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## Algebra |
## Geometry |
## Advanced Algebra |
## College and Career Readiness |

## Algebra

MATHEMATICAL MODELING | |

GA.A.MM.1 | Apply mathematics to real-life situations; model real-life phenomena using mathematics. |

GA.A.MM.1.1 | Explain applicable, mathematical problems using a mathematical model. |

GA.A.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 domains. |

GA.A.MM.1.3 | Use units of measure (linear, area, capacity, rates, and time) as a way to make sense of conceptual problems; identify, use, and record appropriate units of measure within the given framework, within data displays, and on graphs; convert units and rates using proportional reasoning given a conversion factor; use units within multi-step problems and formulas; interpret units of input and resulting units of output. |

GA.A.MM.1.4 | Use various mathematical representations and structures with this information to represent and solve real-life problems. |

GA.A.MM.1.5 | Define appropriate quantities for the purpose of descriptive modeling. |

FUNCTIONAL & GRAPHICAL REASONING -- function notation, modeling linear functions, linear vs. nonlinear comparisons | |

GA.A.FGR.2 | Construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain real-life phenomena. Use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and non-linear functions using parent graphs. |

GA.A.FGR.2.1 | Use mathematically applicable situations algebraically and graphically to build and interpret arithmetic sequences as functions whose domain is a subset of the integers. |

GA.A.FGR.2.2 | Construct and interpret the graph of a linear function that models real-life phenomena and represent key characteristics of the graph using formal notation. |

GA.A.FGR.2.3 | Relate the domain and range of a linear function to its graph and, where applicable, to the quantitative relationship it describes. Use formal interval and set notation to describe the domain and range of linear functions. |

GA.A.FGR.2.4 | Use function notation to build and evaluate linear functions for inputs in their domains and interpret statements that use function notation in terms of a mathematical framework. |

GA.A.FGR.2.5 | Analyze the difference between linear functions and nonlinear functions by informally analyzing the graphs of various parent functions (linear, quadratic, exponential, absolute value, square root, and cube root parent curves). |

GEOMETRIC & SPATIAL REASONING -- distance, midpoint, slope, area, and perimeter | |

GA.A.GSR.3 | Solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena. |

GA.A.GSR.3.1 | Solve real-life problems involving slope, parallel lines, perpendicular lines, area, and perimeter. |

GA.A. GSR.3.2 | Apply the distance formula, midpoint formula, and slope of line segments to solve real-world problems. |

PATTERNING & ALGEBRAIC REASONING -- linear inequalities and systems of linear inequalities | |

GA.A.PAR.4 | Create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model real-life phenomena. |

GA.A.PAR.4.1 | Create and solve linear inequalities in two variables to represent relationships between quantities including mathematically applicable situations; graph inequalities on coordinate axes with labels and scales. |

GA.A.PAR.4.2 | Represent constraints of linear inequalities and interpret data points as possible or not possible. |

GA.A.PAR.4.3 | Solve systems of linear inequalities by graphing, including systems representing a mathematically applicable situation. |

NUMERICAL REASONING - rational and irrational numbers, square roots and cube roots | |

GA.A.NR.5 | Investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots. |

GA.A.NR.5.1 | Rewrite algebraic and numeric expressions involving radicals. |

GA.A.NR.5.2 | Using numerical reasoning, show and explain that the sum or product of rational numbers is rational, the sum of a rational number and an irrational number is irrational, and the product of a nonzero rational number and an irrational number is irrational. |

PATTERNING & ALGEBRAIC REASONING -- quadratic expressions & equations | |

GA.A.PAR.6 | Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. |

GA.A.PAR.6.1 | Interpret quadratic expressions and parts of a quadratic expression that represent a quantity in terms of its context. |

GA.A.PAR.6.2 | Fluently choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the expression. |

GA.A.PAR.6.3 | Create and solve quadratic equations in one variable and explain the solution in the framework of applicable phenomena. |

