G: Geometry

G.1: Compute and determine the reasonableness of a result in mathematical and real-world situations with and without technology.

G.1.a: Apply problem-solving skills to solve and verify the solutions for unknown measures in similar polygons.

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

G.1.c: Solve real-world or application problems that involve square roots and the Pythagorean Theorem.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Square Roots

G.2: Understand relations, functions, and patterns. Analyze change using various geometric properties.

G.2.a: Represent data from geometric and real-world contexts with expressions, formulas, tables, charts, graphs, relations, and functions.

Introduction to Functions
Linear Functions

G.2.b: Recognize and write the equation of a circle in standard form (x-h)_ + (y-k)_ = r_ and identify the center and radius.

Circles

G.2.c: Use slope to analyze and write equations for parallel and perpendicular lines.

Slope - Activity B
Using Algebraic Equations

G.2.d: Apply the Midpoint and Distance Formulas to solve application problems involving the coordinate plane.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

G.2.e: Determine the effects of rigid (translations, rotations, and reflections) and nonrigid (dilations) motions and compositions when performed on objects on the coordinate plane.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

G.3: Investigate, apply, and prove properties and theorems from postulates and definitions related to angles, lines, circles, polygons, and two- and three-dimensional figures. Explore applications of patterns and transformational geometry.

G.3.a: Use inductive reasoning to make conjectures and deductive reasoning to make valid conclusions.

Biconditional Statement
Conditional Statement
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

G.3.b: Develop and evaluate mathematical arguments and proofs to include paragraph, two-column, and flow chart forms.

Biconditional Statement
Conditional Statement
Proving Triangles Congruent
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

G.3.c: Identify, classify, and apply angle relationships formed by parallel lines cut by transversals.

Investigating Angle Theorems - Activity A

G.3.d: Use the properties of altitudes, medians, angle bisectors, and perpendicular bisectors of triangles to solve problems.

Concurrent Lines, Medians, and Altitudes

G.3.e: Classify triangles and apply postulates and theorems to test for triangle inequality, congruence, and similarity.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Triangle Inequalities

G.3.g: Describe and draw cross-sections of prisms, cylinders, pyramids, and cones.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

G.3.h: Graph a vector and determine the magnitude and direction of a given vector.

Vectors

G.3.i: Given the pre-image or image, find figures obtained by applying reflections, translations, rotations, and dilations; describe and justify the method used.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

G.4: Select and apply various strategies, tools, and formulas to calculate length, surface area, volume, and angle measurements.

G.4.b: Solve real-world applications and mathematical problems to find missing measurements in right triangles by applying special right triangle relationships, geometric means, or trigonometric functions.

Cosine Function
Similarity in Right Triangles
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

G.4.c: Solve real-world and mathematical problems involving the lateral area, surface area and volume of three-dimensional figures, including prisms, cylinders, cones, pyramids, and spheres.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

G.4.e: Apply the relationships of sine, cosine, and tangent to problems involving right triangles.

Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
Unit Circle

G.5: Represent, analyze, and make inferences based on data with and without the use of technology.

G.5.a: Apply multiple strategies and representations, including area models, to solve probability problems.

Binomial Probabilities
Geometric Probability - Activity A

AII: Algebra 2

AII.1: Understand relationships among numbers and compute fluently. Verify with technology.

AII.1.a: Diagram the relationship among the subsets of the complex number system.

Points in the Complex Plane - Activity A

AII.1.b: Compute with rational and radical expressions and complex numbers, expressing in simplest form.

Operations with Radical Expressions
Simplifying Radicals - Activity A

AII.1.e: Solve applications and problems in mathematical settings involving arithmetic and geometric sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

AII.1.h: Solve application problems involving exponential functions related to growth and decay.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Simple and Compound Interest

AII.2: Use algebraic concepts to identify patterns, use multiple representations of relations and functions, and apply operations to expressions, equations, and inequalities.

AII.2.a: Solve compound and absolute value inequalities, graphing and writing solutions in interval notation.

Compound Inequalities
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A

AII.2.b: Solve systems of absolute value and quadratic equations using a variety of solution methods including graphing.

Modeling Linear Systems - Activity A

AII.2.c: Given constraints, find the maximum and minimum value(s) of a system of linear inequalities and explain your reasoning.

Linear Programming - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

AII.2.d: Given the solution(s) to a quadratic equation, find a quadratic equation to fit the solution(s) and explain or justify the solution process.

Roots of a Quadratic

AII.2.e: Use the discriminant to classify and predict the types of solutions of quadratic equations and justify the classification.

Roots of a Quadratic

AII.2.f: Factor sums and differences of cubes and factor polynomials by grouping.

