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Skills available for Georgia high school math standards

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K-12 Mathematics Standards: Advanced Algebra (Algebra 2) K-12 Mathematics Standards: Advanced Algebra (Algebra 2)
K-12 Mathematics Standards: Algebra 1 K-12 Mathematics Standards: Algebra 1
K-12 Mathematics Standards: Calculus K-12 Mathematics Standards: Calculus
K-12 Mathematics Standards: Geometry K-12 Mathematics Standards: Geometry
K-12 Mathematics Standards: Mathematical Practices K-12 Mathematics Standards: Mathematical Practices
K-12 Mathematics Standards: Precalculus K-12 Mathematics Standards: Precalculus

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MM Mathematical Modeling

AA.MM.1 Apply mathematics to real-life situations; model real-life phenomena using mathematics.
- AA.MM.1.1 Explain applicable, mathematical problems using a mathematical model.
- AA.MM.1.2 Create mathematical models to explain phenomena that exist in the natural sciences, social sciences, liberal arts, fine and performing arts, and/or humanities contexts.
- AA.MM.1.3 Using abstract and quantitative reasoning, make decisions about information and data from a mathematical, applicable situation.
- AA.MM.1.4 Use various mathematical representations and structures to represent and solve real-life problems.

DSR Data & Statistical Reasoning

Descriptive and inferential statistics
- AA.DSR.2 Communicate descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting real-world data.
  - AA.DSR.2.1 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. Distinguish between primary and secondary data and how it affects the types of conclusions that can be drawn.
    - Experiment design (A2-RR.8)
  - AA.DSR.2.2 When collecting and considering data, critically evaluate ethics, privacy, potential bias, and confounding variables along with their implications for interpretation in answering a statistical investigative question. Implement strategies for organizing and preparing big data sets.
    - Identify biased samples (A2-RR.1)
  - AA.DSR.2.3 Distinguish between population distributions, sample data distributions, and sampling distributions. Use sample statistics to make inferences about population parameters based on a random sample from that population and to communicate conclusions using appropriate statistical language.
    - Find values of normal variables (A2-QQ.5)
    - Distributions of sample means (A2-QQ.6)
  - AA.DSR.2.4 Calculate and interpret z-scores as a measure of relative standing and as a method of standardizing units.
    - Find z-values (A2-QQ.4)
  - AA.DSR.2.5 Given a normally distributed population, estimate percentages using the Empirical Rule, z-scores, and technology.
    - Find probabilities using the normal distribution I (A2-QQ.2)
    - Find probabilities using the normal distribution II (A2-QQ.3)
  - AA.DSR.2.6 Model sample-to-sample variability in sampling distributions of a statistic using simulations taken from a given population.
  - AA.DSR.2.7 Given a margin of error, develop and compare confidence intervals of different models to make conclusions about reliability.
  - AA.DSR.2.8 Summarize and evaluate reports based on data for appropriateness of study design, analysis methods, and statistical measures used.
    - Interpret confidence intervals for population means (A2-RR.7)
    - Analyze the results of an experiment using simulations (A2-RR.9)