GA.A.PAR.6.4 | Represent constraints by quadratic equations and interpret data points as possible or not possible in a modeling framework. |

FUNCTIONAL & GRAPHICAL REASONING -- quadratic functions | |

GA.A.FGR.7 | Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. |

GA.A.FGR.7.1 | Use function notation to build and evaluate quadratic functions for inputs in their domains and interpret statements that use function notation in terms of a given framework. |

GA.A.FGR.7.2 | Identify the effect on the graph generated by a quadratic function when replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. |

GA.A.FGR.7.3 | Graph and analyze the key characteristics of quadratic functions. |

GA.A.FGR.7.4 | Relate the domain and range of a quadratic function to its graph and, where applicable, to the quantitative relationship it describes. |

GA.A.FGR.7.5 | Rewrite a quadratic function representing a mathematically applicable situation to reveal the maximum or minimum value of the function it defines. Explain what the value describes in context. |

GA.A.FGR.7.6 | Create quadratic functions in two variables to represent relationships between quantities; graph quadratic functions on the coordinate axes with labels and scales. |

GA.A.FGR.7.7 | Estimate, calculate, and interpret the average rate of change of a quadratic function and make comparisons to the average rate of change of linear functions. |

GA.A.FGR.7.8 | Write a function defined by a quadratic expression in different but equivalent forms to reveal and explain different properties of the function. |

GA.A.FGR.7.9 | Compare characteristics of two functions each represented in a different way. |

PATTERNING & ALGEBRAIC REASONING -- exponential expressions and equations | |

GA.A.PAR.8 | Create and analyze exponential expressions and equations to represent and model real-life phenomena; solve exponential equations in mathematically applicable situations. |

GA.A.PAR.8.1 | Interpret exponential expressions and parts of an exponential expression that represent a quantity in terms of its framework. |

GA.A.PAR.8.2 | Create exponential equations in one variable and use them to solve problems, including mathematically applicable situations. |

GA.A.PAR.8.3 | Create exponential equations in two variables to represent relationships between quantities, including in mathematically applicable situations; graph equations on coordinate axes with labels and scales. |

GA.A.PAR.8.4 | Represent constraints by exponential equations and interpret data points as possible or not possible in a modeling environment. |

FUNCTIONAL & GRAPHICAL REASONING -- exponential functions | |

GA.A.FGR.9 | Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions. |

GA.A.FGR.9.1 | Use function notation to build and evaluate exponential functions for inputs in their domains and interpret statements that use function notation in terms of a context. |

GA.A.FGR.9.2 | Graph and analyze the key characteristics of simple exponential functions based on mathematically applicable situations. |

GA.A.FGR.9.3 | Identify the effect on the graph generated by an exponential function when replacing f(x) with f(x) + k, and k f(x), for specific values of k (both positive and negative); find the value of k given the graphs. |

GA.A.FGR.9.4 | Use mathematically applicable situations algebraically and graphically to build and interpret geometric sequences as functions whose domain is a subset of the integers. |

GA.A.FGR.9.5 | Compare characteristics of two functions each represented in a different way. |

DATA & STATISTICAL REASONING -- univariate data and single quantitative variables; bivariate data | |

GA.A.DSR.10 | Collect, analyze, and interpret univariate quantitative data to answer statistical investigative questions that compare groups to solve real-life problems; Represent bivariate data on a scatter plot and fit a function to the data to answer statistical questions and solve real-life problems. |

GA.A.DSR.10.1 | Use statistics appropriate to the shape of the data distribution to compare and represent center (median and mean) and variability (interquartile range, standard deviation) of two or more distributions by hand and using technology. |

GA.A.DSR.10.2 | Interpret differences in shape, center, and variability of the distributions based on the investigation, accounting for possible effects of extreme data points (outliers). |

GA.A.DSR.10.3 | Represent data on two quantitative variables on a scatter plot and describe how the variables are related. |

GA.A.DSR.10.4 | Interpret the slope (predicted rate of change) and the intercept (constant term) of a linear model based on the investigation of the data. |

