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Algebra Standard for Grades 9-12




Instructional programs from prekindergarten through grade 12 should enable all students to—  In grades 9–12 all students should— 

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.

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