A.1: The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

A.1.A: describe independent and dependent quantities in functional relationships;

Introduction to Functions
Linear Functions

A.1.C: describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

Using Algebraic Equations

A.1.D: represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and

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
Polynomials and Linear Factors
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 Algebraic Expressions
Using Tables, Rules and Graphs

A.1.E: interpret and make decisions, predictions, and critical judgments from functional relationships.

Linear Functions

A.2: The student uses the properties and attributes of functions.

A.2.A: identify and sketch the general forms of linear (y = x) and quadratic (y = x²) parent functions;

Linear Functions
Point-Slope Form of a Line - 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

A.2.B: identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

Introduction to Functions

A.2.D: collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

A.3: The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations.

A.3.A: use symbols to represent unknowns and variables; and

Using Algebraic Equations

A.3.B: look for patterns and represent generalizations algebraically.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

A.4: The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

A.4.A: find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations;

Dividing Polynomials Using Synthetic Division
Factoring Special Products
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Modeling the Factorization of x²+bx+c
Solving Two-Step Equations

A.4.C: connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.

Point-Slope Form of a Line - Activity A

A.5: The student understands that linear functions can be represented in different ways and translates among their various representations.

A.5.A: determine whether or not given situations can be represented by linear functions;

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

A.5.B: determine the domain and range for linear functions in given situations; and

Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

A.5.C: use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

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

A.6: The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations

A.6.A: develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope - Activity B

A.6.B: interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

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

A.6.C: investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

Parabolas - Activity A
Roots of a Quadratic
Translating and Scaling Functions

A.6.D: graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope 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
Using Tables, Rules and Graphs

A.6.E: determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

Linear Functions
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

A.6.F: interpret and predict the effects of changing slope and y-intercept in applied situations; and

Defining a Line with Two 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
Standard Form of a Line

A.6.G: relate direct variation to linear functions and solve problems involving proportional change.

Direct Variation
Direct and Inverse Variation
Linear Functions
Point-Slope Form of a Line - Activity A
Similar Figures - Activity A
Similar Polygons
Slope-Intercept Form of a Line - Activity A

A.7: The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

A.7.A: analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

Linear Functions
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
Using Tables, Rules and Graphs

A.7.B: investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities; and

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form) - Activity A

A.7.C: interpret and determine the reasonableness of solutions to linear equations and inequalities.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

A.8: The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

A.8.B: solve systems of linear equations using concrete models, graphs, tables, and algebraic methods; and

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

A.9: The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

A.9.A: determine the domain and range for quadratic functions in given situations;

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

A.9.B: investigate, describe, and predict the effects of changes in a on the graph of y = ax² + c;

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
Parabolas - 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
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Using Tables, Rules and Graphs

A.9.C: investigate, describe, and predict the effects of changes in c on the graph of y = ax² + c; and

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
Parabolas - 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
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Using Tables, Rules and Graphs

A.9.D: analyze graphs of quadratic functions and draw conclusions.

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

A.10: The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods.

A.10.A: solve quadratic equations using concrete models, tables, graphs, and algebraic methods; and

Roots of a Quadratic

A.10.B: make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

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

A.11: The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

A.11.A: use patterns to generate the laws of exponents and apply them in problem-solving situations;

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A.11.B: analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods; and

Direct and Inverse Variation

A.11.C: analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life

2A.1: The student uses properties and attributes of functions and applies functions to problem situations.

2A.1.A: identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations; and

Functions Involving Square Roots
Introduction to Functions

2A.1.B: collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

2A.2: The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

2A.2.A: use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations; and

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2A.2.B: use complex numbers to describe the solutions of quadratic equations.

Roots of a Quadratic

2A.3: The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations.

2A.3.A: analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;

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

2A.3.B: use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities; and

Linear Programming - Activity A
Modeling Linear Systems - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

2A.3.C: interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

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

2A.4: The student connects algebraic and geometric representations of functions.

