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National Math Educational Standards as Correlated to MathTrax

National Council of Teachers of Mathematics, Grades 9-12

http://standards.nctm.org/document/chapter7/index.htm

Algebra

Understand patterns, relations, and functions

• 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

Represent and analyze mathematical situations and structures using algebraic symbols

• 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.

Use mathematical models to represent and understand quantitative relationships

• 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.

Analyze change in various contexts

• approximate and interpret rates of change from graphical and numerical data.