A1: Algebra I

A1.1: The student will use expressions and equations to model number relationships.

A1.1.1: Translate word phrases and sentences into expressions and equations and vice versa.

Using Algebraic Equations
Using Algebraic Expressions

A1.1.2: Expressions

A1.1.2.a: Simplify and evaluate linear, absolute value, rational and radical expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Inequalities Involving Absolute Values
Simplifying Radicals - Activity A

A1.1.2.b: Simplify polynomials by adding, subtracting or multiplying.

Addition of Polynomials - Activity A

A1.2: The student will use relations and functions to model number relationships.

A1.2.1: Relations and Functions

A1.2.1.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

A1.2.1.b: Distinguish between relations and functions.

Introduction to Functions
Linear Functions

A1.2.1.c: Identify dependent and independent variables, domain and range.

Introduction to Functions

A1.2.1.d: Evaluate a function using tables, equations or graphs.

Cosine Function
Cubic Function Activity
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 Algebraic Equations
Using Tables, Rules and Graphs

A1.2.2: Recognize the parent graph of the functions y = k, y = x, y = |x|, and predict the effects of transformations on the parent graph (e.g., y = |x| + 2, change slope, change intercepts, change slope and intercept).

Functions Involving Square Roots
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Reflections of a Linear Function
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Using Tables, Rules and Graphs

A1.2.3: Calculate the slope of a line using a graph, an equation, two points or a set of data points.

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

A1.2.4: Develop the equation of a line and graph linear relationships given the following:

A1.2.4.a: slope and y-intercept

Defining a Line with Two Points
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

A1.2.4.b: slope and one point on the line

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B

A1.2.4.c: two points on the line

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

A1.2.4.d: x-intercept and y-intercept

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

A1.2.4.e: a set of data points

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Standard Form of a Line

A1.2.5: Slope Interpretation

A1.2.5.a: Use the slope to differentiate between lines that are parallel, perpendicular, horizontal, or vertical.

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

A1.2.5.b: 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]).

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

A1.2.6: Linear Equations and Inequalities

A1.2.6.a: Solve linear equations by graphing or using properties of equality.

Modeling Linear Systems - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Formulas for any Variable
Solving Linear Systems by Graphing
Solving Two-Step Equations
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

A1.2.6.b: Solve linear inequalities by graphing or using properties of inequalities.

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

A1.2.6.c: Match appropriate equations or inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa.

Ellipse - Activity A
Inequalities Involving Absolute Values
Linear Functions
Linear Inequalities in Two Variables - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - 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
Using Tables, Rules and Graphs

A1.2.7: 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

A1.2.8: Problem Solving

A1.2.8.a: Use the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context.

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

A1.2.8.b: Solve two-step and three-step problems using concepts such as rules of exponents, probability, rate, distance, ratio and proportion, measures of central tendency and percent.

Geometric Probability - Activity A
Mean, Median and Mode
Polling: Neighborhood

A1.2.9: Nonlinear Functions

A1.2.9.a: Match exponential and quadratic functions to a table, graph or situation and vice versa.

Exponential Functions - Activity A
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

A1.2.9.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

A1.3: The student will use data analysis and statistics to formulate and justify predictions from a set of data.

A1.3.2: 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 (e.g., given a scatter plot and several linear equations, which one is the best fit?).

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

GE: Geometry

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

GE.1.1: Properties and Relationships of Figures

GE.1.1.a: Identify the relationships of parallel lines with a transversal.

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

GE.1.1.b: Identify relationships between pairs of angles (e.g., adjacent, complementary, vertical).

Investigating Angle Theorems - Activity A

GE.1.2: Determine and use the relationships of congruency and similarity to determine unknown values.

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

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

GE.2.1: Polygons

GE.2.1.a: Identify and describe polygons (i.e., convex, concave, regular)

Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Special Quadrilaterals

GE.2.1.b: Apply the interior and exterior angle sum of convex polygons to solve problems.

Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

GE.2.1.c: Develop and apply the properties of quadrilaterals to solve problems (e.g., rectangles, parallelograms, rhombi, trapezoids, kites).

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

GE.2.2: Draw and analyze 2- and 3-dimensional figures.

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

GE.2.3: Use properties of 2- and 3-dimensional figures to determine unknown values (e.g., given the perimeter/circumference, find the area).

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

GE.2.4: Compute length, perimeter or circumference, area, volume, and surface area of geometric figures with missing information and correctly identify the appropriate unit of measure of each.

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

GE.2.5: Use geometric tools (e.g., protractor, compass, straight edge) to construct a variety of figures.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

GE.2.7: Chords, Secants and Tangents

GE.2.7.a: Identify and describe the relationship between two chords that intersect in the interior of a circle.

Chords and Arcs
Inscribing Angles

GE.3: The student will solve problems with geometric figures in the coordinate plane.

