Education World ® U.S. Education Standards: National: Math: Algebra: 9

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A L G E B R A -- G R A D E S 9 - 12

In grades 9-12 all students should

NM-ALG.9-12.1: Understand patterns, relations, and functions

NM-ALG.9-12.2: Represent and analyze mathematical situations and structures using algebraic symbols

NM-ALG.9-12.3: Use mathematical models to represent and understand quantitative relationships

generalize patterns using explicitly defined and recursively defined functions;
understand relations and functions and select, convert flexibly among, and use various representations for them;
analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;
understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions;
understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions;
interpret representations of functions of two variables.

understand the meaning of equivalent forms of expressions, equations, inequalities, and relations;
write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency -- mentally or with paper and pencil in simple cases and using technology in all cases;
use symbolic algebra to represent and explain mathematical relationships;
use a variety of symbolic representations, including recursive and parametric equations, for functions and relations;
judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.

identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts;
draw reasonable conclusions about a situation being modeled.