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 rationalnumber
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.