GE.3.1: Use transformations (reflection, rotation, translation) within coordinate geometry (e.g., reflect points across the y-axis).

Reflections
Rotations, Reflections and Translations
Translations

GE.3.2: 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.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Point-Slope Form of a Line - Activity A
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Slope - Activity B

GE.3.3: Given a set of points determine the type of figure based on its properties (e.g., parallelogram, isosceles triangle, regular octagon).

Classifying Triangles
Isosceles and Equilateral Triangles
Parallelogram Conditions

GE.4: The student will use the properties of angles, right triangles and similar polygons to solve problems.

GE.4.1: Solve problems using properties of angles (e.g., interior, exterior, complementary, vertical, angle sums, 30-60-90).

Investigating Angle Theorems - Activity A
Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

GE.4.2: Use the Pythagorean Theorem and its converse to find missing side lengths and to determine acute, right, and obtuse triangles.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

GE.4.4: Express the trigonometric functions as ratios and derive the relationship between sine, cosine, and tangent ratios, and use to solve real-world problems.

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

GE.4.5: Similar Polygons

GE.4.5.a: Use similar figures to construct ratios and solve for a missing side.

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

GE.4.5.b: Use ratios of similar figures to find linear distance, perimeter, area, and volume.

Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area
Similar Figures - Activity A
Similar Polygons

A2: Algebra II

A2.1: The student will perform operations with real numbers, complex numbers and matrices.

A2.1.1: Define and perform operations on real and complex numbers.

Fractions with Unlike Denominators

A2.1.2: Convert expressions from radical notations and vice versa.

Simplifying Radicals - Activity A

A2.2: The student will use functions and relations to solve problems.

A2.2.1: Recognize the parent graph of the function y = x² and predict the effects of transformations on the parent graph (e.g., y = x² + 3 shifts the graph up 3, y = 3x² creates vertical stretching by a factor of 3).

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Translating and Scaling Functions
Unit Circle

A2.2.2: Solve, graph and analyze systems of linear equations and inequalities.

Inequalities Involving Absolute Values
Linear Programming - Activity A
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Linear Systems by Graphing
Solving Two-Step Equations
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

A2.2.3: 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

A2.2.4: Compare the relationship between the x-intercepts (zeros) of a quadratic function and the roots of a quadratic equation to solve problems.

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

A2.2.5: Interpret the maximum and minimum value and the y-intercept of a quadratic function.

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

A2.2.6: Identify, graph, and write the equations of the conic sections.

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

A2.2.7: Define and distinguish between relations and functions.

Introduction to Functions
Linear Functions

A2.2.8: Use functional notation and specify domain and range.

Functions Involving Square Roots

A2.2.9: Find and graph the inverse of a function.

Exponential Functions - Activity A
Functions Involving Square Roots
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

A2.2.10: Exponential and Logarithmic Functions

A2.2.10.a: Interpret and graph exponential and logarithmic functions.

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

A2.2.10.b: Apply the inverse relationship between exponential and logarithmic functions.

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

A2.2.10.c: Use exponential and logarithmic functions to solve problems (e.g., compound interest, exponential growth or exponential decay).

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

A2.2.11: Solve multistep problems using concepts such as rate, distance, ratio and proportion, average, and percent.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Mean, Median and Mode
Polling: Neighborhood
Pythagorean Theorem - Activity A

A2.2.12: Polynomials

A2.2.12.a: Use synthetic division to find the solutions of a polynomial.

Dividing Polynomials Using Synthetic Division

A2.2.12.b: Use factoring to find the solutions of a polynomial.

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

A2.2.12.c: Graph a polynomial and identify the x- and y-intercepts, relative maximums and relative minimums.

Parabolas - Activity A
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

A2.2.13: Rational Expressions and Equations

A2.2.13.a: Simplify rational expressions.

Dividing Exponential Expressions

A2.2.13.c: Graph rational expressions and identify x- and y-intercepts, horizontal asymptotes and vertical asymptotes.

Slope-Intercept Form of a Line - Activity A
Unit Circle
Using Tables, Rules and Graphs

A2.3: The student will use data analysis and statistics to formulate and justify predictions from a set of data.

A2.3.1: Collect data involving two variables and display on a scatter plot, interpret results using a linear, exponential or quadratic model/equation and identify whether the model/equation is a curve of best fit for the data.

Biconditional Statement
Conditional Statement
Correlation
Solving Using Trend Lines

A2.3.2: Analyze and synthesize data using measures of central tendency and standard deviation.

Line Plots

A2.3.3: Identify how given outliers affect representations of data (e.g., a regression line may be strongly affected by a few aberrant points while the same aberrant points might indicate a mistake on a scatter plot).

Correlation

A2.3.4: Differentiate between arithmetic and geometric sequences and series.

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