Principles and Standards for School Mathematics

Algebra Standard

Algebra Standard (pre-K - 2)

illustrate general principles and properties of operations, such as commutativity, using specific numbers;


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use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.


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Algebra Standard (3 - 5)

identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers;


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represent the idea of a variable as an unknown quantity using a letter or a symbol;


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express mathematical relationships using equations.


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Algebra Standard (6 - 8)

develop an initial conceptual understanding of different uses of variables;


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explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;


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use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;


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recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.


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Algebra Standard (9 - 12)

understand the meaning of equivalent forms of expressions, equations, inequalities, and relations;


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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;


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use symbolic algebra to represent and explain mathematical relationships;


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use a variety of symbolic representations, including recursive and parametric equations, for functions and relations;


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judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.


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