GA.A.DSR.10.5 | Calculate the line of best fit and interpret the correlation coefficient, r, of a linear fit using technology. Use r to describe the strength of the goodness of fit of the regression. Use the linear function to make predictions and assess how reasonable the prediction is in context. |

GA.A.DSR.10.6 | Decide which type of function is most appropriate by observing graphed data. |

GA.A.DSR.10.7 | Distinguish between correlation and causation. |

## Geometry

MATHEMATICAL MODELING | |

GA.G.MM.1 | Apply mathematics to real-life situations; model real-life phenomena using mathematics. |

GA.G.MM.1.1 | Explain mathematically applicable problems using a mathematical model. |

GA.G.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. |

GA.G.MM.1.3 | Using abstract and quantitative reasoning, make decisions about information and data from a mathematically applicable situation. |

GA.G.MM.1.4 | Use various mathematical representations and structures with this information to represent and solve real-life problems. |

PATTERNING & ALGEBRAIC REASONING -- polynomial expressions | |

GA.G.PAR.2 | Interpret the structure of and perform operations with polynomials within a geometric framework. |

GA.G.PAR.2.1 | Interpret polynomial expressions of varying degrees that represent a quantity in terms of its given geometric framework. |

GA.G.PAR.2.2 | Perform operations with polynomials and prove that polynomials form a system analogous to the integers in that they are closed under these operations. |

GA.G.PAR.2.3 | Using algebraic reasoning, add, subtract, and multiply single variable polynomials. |

GEOMETRIC & SPATIAL REASONING -- congruence | |

GA.G.GSR.3 | Experiment with transformations in the plane to develop precise definitions for translations, rotations, and reflections and use these to describe symmetries and congruence to model and explain real-life phenomena. |

GA.G.GSR.3.1 | Use geometric reasoning and symmetries of regular polygons to develop definitions of rotations, reflections, and translations. |

GA.G.GSR.3.2 | Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines. |

GA.G.GSR.3.3 | Use geometric descriptions of rigid motions to draw the transformed figures and to predict the effect on a given figure. Describe a sequence of transformations from one figure to another and use transformation properties to determine congruence. |

GA.G.GSR.3.4 | Explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions. Use congruency criteria for triangles to solve problems and to prove relationships in geometric figures. |

GEOMETRIC & SPATIAL REASONING -- geometric foundations, constructions, and proof | |

GA.G.GSR.4 | Establish facts between angle relations and generate valid arguments to defend facts established. Prove theorems and solve geometric problems involving lines and angles to model and explain real-life phenomena. |

GA.G.GSR.4.1 | Use the undefined notions of point, line, line segment, plane, distance along a line segment, and distance around a circular arc to develop and use precise definitions and symbolic notations to prove theorems and solve geometric problems. |

GA.G.GSR.4.2 | Classify quadrilaterals in the coordinate plane by proving simple geometric theorems algebraically. |

GA.G.GSR.4.3 | Make formal geometric constructions with a variety of tools and methods. |

GA.G.GSR.4.4 | Prove and apply theorems about lines and angles to solve problems. |

GA.G.GSR.4.5 | Use geometric reasoning to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. |

GEOMETRIC & SPATIAL REASONING -- similarity | |

GA.G.GSR.5 | Describe dilations in terms of center and scale factor and use these terms to describe properties of dilations; use the precise definition of a dilation to describe similarity and establish the criterion for triangles to be similar; use these terms, definitions, and criterion to prove similarity, model, and explain real-life phenomena. |

GA.G.GSR.5.1 | Verify experimentally the properties of dilations. |

GA.G.GSR.5.2 | Given two figures, use and apply the definition of similarity in terms of similarity transformations. |

GA.G.GSR.5.3 | Use the properties of similarity transformations to establish criterion for two triangles to be similar. Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures. |

GA.G.GSR.5.4 | Construct formal proofs to justify and apply theorems about triangles. |