FGR Functional & Graphical Reasoning

Exponential and logarithmic functions
- AA.FGR.3 Explore and analyze structures and patterns for exponential and logarithmic functions and use exponential and logarithmic expressions, equations, and functions to model real-life phenomena.
  - AA.FGR.3.1 Find the inverse of exponential and logarithmic functions using equations, tables, and graphs, limiting the domain of inverses where necessary to maintain functionality, and prove by composition or verify by inspection that one function is the inverse of another.
  - AA.FGR.3.2 Analyze, graph, and compare exponential and logarithmic functions.
  - AA.FGR.3.3 Use the definition of a logarithm, logarithmic properties, and the inverse relationship between exponential and logarithmic functions to solve problems in context.
  - AA.FGR.3.4 Create exponential equations and use logarithms to solve mathematical, applicable problems for which only one variable is unknown.
  - AA.FGR.3.5 Create and interpret logarithmic equations in one variable and use them to solve problems.
  - AA.FGR.3.6 Create, interpret, and solve exponential equations to represent relationships between quantities and analyze the relationships numerically with tables, algebraically, and graphically.
    - Exponential functions over unit intervals (A2-Z.6)
  - AA.FGR.3.7 Create, interpret, and solve logarithmic equations in two or more variables to represent relationships between quantities.
Radical functions
- AA.FGR.4 Explore and analyze structures and patterns for radical functions and use radical expressions, equations, and functions to model real-life phenomena.
  - AA.FGR.4.1 Rewrite radical expressions as expressions with rational exponents. Extend the properties of integer exponents to rational exponents.
  - AA.FGR.4.2 Solve radical equations in one variable, and give examples showing how extraneous solutions may arise.
    - Solve radical equations (A2-S.4)
  - AA.FGR.4.3 Analyze and graph radical functions.
    - Domain and range of radical functions (A2-S.1)
    - Graph square root functions (A2-S.2)
  - AA.FGR.4.4 Create, interpret and solve radical equations with one unknown value and use them to solve problems that model real-world situations.
  - AA.FGR.4.5 Create, interpret, and solve radical equations in two or more variables to represent relationships between quantities.
Polynomial functions
- AA.FGR.5 Extend exploration of quadratic solutions to include real and non-real numbers and explore how these numbers behave under familiar operations and within real-world situations; create polynomial expressions, solve polynomial equations, graph polynomial functions, and model real-world phenomena.
  - AA.FGR.5.1 Graph and analyze quadratic functions in contextual situations and include analysis of data sets with regressions.
  - AA.FGR.5.2 Define complex numbers i such that i² = -1 and show that every complex number has the form a + bi where a and b are real numbers and that the complex conjugate is a - bi.
  - AA.FGR.5.3 Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
    - Add and subtract complex numbers (A2-K.2)
    - Multiply complex numbers (A2-K.4)
  - AA.FGR.5.4 Use the structure of an expression to factor quadratics.
  - AA.FGR.5.5 Write and solve quadratic equations and inequalities with real coefficients and use the solution to explain a mathematical, applicable situation.
  - AA.FGR.5.6 Solve systems of quadratic and linear functions to determine points of intersection.
    - Solve a system of linear and quadratic equations by graphing: parabolas (A2-P.1)
  - AA.FGR.5.7 Create and analyze quadratic equations to represent relationships between quantities as a model for contextual situations.
  - AA.FGR.5.8 Identify the number of zeros that exist for any polynomial based upon the greatest degree of the polynomial and the end behavior of the polynomial by observing the sign of the leading coefficient.
    - Fundamental Theorem of Algebra (A2-Q.8)
    - Match polynomials and graphs using end behavior (A2-Q.9)
  - AA.FGR.5.9 Identify zeros of polynomial functions using technology or pre-factored polynomials and use the zeros to construct a graph of the function defined by the polynomial function. Analyze and identify key features of these polynomial functions.
  - AA.FGR.5.10 Use the structure of an expression to factor polynomials, including the sum of cubes, the difference of cubes, and higher-order polynomials that may be expressed as a quadratic within a quadratic.
  - AA.FGR.5.11 Using all the zeros of a polynomial function, list all the factors and multiply to write a multiple of the polynomial function in standard form.
    - Multiply polynomials (A2-L.3)
    - Write a polynomial from its roots (A2-Q.3)
- AA.FGR.8 Analyze the behaviors of rational functions to model applicable, mathematical problems.
  - AA.FGR.8.1 Rewrite simple rational expressions in equivalent forms.
    - Divide polynomials using long division (A2-L.4)
    - Simplify rational expressions (A2-X.4)
  - AA.FGR.8.2 Add, subtract, multiply and divide rational expressions, including problems in context and express rational expressions in irreducible form.
    - Multiply and divide rational expressions (A2-X.5)
    - Add and subtract rational expressions (A2-X.6)
  - AA.FGR.8.3 Graph rational functions, identifying key characteristics.
    - Rational functions: asymptotes and excluded values (A2-X.1)
  - AA.FGR.8.4 Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise.
    - Solve rational equations (A2-X.8)

