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AL.AC.ALGEBRAIC CONNECTIONS
ALGEBRAIC CONNECTIONS
GEOMETRY: Symmetry
AC.9. Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio.
AC.1. Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation.
AF.4. Read, interpret, and algebraically model stock ownership and transaction data.
AF.4.a. Constructing, interpreting, and analyzing scatterplots by utilizing linear, quadratic, and regression equations to see a complete picture of supply, demand, revenue, and profit
AF.15.c. Using exponential growth and decay equations that model given relationships between quantities
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Employment and Income Taxes
AF.7. Use linear and polynomial functions to model Internal Revenue Service and Social Security Administration regulations using linear and polygonal functions.
AF.7.b. Graphing pay schedules
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Banking Services
AF.3. Utilize exponential functions to compare compound interest and simple interest.
AF.3.b. Creating, interpreting, and analyzing a graph, table, and equation to compare compound interest and simple interest
AF.18.c. Determining area of various shapes including rectangles, squares, parallelograms, triangles, trapezoids, circles, regular polygons, irregular polygons
AF.9. Use mathematical operations in the workforce using whole numbers including addition, subtraction, multiplication, and division to solve complex problems.
AF.9.a. Using mathematical operations including addition and subtraction using negative numbers
Write expressions in equivalent forms to solve problems. (Quadratic and exponential.)
AI.9. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. [A-SSE3]
AI.9.d. Use the properties of exponents to transform expressions for exponential functions. [A-SSE3c]
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
STATISTICS AND PROBABILITY: Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on two categorical and quantitative variables. (Linear focus, discuss general principle.)
AI.44. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
ALGEBRA: Reasoning With Equations and Inequalities
Solve equations and inequalities in one variable. (Linear inequalities; literal that are linear in the variables being solved for; quadratics with real solutions.)
AI.17. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI3]
Solve systems of equations. (Linear-linear and linear-quadratic.)
AI.19. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [A-REI5]
AI.20. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [A-REI6]
Understand solving equations as a process of reasoning and explain the reasoning. (Master linear; learn as general principle.)
AI.16. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [A-RE
Represent and solve equations and inequalities graphically. (Linear and exponential; learn as general principle.)
AI.23. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
AI.24. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the correspondin
ALGEBRA: Arithmetic With Polynomials and Rational Expressions
Perform arithmetic operations on polynomials. (Linear and quadratic.)
AI.10. Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [A-APR1]
STATISTICS AND PROBABILITY: Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data. (Link to data from simulations or experiments.)
AI.47. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [S-CP2]
Use properties of rational and irrational numbers.
AI.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. [N-RN3]
FUNCTIONS: Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems.
AI.37. Distinguish between situations that can be modeled with linear functions and with exponential functions. [F-LE1]
AI.37.a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. [F-LE1a]
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
FUNCTIONS: Interpreting Functions
Interpret functions that arise in applications in terms of the context. (Linear, exponential, and quadratic.)
AI.28. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercept
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.30. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [F-IF6]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Analyze functions using different representations. (Linear, exponential, quadratic, absolute value, step, and an awareness of piecewise-defined.)
AI.31. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [F-IF7]
AI.31.a. Graph linear and quadratic functions, and show intercepts, maxima, and minima. [F-IF7a]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.32. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]
AI.32.b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b]
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Understand the concept of a function and use function notation. (Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences.)
AI.25. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f c
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
AI.27. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [F-IF3]
Quiz, Flash Cards, Worksheet, Game & Study GuideSequences
ALGEBRA: Creating Equations
Create equations that describe numbers or relationships. (Linear, quadratic, and exponential (integer inputs only); for Standard 14, linear only.)
AI.12. Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]
AI.13. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.14. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. [A-CED3]
Create equations that describe numbers or relationships. (Equations using all available types of expressions, including simple root functions.)
AII.20. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]
AII.21. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AII.22. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]
ALGEBRA: Reasoning With Equations and Inequalities
Represent and solve equations and inequalities graphically. (Combine polynomial, rational, radical, absolute value, and exponential functions.)
AII.27. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
ALGEBRA: Arithmetic With Polynomials and Rational Expressions
Perform arithmetic operations on polynomials. (Beyond quadratic.)
AII.15. Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [A-APR1]
Analyze functions using different representations. (Focus on using key features to guide selection of appropriate type of model function.)
AII.31. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]
AII.31.b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b]
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
AL.AIIT.ALGEBRA II WITH TRIGONOMETRY
ALGEBRA II WITH TRIGONOMETRY
ALGEBRA: Creating Equations
Create equations that describe numbers or relationships. (Equations using all available types of expressions, including simple root functions.)
AIIT.20. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]
AIIT.21. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AIIT.22. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]
ALGEBRA: Reasoning With Equations and Inequalities
Represent and solve equations and inequalities graphically. (Combine polynomial, rational, radical, absolute value, and exponential functions.)
AIIT.27. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
ALGEBRA: Arithmetic With Polynomials and Rational Expressions
Perform arithmetic operations on polynomials. (Beyond quadratic.)
AIIT.15. Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [A-APR1]
Analyze functions using different representations. (Focus on using key features to guide selection of appropriate type of model function.)
AIIT.31. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]
AIIT.31.b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b]
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
AL.DM.DISCRETE MATHEMATICS
DISCRETE MATHEMATICS
STATISTICS AND PROBABILITY
DM.12. Use combinatorial reasoning and counting techniques to solve application-based problems.
Quiz, Flash Cards, Worksheet, Game & Study GuideSequences
DM.3. Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models.
Understand similarity in terms of similarity transformations.
G.14. Verify experimentally the properties of dilations given by a center and a scale factor. [G-SRT1]
G.14.a. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged. [G-SRT1a]
G.15. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles
GEOMETRY: Expressing Geometric Properties With Equations
Use coordinates to prove simple geometric theorems algebraically.
G.34. Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
Use coordinates to prove simple geometric theorems algebraically. (Include distance formula; relate to Pythagorean Theorem.)
G.31. Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
G.33. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. [G-GPE7]
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
GEOMETRY: Congruence
Understand congruence in terms of rigid motions. (Build on rigid motions as a familiar starting point for development of concept of geometric proof.)
G.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [G-CO6]
Prove geometric theorems. (Focus on validity of underlying reasoning while using variety of ways of writing proofs.)
G.9. Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a l
G.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1]
G.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
G.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. [G-CO4]
G.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [G-CO5]
MI.12. Summarize the history of probability, including the works of Blaise Pascal; Pierre de Fermat; Abraham de Moivre; and Pierre-Simon, marquis de Laplace.
STATISTICS AND PROBABILITY: Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable.
P.39. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. (Focus on increasing rigor using standard deviation.) [S-ID2]
Interpret functions that arise in applications in terms of the context. (Emphasize selection of appropriate models. Understand limits of functions.)
P.16. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Key features include intercep
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
P.17. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [F-IF6]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations