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Number and Operations Standard for Grades 3-5




Instructional programs from prekindergarten through grade 12 should enable all students to—  In grades 3–5 all students should— 
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
  • understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
  • recognize equivalent representations for the same number and generate them by decomposing and composing numbers;
  • develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
  • use models, benchmarks, and equivalent forms to judge the size of fractions;
  • recognize and generate equivalent forms of commonly used fractions, decimals, and percents;
  • explore numbers less than 0 by extending the number line and through familiar applications;
  • describe classes of numbers according to characteristics such as the nature of their factors.
Understand meanings of operations and how they relate to one another
  • understand various meanings of multiplication and division;
  • understand the effects of multiplying and dividing whole numbers;
  • identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems;
  • understand and use properties of operations, such as the distributivity of multiplication over addition.
Compute fluently and make reasonable estimates
  • develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50 ;
  • develop fluency in adding, subtracting, multiplying, and dividing whole numbers;
  • develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results;
  • develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;
  • use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals;
  • select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

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