AI: Algebra

AI.1: The student will use expressions and equations to model number relationships.

AI.1.1: Equations and Formulas

AI.1.1.a: Translate word phrases and sentences into expressions and equations and vice versa.

Using Algebraic Equations
Using Algebraic Expressions

AI.1.1.b: Solve literal equations involving several variables for one variable in terms of the others.

Solving Formulas for any Variable

AI.1.1.c: Use the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context.

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

AI.1.1.d: Solve two-step and three-step problems using concepts such as rules of exponents, rate, distance, ratio and proportion, and percent.

Compound Independent Events
Compound Independent and Dependent Events
Distance Formula - Activity A
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Dividing Exponential Expressions
Estimating Population Size
Exponents and Power Rules
Geoboard: The Pythagorean Theorem
Geometric Probability - Activity A
Independent and Dependent Events
Multiplying Exponential Expressions
Part:Part and Part:Whole Ratios
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Probability Simulations
Pythagorean Theorem - Activity A
Similar Figures - Activity A
Similar Polygons
Theoretical and Experimental Probability

AI.1.2: Expressions

AI.1.2.a: Simplify and evaluate linear, absolute value, rational and radical expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Simplifying Radicals - Activity A
Solving Equations By Graphing Each Side

AI.1.2.b: Simplify polynomials by adding, subtracting or multiplying.

Addition of Polynomials - Activity A

AI.1.2.c: Factor polynomial expressions.

Factoring Special Products
Modeling the Factorization of x²+bx+c

AI.2: The student will use relations and functions to model number relationships.

AI.2.1: Relations and Functions

AI.2.1.a: Distinguish between linear and nonlinear data.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function
Unit Circle
Using Tables, Rules and Graphs

AI.2.1.b: Distinguish between relations and functions.

Introduction to Functions
Linear Functions

AI.2.1.c: Identify dependent and independent variables, domain and range.

Functions Involving Square Roots
Introduction to Functions

AI.2.1.d: Evaluate a function using tables, equations or graphs.

Cosine Function
Cubic Function Activity
Describing Data Using Statistics
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function

AI.2.2: Linear Equations and Graphs

AI.2.2.a: Solve linear equations by graphing or using properties of equality.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Point-Slope Form of a Line - Activity A
Solving Equations By Graphing Each Side
Solving Formulas for any Variable
Solving Two-Step Equations

AI.2.2.b: Recognize the parent graph of the functions y = k, y = x, y = |x|, and predict the effects of transformations on the parent graph.

Inequalities Involving Absolute Values
Linear Functions
Quadratic and Absolute Value Functions
Reflections of a Linear Function
Translating and Scaling Functions
Using Tables, Rules and Graphs

AI.2.2.c: Slope

AI.2.2.c.I: Calculate the slope of a line using a graph, an equation, two points or a set of data points.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations

AI.2.2.c.II: Use the slope to differentiate between lines that are parallel, perpendicular, horizontal, or vertical.

Construct Parallel and Perpendicular Lines
Point-Slope Form of a Line - Activity A
Slope - Activity B

AI.2.2.c.III: Interpret the slope and intercepts within the context of everyday life (e.g., telephone charges based on base rate [y-intercept] plus rate per minute [slope]).

Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

AI.2.2.d: Develop the equation of a line and graph linear relationships given the following: slope and y-intercept, slope and one point on the line, two points on the line, x-intercept and y-intercept, a set of data points.

Defining a Line with Two Points
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

AI.2.2.e: Match appropriate equations to a graph, table, or situation and vice versa.

Cosine Function
Cubic Function Activity
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Introduction to Functions
Linear Functions
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
Slope-Intercept Form of a Line - Activity A
Tangent Function
Using Tables, Rules and Graphs

AI.2.3: Linear Inequalities and Graphs

AI.2.3.a: Solve linear inequalities by graphing or using properties of inequalities.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AI.2.3.b: Match appropriate inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa.

Cosine Function
Cubic Function Activity
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Inequalities Involving Absolute Values
Introduction to Functions
Linear Functions
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
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
Slope-Intercept Form of a Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Tangent Function
Using Tables, Rules and Graphs

AI.2.4: Solve a system of linear equations by graphing, substitution or elimination.

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

AI.2.5: Nonlinear Functions

AI.2.5.a: Match exponential and quadratic functions to a table, graph or situation and vice versa.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Introduction to Functions
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Using Tables, Rules and Graphs

AI.2.5.b: Solve quadratic equations by graphing, factoring, or using the quadratic formula.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

AI.3: The student will use data analysis, probability and statistics to formulate and justify predictions from a set of data.

AI.3.1: Data Analysis

AI.3.1.a: Translate from one representation of data to another and understand that the data can be represented using a variety of tables, graphs, or symbols and that different modes of representation often convey different messages.