GEOMETRIC & SPATIAL REASONING -- right triangle trigonometry | |

GA.G.GSR.6 | Examine side ratios of similar triangles; use the relationship between right triangles to develop an understanding of sine, cosine, and tangent to solve mathematically applicable geometric problems and to model and explain real-life phenomena. |

GA.G.GSR.6.1 | Explain that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. |

GA.G.GSR.6.2 | Explain and use the relationship between the sine and cosine of complementary angles. |

GA.G.GSR.6.3 | Use trigonometric ratios and the Pythagorean Theorem to solve for sides and angles of right triangles in applied problems. |

GEOMETRIC & SPATIAL REASONING -- Trigonometry and the Unit Circle | |

GA.G.GSR.7 | Explore the concept of a radian measure and special right triangles. |

GA.G.GSR.7.1 | Explore and interpret a radian as the ratio of the arc length to the radius of a circle. |

GA.G.GSR.7.2 | Explore and explain the relationship between radian measures and degree measures and convert fluently between degree and radian measures. |

GA.G.GSR.7.3 | Use special right triangles on the unit circle to determine the values of sine, cosine, and tangent for 30° ( 𝜋/6), 45° ( 𝜋/4) and 60° ( 𝜋/3) angle measures. Use reflections of triangles to determine reference angles and identify coordinate values in all four quadrants of the coordinate plane. |

GEOMETRIC & SPATIAL REASONING -- circles | |

GA.G.GSR.8 | Examine and apply theorems involving circles; describe and derive arc length and area of a sector; and model and explain real-life frameworks involving circles. |

GA.G.GSR.8.1 | Identify and apply angle relationships formed by chords, tangents, secants and radii with circles. |

GA.G.GSR.8.2 | Using similarity, derive the fact that the length of the arc (arc length) intercepted by an angle is proportional to the radius; derive the formula for the area of a sector. Solve mathematically applicable problems involving applications of arc length and area of sector. |

GA.G.GSR.8.3 | Write and graph the equation of circles in standard form. |

GEOMETRIC & SPATIAL REASONING -- equations and measurement | |

GA.G.GSR.9 | Develop informal arguments for geometric formulas using dissection arguments, limit arguments, and Cavalieri’s principle; solve mathematically applicable problems involving volume; explore and visualize relationships between two-dimensional and three-dimensional objects to model and explain real-life phenomena. |

GA.G.GSR.9.1 | Use volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems including right and oblique solids. |

GA.G.GSR.9.2 | Use geometric shapes, their measures, and their properties to describe objects and approximate volumes. |

GA.G.GSR.9.3 | Apply concepts of density based on area and volume in modeling situations |

PROBABILISTIC REASONING -- compound events and expected values | |

GA.G.PR.10 | Solve problems involving the probability of compound events to make informed decisions; interpret expected value and measures of variability to analyze probability distributions. |

GA.G.PR.10.1 | Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events. Apply the Addition Rule conceptually, P(A or B)= P(A) + P(B)-P(A and B), and interpret the answers in context. |

GA.G.PR.10.2 | Apply and interpret the general Multiplication Rule conceptually to independent events of a sample space, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)] using contingency tables or tree diagrams. |

GA.G.PR.10.3 | Use conditional probability to interpret risk in terms of decision-making and investigate questions such as those involving false positives or false negatives from screening tests. |

GA.G.PR.10.4 | Define permutations and combinations and apply this understanding to compute probabilities of compound events and solve meaningful problems. |

GA.G.PR.10.5 | Interpret the probability distribution for a given random variable and interpret the expected value. |

GA.G.PR.10.6 | Develop a probability distribution for variables of interest using theoretical and empirical (observed) probabilities and calculate and interpret the expected value. |

GA.G.PR.10.7 | Calculate the expected value of a random variable and interpret it as the mean of a given probability distribution. |

GA.G.PR.10.8 | Compare the payoff values associated with the probability distribution for a random variable and make informed decisions based on expected value and measures of variability. |

DATA & STATISTICAL REASONING; PROBABLISTIC REASONING -- categorical data in two-way frequency tables; conditional probability | |

GA.G.DSR.11 | Examine real-life situations presented in a two-way frequency table to calculate probabilities, to model categorical data, and to explain real-life phenomena. |

GA.G.DSR.11.1 | Construct and summarize categorical data for two categories in two-way frequency tables. |

GA.G.DSR.11.2 | Use categorical data in two-way frequency tables to calculate and interpret probabilities based on the investigation. |

## Advanced Algebra

MATHEMATICAL MODELING | |

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

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

GA.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. |

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

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

DATA & STATISTICAL REASONING -- descriptive and inferential statistics | |

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

GA.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. |

GA.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. |

GA.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. |

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

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

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

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

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

FUNCTIONAL & GRAPHICAL REASONING -- exponential and logarithmic functions | |

GA.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. |

GA.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. |

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

GA.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. |

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

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

GA.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. |

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

FUNCTIONAL & GRAPHICAL REASONING -- radical functions | |

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

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

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

GA.AA.FGR.4.3 | Analyze and graph radical functions. |

GA.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. |

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

FUNCTIONAL & GRAPHICAL REASONING -- polynomial functions | |

GA.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. |

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

GA.AA.FGR.5.2 | Define complex numbers i such that i^2 = –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. |

GA.AA.FGR.5.3 | Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. |

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

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

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

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

GA.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. |

GA.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 identify key features of these polynomial functions. |

GA.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. |

GA.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. |

PATTERNING & ALGEBRAIC REASONING -- linear algebra and matrices | |

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

GA.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. |

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

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

GA.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. |

GEOMETRIC & SPATIAL REASONING -- Trigonometry and the Unit Circle | |

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

GA.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. |

GA.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. |

FUNCTIONAL & GRAPHICAL REASONING -- rational functions | |

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

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

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

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

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

## College and Career Readiness

MATHEMATICAL MODELING | |

GA.CRM.MM.1 | Apply mathematics to real-life situations; model real-life phenomena using mathematics. |

GA.CRM.MM.1.1 | Explain contextual, mathematical problems using a mathematical model. |

GA.CRM.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. |

GA.CRM.MM.1.3 | Using abstract and quantitative reasoning, make decisions about information and data from a contextual situation. |

GA.CRM.MM.1.4 | Use various mathematical representations and structures with this information to represent and solve real-life problems. |

NUMERICAL & QUANTITATIVE REASONING -- Real Number System | |

GA.CRM.NR.2 | Utilize exact and approximate calculations to quantify real-world phenomena and solve problems. |

GA.CRM.NR.2.1 | Through multi-step/multi-operational problems, perform mathematical operations on real numbers demonstrating fluency using the order of operations. |

GA.CRM.NR.2.2 | Represent and solve problems using proportional reasoning with ratios, rates, proportions, and scaling. |

GA.CRM.NR.2.3 | Apply the rules of exponents to simplify numerical expressions, extending the properties of exponents to rational exponents. |

GA.CRM.NR.2.4 | Perform mathematical operations on real numbers to include numerical radical expressions and complex fractions. |

GA.CRM.NR.2.5 | Estimate solutions to problems with real numbers and use the estimates to assess the reasonableness of results in the context of the problem. |

PATTERNING & ALGEBRAIC REASONING -- Expressions, Equations, & Inequalities | |

GA.CRM.PAR.3 | Construct expressions, equations, and inequalities, and use them to represent and solve problems by choosing appropriate procedures and interpreting solutions in context. |

GA.CRM.PAR.3.1 | Create equations in one variable and use them to solve problems. |

GA.CRM.PAR.3.2 | Create inequalities in one variable and use them to solve problems. |

GA.CRM.PAR.3.3 | Using multiple representations, solve equations and inequalities and use the solutions to draw reasonable conclusions about a situation being modeled, including possible constraints. |

