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Number and Operations Standard for Grades 6-8



Instructional programs from prekindergarten through grade 12 should enable all students to—  In grades 6–8 all students should— 
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
  • work flexibly with fractions, decimals, and percents to solve problems;
  • compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line;
  • develop meaning for percents greater than 100 and less than 1;
  • understand and use ratios and proportions to represent quantitative relationships;
  • develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation;
  • use factors, multiples, prime factorization, and relatively prime numbers to solve problems;
  • develop meaning for integers and represent and compare quantities with them.
Understand meanings of operations and how they relate to one another
  • understand the meaning and effects of arithmetic operations with fractions, decimals, and integers;
  • use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals;
  • understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.
Compute fluently and make reasonable estimates
  • select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods;
  • develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use;
  • develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results;
  • develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

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