Factoring Special Products
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors

AII.2.l: Interpret the zeros and maximum or minimum value(s) of quadratic functions.

Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

AII.3: Use coordinate geometry to specify locations, describe relationships, and apply transformations to analyze algebraic relationships.

AII.3.a: Determine and justify whether the inverse of a relation or a function exists.

Introduction to Functions

AII.3.b: Classify functions based on sketches of their graphs.

Cosine Function
Point-Slope Form of a Line - Activity A
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function

AII.3.c: Sketch and describe transformations of quadratic and absolute value functions.

Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions

AII.3.d: Represent complex numbers and the sum of complex numbers in a complex coordinate plane.

Complex Numbers in Polar Form
Points in the Complex Plane - Activity A

AII.3.e: Identify and sketch the essential graphs of the four conic sections: circle, parabola, ellipse, and hyperbola.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

AII.4: Understand measurable attributes of objects and apply appropriate techniques and formulas to determine measurements.

AII.4.b: Describe the level of accuracy of measurements in real-world situations by using absolute value inequalities.

Inequalities Involving Absolute Values

AII.5: Use technology to represent, analyze, and make inferences based on data.

AII.5.a: Through the use of technology, use scatter plots and linear and quadratic regression analysis to determine an appropriate function to model real-life data.

Correlation
Lines of Best Fit Using Least Squares - Activity A
Solving Using Trend Lines

AII.5.b: Solve simple combinations.

Binomial Probabilities
Permutations and Combinations

AII.5.d: Identify the difference between permutations and combinations and use them to solve real-world problems.

Binomial Probabilities
Permutations
Permutations and Combinations

AA: Advanced Algebra

AA.1: Understand and perform computations with different representations of numbers.

AA.1.e: Solve application problems involving e and exponential functions related to growth and decay.

Exponential Functions - Activity A

AA.2: Use algebraic concepts to identify patterns and use multiple representations of relations and functions. Apply operations to expressions and equations.

AA.2.a: Find the sum, difference, product, and quotient of functions, noting any restrictions on the domain.

Addition and Subtraction of Polynomials

AA.2.c: Describe patterns found in Pascal's Triangle and explain the relationship to the Binomial Theorem.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

AA.2.d: Write and graph the equations of conic sections.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

AA.2.e: Solve linear-quadratic and quadratic-quadratic systems of equations and inequalities.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AA.3: Recognize, analyze, and graph conic sections.

AA.3.a: Describe and explain the conic sections resulting from cutting a cone.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

AA.3.b: Explain and perform the geometric constructions of conic sections.

Circles
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

AA.4: Apply simple probability and curve fitting to data.

AA.4.a: Use technology and regression analysis to determine appropriate quadratic and cubic functions modeling real-life data.

Cubic Function Activity
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

T: Trigonometry

T.1: Represent and compare numbers in various forms and perform operations.

T.1.a: Perform conversions across measurement systems including degree to radian measurements of angles, radian measurements to degree measurements of angles, polar to rectangular coordinates, rectangular to polar coordinates, rectangular to trigonometric forms of complex numbers, and trigonometric to rectangular forms of complex numbers.

Complex Numbers in Polar Form
Points in Polar Coordinates

T.1.b: Determine the product and quotient of complex numbers in trigonometric form.

Complex Numbers in Polar Form

T.1.c: Apply De Moivre's theorem to determine the nth roots of a complex number given in polar form.

Complex Numbers in Polar Form

T.1.d: Explain the addition formulas for sine and cosine and use them to prove (or simplify) other trigonometric functions.

Cosine Function
Sine Function
Sine, Cosine and Tangent
Sum and Difference Identities for Sine and Cosine
Tangent Function
Unit Circle

T.2: Investigate basic concepts of vectors and operations with vectors.

T.2.a: Recognize and draw different notations for vectors to represent a quantity.

Vectors

T.2.b: Analyze properties of vectors and the effects of these properties on operations with vectors.

Vectors

T.3: Compare and produce equivalent forms of trigonometric expressions and solve trigonometric equations.

T.3.a: Determine the domain and range of trigonometric functions.

Cosine Function
Sine Function
Tangent Function

T.3.b: Identify and apply trigonometric identities.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

T.3.c: Verify identities analytically and with technology.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

T.3.d: Solve trigonometric equations in real-world situations or mathematical settings.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

T.4: Use geometric modeling to analyze trigonometric relationships.

T.4.a: Use the unit circle to solve real-world applications and problems in mathematical settings.

Cosine Function
Sine Function
Tangent Function
Unit Circle

T.4.b: Apply the six trigonometric functions in relation to a right triangle to solve real-world applications and problems in mathematical settings.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

T.4.c: Find exact values of trigonometric functions of special angles in the unit circle.

