
Computational fluency--having and using efficient and accurate methods for computing--is essential. Students should be able to perform computations in different ways, including mental calculations, estimation, and paper-and-pencil calculations using mathematical sound algorithms. Computational fluency should develop in tandem with understanding. (Principles and Standards for School Mathematics: An Overview, NCTM)