GA.CRM.PAR.3.4 | Solve quadratic equations using a variety of methods. |

GA.CRM.PAR.3.5 | Rearrange literal equations to highlight a specified variable using the same reasoning as in solving equations. |

GA.CRM.PAR.3.6 | Solve inequalities in one variable graphically and algebraically. |

GA.CRM.PAR.3.7 | Using multiple methods, create and solve systems of linear equations and inequalities. |

GA.CRM.PAR.3.8 | Solve a simple system of equations consisting of a linear and a quadratic equation in two variables. algebraically and graphically. |

FUNCTIONAL & GRAPHICAL REASONING -- Building & Interpreting Functions | |

GA.CRM.FGR.4 | Define, build and interpret functions that arise in various contexts by applying knowledge of the characteristics of the different families of functions, and analyze the effects of parameters. |

GA.CRM.FGR.4.1 | Define a function through maps, sets, equations and graphs using function notation. |

GA.CRM.FGR.4.2 | Identify and sketch by hand the parent graph of functions expressed algebraically and show key characteristics of the graph using technology. |

GA.CRM.FGR.4.3 | Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function. |

GA.CRM.FGR.4.4 | Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph. |

GA.CRM.FGR.4.5 | Compare characteristics of two functions each represented in a different way. |

GA.CRM.FGR.4.6 | Construct linear and exponential functions, given a graph, a description of a relationship, or two input-output pairs. |

GA.CRM.FGR.4.7 | Construct arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect linear functions to arithmetic sequences and exponential functions to geometric sequences. |

GA.CRM.FGR.4.8 | Identify the effect on the parent graph of replacing f(x) by f(x) + k, kf(x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. |

GEOMETRIC & SPATIAL REASONING -- Measurement, Surface Area, Volume, & Right Triangle Trigonometry | |

GA.CRM.GR.5 | Reason deductively and inductively about figures and their properties and make sense of geometric situations using measurements in real-world contexts. |

GA.CRM.GSR.5.1 | Use the distance formula, midpoint formula or slope to verify simple geometric properties. |

GA.CRM.GSR.5.2 | Use coordinates to compute perimeters of polygons, circumference of circles and areas of triangles, rectangles and circles. |

GA.CRM.GSR.5.3 | Informally derive the formulas for the volume and surface area of a cylinder, sphere, prism, pyramid, and cone. |

GA.CRM.GSR.5.4 | Use formulas for finding the volume and surface area of spheres, right and oblique prisms, cylinders, pyramids, and cones. |

GA.CRM.GSR.5.5 | Apply the Pythagorean Theorem and trigonometric ratios to solve problems involving right triangles. |

DATA & STATISTICAL REASONING -- Interpreting Data & Calculating Probabilities of Compound Events | |

GA.CRM.DSR.6 | Make sense of and reason about variation in data using graphs, tables and probability models to solve problems and draw appropriate conclusions from solutions. |

GA.CRM.DSR.6.1 | Represent univariate data on the real number line. |

GA.CRM.DSR.6.2 | Calculate, compare, and interpret shape, center, and spread of two or more univariate data sets, accounting for possible effects of extreme data points. |

GA.CRM.DSR.6.3 | Summarize categorical data for two categories in two-way frequency tables using relative frequencies in the context of the data. |

GA.CRM.DSR.6.4 | Represent bivariate data on a scatter plot and describe how the variables are related in terms of strength and direction. |

GA.CRM.DSR.6.5 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. |

GA.CRM.DSR.6.6 | Compute using technology and interpret the correlation coefficient �r� of a linear fit. |

GA.CRM.DSR.6.7 | Distinguish between correlation and causation, and interpolation and extrapolation. |

GA.CRM.DSR.6.8 | Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events. |

GA.CRM.DSR.6.9 | Use the two-way frequency table to calculate conditional probabilities. |

GA.CRM.DSR.6.10 | Calculate the conditional probability of A given B. |