Math Standards

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Texas Math Standards (TEKS)

a) Basic understandings.

(3) Functions, equations, and their relationship. The study of functions, equations, and their relationship is central to all of mathematics. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations.

            (5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, numerical, algorithmic, graphical), tools, and technology, including, but not limited to, powerful and accessible hand-held calculators and computers with graphing capabilities and model mathematical situations to solve meaningful problems.

(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof.

(b) Foundations for functions: knowledge and skills and performance descriptions.

(1) The student uses properties and attributes of functions and applies functions to problem situations. Following are performance descriptions.

(A) For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations.

(B) In solving problems, the student collects data and records results, organizes the data, makes scatterplots, fits the curves to the appropriate parent function, interprets the results, and proceeds to model, predict, and make decisions and critical judgments.

(2) The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. Following are performance descriptions.

                        (C) The student connects the function notation of y = and f(x) =.

(c) Algebra and geometry: knowledge and skills and performance descriptions.

(1) The student connects algebraic and geometric representations of functions. Following are performance descriptions.

(A) The student identifies and sketches graphs of parent functions, including linear (y = x), quadratic (y = x2), square root (y = ึ x), inverse (y = 1/x), exponential (y = ax), and logarithmic (y = logax) functions.

(B) The student extends parent functions with parameters such as m in  y = mx and describes parameter changes on the graph of parent functions.

National Math Standards

 Understand patterns, relations, and functions

           

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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

 

Represent and analyze mathematical situations and structures using algebraic symbols

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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.

 

Use mathematical models to represent and understand quantitative relationships

 

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identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;

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use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts;

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draw reasonable conclusions about a situation being modeled.

 

Analyze change in various contexts

 

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