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Number and Operations Standard for Grades 6–8
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Expectations |
| 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;
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develop meaning for percents greater than 100 and less
than 1; |
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understand and use ratios and proportions to represent
quantitative relationships; |
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develop an understanding of large numbers and recognize
and appropriately use exponential, scientific, and calculator
notation; |
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use factors, multiples, prime factorization, and relatively
prime numbers to solve problems; |
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develop meaning for integers and represent and compare
quantities with them. |
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| Understand
meanings of operations and how they relate to one another |
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understand the meaning and effects of arithmetic operations
with fractions, decimals, and integers; |
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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; |
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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. |
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| Compute
fluently and make reasonable estimates |
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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;
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develop and analyze algorithms for computing with fractions,
decimals, and integers and develop fluency in their use;
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develop and use strategies to estimate the results of
rational-number computations and judge the reasonableness
of the results; |
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develop, analyze, and explain methods for solving problems
involving proportions, such as scaling and finding equivalent
ratios. |
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