Describing Data Using Statistics

AI.3.1.c: Solve two-step and three-step problems using concepts such as probability and measures of central tendency.

Binomial Probabilities
Describing Data Using Statistics
Mean, Median and Mode

AI.3.2: Collect data involving two variables and display on a scatter plot; interpret results using a linear model/equation and identify whether the model/equation is a line best fit for the data.

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

G: Geometry

G.1: The student will use deductive and inductive reasoning to solve problems.

G.1.1: Identify and use logical reasoning skills (inductive and deductive) to make and test conjectures, formulate counter examples, and follow logical arguments.

Proving Triangles Congruent

G.1.3: Compare the properties of Euclidean geometry to non-Euclidean geometries (for example, elliptical geometry, as shown on the surface of a globe, does not uphold the parallel postulate).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

G.2: The student will use the properties and formulas of geometric figures to solve problems.

G.2.1: Use geometric tools (for example, protractor, compass, straight edge) to construct a variety of figures.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

G.2.2: Line and Angle Relationships

G.2.2.a: Use the angle relationships formed by parallel lines cut by a transversal to solve problems.

Investigating Angle Theorems - Activity A

G.2.2.b: Use the angle relationships formed by two lines cut by a transversal to determine if the two lines are parallel and verify, using algebraic and deductive proofs.

Biconditional Statement
Conditional Statement
Investigating Angle Theorems - Activity A
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

G.2.2.c: Use relationships between pairs of angles (for example, adjacent, complementary, vertical) to solve problems.

Investigating Angle Theorems - Activity A

G.2.3: Polygons and Other Plane Figures

G.2.3.a: Identify, describe, and analyze polygons (for example, convex, concave, regular, pentagonal, hexagonal, n-gonal).

Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Special Quadrilaterals

G.2.3.b: Apply the interior and exterior angle sum of convex polygons to solve problems, and verify using algebraic and deductive proofs.

Biconditional Statement
Conditional Statement
Polygon Angle Sum - Activity A
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
Triangle Angle Sum - Activity A

G.2.3.c: Develop and apply the properties of quadrilaterals to solve problems (for example, rectangles, parallelograms, rhombi, trapezoids, kites).

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

G.2.3.d: Use properties of 2-dimensional figures and side length, perimeter or circumference, and area to determine unknown values and correctly identify the appropriate unit of measure of each.

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

G.2.4: Similarity

G.2.4.a: Determine and verify the relationships of similarity of triangles, using algebraic and deductive proofs.

Biconditional Statement
Conditional Statement
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

G.2.4.b: Use ratios of similar 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

Circle: Circumference and Area
Part:Part and Part:Whole Ratios
Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Rectangle: Perimeter and Area
Similar Figures - Activity A
Similar Polygons

G.2.5: Congruence

G.2.5.a: Determine and verify the relationships of congruency of triangles, using algebraic and deductive proofs.

Biconditional Statement
Conditional Statement
Congruence in Right Triangles
Proving Triangles Congruent

G.2.5.b: Use the relationships of congruency of 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

Circle: Circumference and Area
Congruence in Right Triangles
Constructing Congruent Segments and Angles
Perimeter, Circumference, and Area - Activity B
Proving Triangles Congruent

G.2.6: Circles

G.2.6.b: Find angle measures and segment lengths using the relationships among radii, chords, secants, and tangents of a circle.

Chords and Arcs

G.3: The student will use the properties of right triangles and trigonometric ratios to solve problems.

G.3.1: Use the Pythagorean Theorem and its converse to find missing side lengths and to determine acute, right, and obtuse triangles, and verify using algebraic and deductive proofs.

Biconditional Statement
Conditional Statement
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
Triangle Angle Sum - Activity A

G.3.2: Apply the 45-45-90 and 30-60-90 right triangle relationships to solve problems, and verify using algebraic and deductive proofs.

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

G.3.3: Express the trigonometric functions as ratios and use sine, cosine, and tangent ratios to solve real-world problems.

Cosine Function
Estimating Population Size
Part:Part and Part:Whole Ratios
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

G.4: The student will use the properties and formulas of geometric figures to solve problems.

G.4.1: Polyhedra and Other Solids

G.4.1.a: Identify, describe, and analyze polyhedra (for example, regular, decahedral).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

G.4.1.b: Use properties of 3-dimensional figures; side lengths, perimeter or circumference, and area of a face; and volume, lateral area, and surface area to determine unknown values and correctly identify the appropriate unit of measure of each.

Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

G.4.2: Similarity and Congruence

G.4.2.a: Use ratios of similar 3-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume.

Circle: Circumference and Area
Estimating Population Size
Geometric Probability - Activity A
Part:Part and Part:Whole Ratios
Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

G.4.2.b: Use the relationships of congruency of 3-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume.

Circle: Circumference and Area
Congruence in Right Triangles
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Proving Triangles Congruent
Pyramids and Cones - Activity A

G.4.3: Create a model of a 3-dimensional figure from a 2-dimensional drawing and make a 2-dimensional representation of a 3-dimensional object (for example, nets, blueprints, perspective drawings).

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

G.5: The student will solve problems with geometric figures in the coordinate plane.

G.5.1: Use coordinate geometry to find the distance between two points; the midpoint of a segment; and to calculate the slopes of parallel, perpendicular, horizontal, and vertical lines.

Construct Parallel and Perpendicular Lines
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Point-Slope Form of a Line - Activity A
Pythagorean Theorem - Activity A
Slope - Activity B

G.5.2: Properties of Figures

G.5.2.a: Given a set of points determine the type of figure formed based on its properties.

Classifying Triangles

G.5.2.b: Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

AII: Algebra II

AII.1: The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers.

AII.1.1: Rational Exponents

AII.1.1.b: Add, subtract, multiply, divide, and simplify radical expressions and expressions containing rational exponents.

Operations with Radical Expressions
Simplifying Radicals - Activity A

AII.1.2: Polynomial and Rational Expressions

AII.1.2.a: Divide polynomial expressions by lower degree polynomials.

Dividing Polynomials Using Synthetic Division

AII.1.3: Complex Numbers

AII.1.3.a: Recognize that to solve certain problems and equations, number systems need to be extended from real numbers to complex numbers.

Points in the Complex Plane - Activity A

AII.2: The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.

AII.2.1: Functions and Function Notation

AII.2.1.a: Recognize the parent graphs of polynomial, exponential, and logarithmic functions and predict the effects of transformations on the parent graphs, using various methods and tools which may include graphing calculators.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Translating and Scaling Functions

AII.2.1.b: Add, subtract, multiply, and divide functions using function notation.

Addition and Subtraction of Polynomials

AII.2.1.d: Use algebraic, interval, and set notations to specify the domain and range of functions of various types.

Functions Involving Square Roots

AII.2.2: Systems of Equations

AII.2.2.a: Model a situation that can be described by a system of equations or inequalities and use the model to answer questions about the situation.

Linear Programming - Activity A
Modeling Linear Systems - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AII.2.2.b: Solve systems of linear equations and inequalities using various methods and tools which may include substitution, elimination, matrices, graphing, and graphing calculators.

Linear Programming - Activity A
Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AII.2.3: Quadratic Equations and Functions

AII.2.3.a: Solve quadratic equations by graphing, factoring, completing the square and quadratic formula.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

AII.2.3.b: Graph a quadratic function and identify the x- and y-intercepts and maximum or minimum value, using various methods and tools which may include a graphing calculator.

Defining a Line with Two Points
Parabolas - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line

AII.2.3.c: Model a situation that can be described by a quadratic function and use the model to answer questions about the situation.

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

AII.2.4: Identify, graph, and write the equations of the conic sections (circle, ellipse, parabola, and hyperbola).

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

AII.2.5: Exponential and Logarithmic Functions

AII.2.5.a: Graph exponential and logarithmic functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

AII.2.5.b: Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

AII.2.5.c: Model a situation that can be described by an exponential or logarithmic function and use the model to answer questions about the situation.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Simple and Compound Interest

AII.2.6: Polynomial Equations and Functions

AII.2.6.a: Solve polynomial equations using various methods and tools which may include factoring and synthetic division.

Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

AII.2.6.b: Sketch the graph of a polynomial function.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A

AII.2.6.c: Given the graph of a polynomial function, identify the x- and y-intercepts, relative maximums and relative minimums, using various methods and tools which may include a graphing calculator.

Cubic Function Activity
Defining a Line with Two Points
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

AII.2.6.d: Model a situation that can be described by a polynomial function and use the model to answer questions about the situation.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A

AII.2.7: Rational Equations and Functions

AII.2.7.c: Given the graph of a rational function, identify the x- and y-intercepts, asymptotes, using various methods and tools which may include a graphing calculator.

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

AII.3: The student will use data analysis and statistics to formulate and justify predictions from a set of data.

AII.3.1: Analysis of Collected Data Involving Two Variables

AII.3.1.a: Display data on a scatter plot.

Scatter Plots - Activity A
Solving Using Trend Lines

AII.3.2: Measures of Central Tendency and Variability

AII.3.2.a: Analyze and synthesize data from a sample using appropriate measures of central tendency (mean, median, mode, weighted average).

Describing Data Using Statistics
Mean, Median and Mode

AII.3.2.b: Analyze and synthesize data from a sample using appropriate measures of variability (range, variance, standard deviation).

Describing Data Using Statistics

AII.3.3: Identify and use arithmetic and geometric sequences and series to solve problems.

Arithmetic and Geometric Sequences
Geometric Sequences