Cosine Function
Sine Function
Tangent Function
Unit Circle

T.4.d: Recognize, sketch, and interpret graphs of the six trigonometric functions and include restrictions on their domain.

Cosine Function
Sine Function
Tangent Function
Unit Circle

T.4.e: Model and apply right triangle formulas, Law of Sines, and Law of Cosines to problem-solving situations.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

T.4.f: Use the graph of polar coordinates and associated equations to model real-world applications and mathematical situations.

Complex Numbers in Polar Form
Points in Polar Coordinates

T.5: Select and apply formulas to determine length and area.

T.5.a: Find arc length and sector area of a circle.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

T.5.b: Using graphs of functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C), interpret A, B, C in terms of amplitude, frequency, period, and phase shift.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

T.5.c: Given one angle and the measures of two adjacent sides, determine the area of a triangle and explain the process used.

Isosceles and Equilateral Triangles
Triangle Angle Sum - Activity A

PC: Pre-Calculus

PC.1: Explore and illustrate the characteristics and operations connecting sequences and series.

PC.1.a: Express sequences and series using recursive and explicit formulas.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.1.b: Evaluate and apply formulas for arithmetic and geometric sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.1.d: Evaluate and apply infinite geometric series.

Arithmetic and Geometric Sequences
Geometric Sequences

PC.2: Analyze, manipulate, and solve equations and inequalities.

PC.2.a: Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).

Exponential Functions - Activity A
Functions Involving Square Roots
Introduction to Functions
Logarithmic Functions: Translating and Scaling
Tangent Function

PC.2.b: Determine horizontal, vertical, and slant asymptotes and holes of rational functions and explain how each was found.

General Form of a Rational Function
Rational Functions

PC.2.c: Determine the domain and range of functions, including piece-wise functions.

Functions Involving Square Roots

PC.2.d: Determine the end behavior of polynomial functions.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A

PC.2.f: Solve exponential and logarithmic equations to include real-world applications.

Using Algebraic Equations

PC.2.h: Find the zeros of polynomial functions by synthetic division and the Factor Theorem.

Cubic Function Activity
Dividing Polynomials Using Synthetic Division
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors

PC.2.i: Graph and solve quadratic inequalities.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

PC.2.j: Decompose a rational function into partial fractions.

General Form of a Rational Function
Rational Functions

PC.3: Recognize, sketch, and transform graphs of functions.

PC.3.a: Describe the attributes of graphs and the general equations of parent functions (linear, quadratic, cubic, absolute value, rational, exponential, logarithmic, square root, cube root, and greatest integer).

Exponential Functions - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Roots of a Quadratic

PC.3.b: Explain the effects of changing the parameters in transformations of functions.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

PC.3.c: Predict the shapes of graphs of exponential, logarithmic, rational, and piece-wise functions, and verify the prediction with and without technology.

Exponential Functions - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions

PC.3.d: Relate symmetry of the behavior of even and odd functions.

Holiday Snowflake Designer

PC.4: Adapt curves to data.

PC.4.a: Use regression methods available through technology to determine appropriate exponential and logarithmic functions that model real-life data.

Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

PC.4.b: Use regression methods available through technology to determine appropriate cubic functions that model real-life data.

Cubic Function Activity
Polynomials and Linear Factors

DM: Discrete Math

DM.2: Use algebraic methods to represent simple and complex relationships among statements. Use models to represent patterns and operations.

DM.2.a: Define sentence (proposition), and use logic to determine if the sentence is true or false.

Conditional Statement

DM.2.c: Define a conditional statement using truth tables.

Conditional Statement

DM.2.e: Define a sequence recursively and explicitly.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

DM.2.f: Find the explicit formula for a recursively-defined sequence using iteration.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

DM.2.g: Use mathematical induction to verify explicit formulas for arithmetic, geometric, and other sequences and/or series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

DM.3: Use geometric models to describe and analyze mathematical relationships, establish the validity of conjectures, and determine solutions to real applications.

DM.3.a: Construct a logic circuit from a Boolean expression to determine output.

Biconditional Statement
Conditional Statement

DM.3.b: Construct a Boolean expression given a logic circuit.

Biconditional Statement
Conditional Statement

DM.3.c: Construct a logic circuit and Boolean expression given an input/output table.

Biconditional Statement
Conditional Statement
Linear Functions
Using Tables, Rules and Graphs

DM.4: Investigate and explain strategies for solving simple games.

DM.4.c: Create and use simulations for probability models.

Binomial Probabilities
Geometric Probability - Activity A
Probability Simulations

C: Calculus

C.2: Demonstrate basic knowledge of functions, including their behavior and characteristics.

