Principles and Standards for School Mathematics

Algebra Standard

Algebra Standard (pre-K - 2)

sort, classify, and order objects by size, number, and other properties;


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recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another;


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analyze how both repeating and growing patterns are generated.


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Algebra Standard (3 - 5)

describe, extend, and make generalizations about geometric and numeric patterns;


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represent and analyze patterns and functions, using words, tables, and graphs.


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Algebra Standard (6 - 8)

represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;


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relate and compare different forms of representation for a relationship;


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identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.


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Algebra Standard (9 - 12)

generalize patterns using explicitly defined and recursively defined functions;


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understand relations and functions and select, convert flexibly among, and use various representations for them;


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analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;


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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;


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understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions;


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interpret representations of functions of two variables.


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