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## AL.AC.ALGEBRAIC CONNECTIONS

ALGEBRAIC CONNECTIONS
GEOMETRY: Symmetry - Students will:
AC.9. Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

GEOMETRY: Measurement - Students will:
AC.11. Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems.
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

ALGEBRA: Modeling – Students will:
AC.1. Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

## AL.AI.ALGEBRA I

ALGEBRA I
STATISTICS AND PROBABILITY: Conditional Probability and the Rules of Probability – Students will:
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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

STATISTICS AND PROBABILITY: Interpreting Categorical and Quantitative Data – Students will:
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. [S-ID5]
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

AI.45. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [S-ID6]
AI.45.b. Informally assess the fit of a function by plotting and analyzing residuals. [S-ID6b]

AI.45.c. Fit a linear function for a scatter plot that suggests a linear association. [S-ID6c]
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

FUNCTIONS: Linear, Quadratic, and Exponential Models – Students will:
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 Guide Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

FUNCTIONS: Building Functions – Students will:
Build a function that models a relationship between two quantities. (For standards 34 and 35, linear, exponential, and quadratic.)
AI.34. Write a function that describes a relationship between two quantities. [F-BF1]
AI.34.a. Determine an explicit expression, a recursive process, or steps for calculation from a context. [F-BF1a]
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

FUNCTIONS: Interpreting Functions – Students will:
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 intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. [F-IF4]
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear 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 Guide Linear equations

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 corresponding to the input x. The graph of f is the graph of the equation y = f(x). [F-IF1]
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

AI.27. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [F-IF3]
Flip Charts Circle Around
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

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 Guide Linear 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 Guide Functions

ALGEBRA: Reasoning With Equations and Inequalities – Students will:
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 values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. [A-REI11]

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 corresponding half-planes. [A-REI12]
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

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]

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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

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-REI1]
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

ALGEBRA: Creating Equations – Students will:
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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

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 Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear 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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

AI.15. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4]
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

ALGEBRA: Arithmetic With Polynomials and Rational Expressions - Students will:
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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

ALGEBRA: Seeing Structure in Expressions – Students will:
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 Guide Functions

NUMBER AND QUANTITY: The Real Number System – Students will:
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]
Flip Charts The Real Numbers

Extend the properties of exponents to rational exponents.
AI.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. [N-RN2]
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

## AL.AII.ALGEBRA II

ALGEBRA II
ALGEBRA: Reasoning With Equations and Inequalities – Students will:
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 values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. [A-REI11]

ALGEBRA: Creating Equations – Students will:
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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

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 Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear 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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

AII.23. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4]
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

ALGEBRA: Arithmetic With Polynomials and Rational Expressions – Students will:
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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

## AL.AIIT.ALGEBRA II WITH TRIGONOMETRY

ALGEBRA II WITH TRIGONOMETRY
ALGEBRA: Reasoning With Equations and Inequalities – Students will:
Represent and solve equations and inequalities graphically. (Combine polynomial, rational, radical, absolute value, and exponential functions.)
AIII.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 values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. [A-REI11]

ALGEBRA: Creating Equations – Students will:
Create equations that describe numbers or relationships. (Equations using all available types of expressions, including simple root functions.)
AIII.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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

AIII.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 Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

AIII.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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

AIII.23. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4]
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

ALGEBRA: Arithmetic With Polynomials and Rational Expressions – Students will:
Perform arithmetic operations on polynomials. (Beyond quadratic.)
AIII.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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

## AL.DM.DISCRETE MATHEMATICS

DISCRETE MATHEMATICS
STATISTICS AND PROBABILITY – Students will:
DM.12. Use combinatorial reasoning and counting techniques to solve application-based problems.
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

NUMBER AND QUANTITY – Students will:
DM.1. Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine properties of integers.
Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers

DM.2. Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers.
Flip Charts Circle Around
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

DM.3. Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models.
Flip Charts Circle Around
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

## AL.G.GEOMETRY

GEOMETRY
GEOMETRY: Expressing Geometric Properties With Equations – Students will:
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 Guide Plane 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 Guide Plane 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 Guide Plane figures

GEOMETRY: Similarity, Right Triangles, and Trigonometry – Students will:
Prove theorems involving similarity.
G.18. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [G-SRT5]

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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

G.14.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. [G-SRT1b]
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

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 and the proportionality of all corresponding pairs of sides. [G-SRT2]
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

GEOMETRY: Congruence – Students will:
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 line segment are exactly those equidistant from the segment’s endpoints. [G-CO9]
Flip Charts Plane Geometry

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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Experiment with transformations in the plane.
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]
Flip Charts Dot to Dot
Flip Charts Perimeter & Area
Flip Charts Plane Geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

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 angle to those that do not (e.g., translation versus horizontal stretch). [G-CO2]
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

G.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [G-CO3]
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

G.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. [G-CO4]
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

GEOMETRY: Geometric Measurement and Dimension – Students will:
Explain volume formulas and use them to solve problems.
G.36. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. [G-GMD3]
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

G.37. Determine the relationship between surface areas of similar figures and volumes of similar figures.
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

## AL.MI.MATHEMATICAL INVESTIGATIONS

MATHEMATICAL INVESTIGATIONS
STATISTICS AND PROBABILITY – Students will:
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.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

NUMBER AND QUANTITY – Students will:
MI.3. Use special numbers, including e, i, π, and the golden ratio, to solve application-based problems.
MI.3.a. Identify transcendental numbers.
Flip Charts Dot to Dot
Flip Charts Perimeter & Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

## AL.MP.Standards for Mathematical Practice: Mathematically proficient students:

Standards for Mathematical Practice: Mathematically proficient students:
MP.1. Make sense of problems and persevere in solving them.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

MP.2. Reason abstractly and quantitatively.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

## AL.P.PRECALCULUS

PRECALCULUS
STATISITCS AND PROBABILITY: Interpreting Categorical and Quantitative Data – Students will:
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]
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

FUNCTIONS: Interpreting Functions – Students will:
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 intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.) [F-IF4]
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear 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 Guide Linear equations

Science