PAR Patterning & Algebraic Reasoning

Linear algebra and matrices
- AA.PAR.6 Represent data with matrices, perform mathematical operations, and solve systems of linear equations leading to real-world linear programming applications.
  - AA.PAR.6.1 Use matrices to represent data, and perform mathematical operations with matrices and scalars, demonstrating that some properties of real numbers hold for matrices, but that others do not.
  - AA.PAR.6.2 Rewrite a system of linear equations using a matrix representation.
    - Solve a system of equations using augmented matrices (A2-TT.18)
    - Solve a system of equations using augmented matrices: word problems (A2-TT.19)
  - AA.PAR.6.3 Use the inverse of an invertible matrix to solve systems of linear equations.
    - Solve matrix equations using inverses (A2-TT.14)
  - AA.PAR.6.4 Utilize linear programming to represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as solutions or non-solutions under the established constraints in real-world problems.
    - Find the vertices of a solution set for a system of linear inequalities (A2-F.5)
    - Linear programming (A2-F.6)

GSR Geometric & Spatial Reasoning

Trigonometry and the unit circle
- AA.GSR.7 Develop an introductory understanding of the unit circle; solve trigonometric equations using the unit circle.
  - AA.GSR.7.1 Define the three basic trigonometric ratios in terms of x, y, and r using the unit circle centered at the origin of the coordinate plane.
    - Find trigonometric ratios using the unit circle (A2-II.6)
    - Sin, cos, and tan of special angles (A2-II.7)
  - AA.GSR.7.2 Apply understanding of the angle measures and coordinates of the unit circle to solve practical, real-life problems involving trigonometric equations.

Georgia

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MM Mathematical Modeling

AA.MM.1 Apply mathematics to real-life situations; model real-life phenomena using mathematics.

AA.MM.1.1 Explain applicable, mathematical problems using a mathematical model.

AA.MM.1.2 Create mathematical models to explain phenomena that exist in the natural sciences, social sciences, liberal arts, fine and performing arts, and/or humanities contexts.

AA.MM.1.3 Using abstract and quantitative reasoning, make decisions about information and data from a mathematical, applicable situation.

AA.MM.1.4 Use various mathematical representations and structures to represent and solve real-life problems.

DSR Data & Statistical Reasoning

Descriptive and inferential statistics

AA.DSR.2 Communicate descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting real-world data.

AA.DSR.2.1 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. Distinguish between primary and secondary data and how it affects the types of conclusions that can be drawn.

AA.DSR.2.2 When collecting and considering data, critically evaluate ethics, privacy, potential bias, and confounding variables along with their implications for interpretation in answering a statistical investigative question. Implement strategies for organizing and preparing big data sets.

AA.DSR.2.3 Distinguish between population distributions, sample data distributions, and sampling distributions. Use sample statistics to make inferences about population parameters based on a random sample from that population and to communicate conclusions using appropriate statistical language.

AA.DSR.2.4 Calculate and interpret z-scores as a measure of relative standing and as a method of standardizing units.

AA.DSR.2.5 Given a normally distributed population, estimate percentages using the Empirical Rule, z-scores, and technology.

AA.DSR.2.6 Model sample-to-sample variability in sampling distributions of a statistic using simulations taken from a given population.

AA.DSR.2.7 Given a margin of error, develop and compare confidence intervals of different models to make conclusions about reliability.

AA.DSR.2.8 Summarize and evaluate reports based on data for appropriateness of study design, analysis methods, and statistical measures used.

FGR Functional & Graphical Reasoning

Exponential and logarithmic functions

AA.FGR.3 Explore and analyze structures and patterns for exponential and logarithmic functions and use exponential and logarithmic expressions, equations, and functions to model real-life phenomena.

AA.FGR.3.1 Find the inverse of exponential and logarithmic functions using equations, tables, and graphs, limiting the domain of inverses where necessary to maintain functionality, and prove by composition or verify by inspection that one function is the inverse of another.

AA.FGR.3.2 Analyze, graph, and compare exponential and logarithmic functions.

AA.FGR.3.3 Use the definition of a logarithm, logarithmic properties, and the inverse relationship between exponential and logarithmic functions to solve problems in context.

AA.FGR.3.4 Create exponential equations and use logarithms to solve mathematical, applicable problems for which only one variable is unknown.

AA.FGR.3.5 Create and interpret logarithmic equations in one variable and use them to solve problems.

AA.FGR.3.6 Create, interpret, and solve exponential equations to represent relationships between quantities and analyze the relationships numerically with tables, algebraically, and graphically.

AA.FGR.3.7 Create, interpret, and solve logarithmic equations in two or more variables to represent relationships between quantities.

Radical functions

AA.FGR.4 Explore and analyze structures and patterns for radical functions and use radical expressions, equations, and functions to model real-life phenomena.

AA.FGR.4.1 Rewrite radical expressions as expressions with rational exponents. Extend the properties of integer exponents to rational exponents.

AA.FGR.4.2 Solve radical equations in one variable, and give examples showing how extraneous solutions may arise.

AA.FGR.4.3 Analyze and graph radical functions.

AA.FGR.4.4 Create, interpret and solve radical equations with one unknown value and use them to solve problems that model real-world situations.

AA.FGR.4.5 Create, interpret, and solve radical equations in two or more variables to represent relationships between quantities.

Polynomial functions

AA.FGR.5.1 Graph and analyze quadratic functions in contextual situations and include analysis of data sets with regressions.

AA.FGR.5.2 Define complex numbers i such that i² = -1 and show that every complex number has the form a + bi where a and b are real numbers and that the complex conjugate is a - bi.

AA.FGR.5.3 Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

AA.FGR.5.4 Use the structure of an expression to factor quadratics.

AA.FGR.5.5 Write and solve quadratic equations and inequalities with real coefficients and use the solution to explain a mathematical, applicable situation.

AA.FGR.5.6 Solve systems of quadratic and linear functions to determine points of intersection.

AA.FGR.5.7 Create and analyze quadratic equations to represent relationships between quantities as a model for contextual situations.

AA.FGR.5.8 Identify the number of zeros that exist for any polynomial based upon the greatest degree of the polynomial and the end behavior of the polynomial by observing the sign of the leading coefficient.

AA.FGR.5.9 Identify zeros of polynomial functions using technology or pre-factored polynomials and use the zeros to construct a graph of the function defined by the polynomial function. Analyze and identify key features of these polynomial functions.

AA.FGR.5.10 Use the structure of an expression to factor polynomials, including the sum of cubes, the difference of cubes, and higher-order polynomials that may be expressed as a quadratic within a quadratic.

AA.FGR.5.11 Using all the zeros of a polynomial function, list all the factors and multiply to write a multiple of the polynomial function in standard form.

AA.FGR.8 Analyze the behaviors of rational functions to model applicable, mathematical problems.

AA.FGR.8.1 Rewrite simple rational expressions in equivalent forms.

AA.FGR.8.2 Add, subtract, multiply and divide rational expressions, including problems in context and express rational expressions in irreducible form.

AA.FGR.8.3 Graph rational functions, identifying key characteristics.

AA.FGR.8.4 Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise.

PAR Patterning & Algebraic Reasoning

Linear algebra and matrices

AA.PAR.6 Represent data with matrices, perform mathematical operations, and solve systems of linear equations leading to real-world linear programming applications.

AA.PAR.6.1 Use matrices to represent data, and perform mathematical operations with matrices and scalars, demonstrating that some properties of real numbers hold for matrices, but that others do not.

AA.PAR.6.2 Rewrite a system of linear equations using a matrix representation.

AA.PAR.6.3 Use the inverse of an invertible matrix to solve systems of linear equations.

AA.PAR.6.4 Utilize linear programming to represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as solutions or non-solutions under the established constraints in real-world problems.

GSR Geometric & Spatial Reasoning

Trigonometry and the unit circle

AA.GSR.7 Develop an introductory understanding of the unit circle; solve trigonometric equations using the unit circle.

AA.GSR.7.1 Define the three basic trigonometric ratios in terms of x, y, and r using the unit circle centered at the origin of the coordinate plane.

AA.GSR.7.2 Apply understanding of the angle measures and coordinates of the unit circle to solve practical, real-life problems involving trigonometric equations.