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Number and Operations


Instructional programs from prekindergarten through grade 12 should enable all students to--
  • understand numbers, ways of representing numbers, relationships among numbers, and number systems;
  • understand meanings of operations and how they relate to one another;
  • compute fluently and make reasonable estimates.

Number pervades all areas of mathematics. The other four Content Standards as well as all five Process Standards are grounded in number.

Central to the Number and Operations Standard is the development of number sense. 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 mathematically sound algorithms. All students should use calculators at appropriate times, setting the calculator aside when the instructional focus is on developing computational algorithms. Computational fluency should develop in tandem with understanding.

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