C.2.a: Predict and explain the characteristics and behavior of functions and their graphs (domain, range, increasing/decreasing intervals, intercepts, symmetry, and end behavior).

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Tangent Function

C.2.b: Investigate, describe, and determine asymptotic behavior using tables, graphs, and analytical methods.

General Form of a Rational Function
Rational Functions
Tangent Function

C.2.c: Determine and justify the continuity and discontinuity of functions.

Exponential Functions - Activity A
Functions Involving Square Roots

C.8: Adapt integration methods to model situations to problems.

C.8.a: Apply integration to solve problems of area.

Perimeter, Circumference, and Area - Activity B

C.9: Apply appropriate techniques, tools, and formulas to determine values for the definite integral.

C.9.a: Interpret the concept of definite integral as a limit of Riemann sums over equal subdivisions.

Riemann Sum

S: Statistics

S.1: Explore phenomena using probability and simulation. Compute appropriate statistical and probabilistic measures.

S.1.a: Describe the comparison of center and spread within groups and between or across group variation.

Describing Data Using Statistics
Mean, Median and Mode

S.1.b: Interpret and apply the concept of the Law of Large Numbers.

Geometric Probability - Activity A
Polling: City

S.1.c: Apply the counting principles, including permutations and combinations.

Binomial Probabilities
Permutations
Permutations and Combinations

S.1.d: Construct and interpret sample spaces, events, and tree diagrams.

Binomial Probabilities
Permutations
Permutations and Combinations

S.1.e: Identify types of events, including mutually exclusive, independent, and complements.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

S.1.f: Calculate geometric probability using two-dimensional models, and explain the processes used.

Geometric Probability - Activity A

S.1.g: Create simulations and experiments that correlate to theoretical probability.

Binomial Probabilities
Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

S.1.h: Use Markov Chains to calculate probability by constructing matrix models.

Binomial Probabilities

S.1.i: Apply the concept of a random variable to generate and interpret probability distributions.

Populations and Samples

S.2: Analyze one and two variable data using algebraic concepts and methods.

S.2.a: Analyze and describe outliers and shape of the data including linearity and correlation across graphs and data sets.

Correlation
Roots of a Quadratic
Solving Using Trend Lines

S.2.b: Calculate mean, median, mode, standard deviation, z-scores, t-scores, quartiles, and ranges, and explain their applications.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median and Mode

S.2.d: Use algebraic concepts and methods to determine mathematical models of best fit.

Linear Functions

S.3: Design an appropriate form of displaying data collected, whether in tabular or graphic form.

S.3.a: Organize data using graphs that are appropriate to the data set, including frequency distributions, stacked line and bar graphs, stem-and-leaf plots, scatter plot, frequency polygon, and histograms.

Histograms
Populations and Samples
Scatter Plots - Activity A
Stem-and-Leaf Plots

S.3.b: Determine and justify the graph type that best represents a given set of data.

Describing Data Using Statistics

S.4: Collect, read, interpret, and analyze data as it relates to the real world.

S.4.a: Make inferences and predictions from charts, tables, and graphs that summarize data.

Histograms

S.4.b: Determine the most appropriate measure to describe a data set, including mean, median, mode, standard deviation, and variance.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

S.4.d: Explain and defend regression models using correlation coefficients and residuals.

Correlation

S.5: Design a study by clarifying a question and deciding upon a method of data collection and analysis.

S.5.c: Analyze sources of bias and sampling error(s) in studies.

Polling: Neighborhood

S.5.d: Compare and contrast sampling methods, including simple random sampling, stratified random sampling, and cluster sampling with regard to benefits and trade-offs.

Polling: Neighborhood

SMT: Survey of Mathematical Topics

SMT.2: Identify and apply the practices that affect employer and employee decision-making.

SMT.2.a: Identify and apply appropriate algebraic formulas to personal finance situations.

Percent of Change

SMT.2.b: Apply linear programming to business decisions.

Linear Programming - Activity A

IE: Introduction to Engineering

IE.1: Compute unit conversions and illustrate graphical interpretations.

IE.1.b: Convert decimal to binary numbers and binary to decimal numbers.

Number Systems

IE.2: Apply algebraic equations and functions to engineering situations.

IE.2.a: Write mass and energy balance equations to solve for some unknown value.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

IE.2.b: Find voltage, current, resistance, and solve power in series, parallel, and complex electric circuit theory problems using simultaneous equations generated from Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law (i.e., 3 equations and 3 unknowns).

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

IE.2.c: Graph a "Line of Best Fit" from given lab data and determine the degree of linearity (R_ value), slope of the line, and equation of the line.

Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A