2A.4.A: identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x²), exponential (f(x) = a to the x power), and logarithmic (f(x) = log of a(x)) functions, absolute value of x (f(x) = |x|), square root of x (f(x) = square root of x), and reciprocal of x (f(x) = 1/x);

Exponential Functions - Activity A
Functions Involving Square Roots
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
Roots of a Quadratic

2A.4.B: extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions; and

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
Parabolas - 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
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Using Tables, Rules and Graphs

2A.5: The student knows the relationship between the geometric and algebraic descriptions of conic sections.

2A.5.A: describe a conic section as the intersection of a plane and a cone;

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

2A.5.B: sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
Quadratics in Factored Form
Roots of a Quadratic
Translating and Scaling Functions

2A.5.C: identify symmetries from graphs of conic sections;

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
Quadratics in Factored Form

2A.5.D: identify the conic section from a given equation; and

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

2A.6: The student understands that quadratic functions can be represented in different ways and translates among their various representations.

2A.6.A: determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

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

2A.6.B: relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; and

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

2A.6.C: determine a quadratic function from its roots or a graph.

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

2A.7: The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations.

2A.7.B: use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)² + k form of a function in applied and purely mathematical situations.

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

2A.8: The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

2A.8.A: analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

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

2A.8.B: analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

Roots of a Quadratic

2A.8.D: solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

Quadratic Inequalities - Activity A
Roots of a Quadratic
Using Tables, Rules and Graphs

2A.9: The student formulates equations and inequalities based on square root functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

2A.9.A: use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;

Functions Involving Square Roots
Radical Functions
Translating and Scaling Functions

2A.9.B: relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

Functions Involving Square Roots
Radical Functions
Using Algebraic Equations

2A.9.C: determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

Functions Involving Square Roots
Radical Functions

2A.9.D: determine solutions of square root equations using graphs, tables, and algebraic methods;

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

2A.9.E: determine solutions of square root inequalities using graphs and tables;

Functions Involving Square Roots
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Radical Functions
Systems of Linear Inequalities (Slope-intercept form) - Activity A

2A.9.F: analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems; and

Functions Involving Square Roots
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Radical Functions
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

2A.9.G: connect inverses of square root functions with quadratic functions.

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

2A.10: The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

2A.10.A: use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

General Form of a Rational Function
Rational Functions
Translating and Scaling Functions

2A.10.B: analyze various representations of rational functions with respect to problem situations;

General Form of a Rational Function
Rational Functions
Using Algebraic Equations

2A.10.C: determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

General Form of a Rational Function
Rational Functions

2A.10.D: determine the solutions of rational equations using graphs, tables, and algebraic methods;

Using Tables, Rules and Graphs

2A.10.F: analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem; and

General Form of a Rational Function
Linear Functions
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Roots of a Quadratic
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

2A.10.G: use functions to model and make predictions in problem situations involving direct and inverse variation.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

2A.11: The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

2A.11.A: develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

2A.11.B: use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

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

2A.11.C: determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

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

2A.11.D: determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

Using Tables, Rules and Graphs

2A.11.E: determine solutions of exponential and logarithmic inequalities using graphs and tables; and

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

2A.11.F: analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

G.1: The student understands the structure of, and relationships within, an axiomatic system.

G.1.A: develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems;

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

G.2: The student analyzes geometric relationships in order to make and verify conjectures.

G.2.A: use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships; and

Classifying Quadrilaterals - Activity B
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

G.2.B: make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

Circles

G.3: The student applies logical reasoning to justify and prove mathematical statements.

G.3.A: determine the validity of a conditional statement, its converse, inverse, and contrapositive;

Conditional Statement

G.3.B: construct and justify statements about geometric figures and their properties;

Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Special Quadrilaterals

G.3.E: use deductive reasoning to prove a statement.

Biconditional Statement
Conditional Statement

G.5: The student uses a variety of representations to describe geometric relationships and solve problems.

G.5.A: use numeric and geometric patterns to develop algebraic expressions representing geometric properties;

Arithmetic and Geometric Sequences
Classifying Triangles
Ellipse - Activity A
Finding Patterns
Geometric Sequences
Hyperbola - Activity A

G.5.B: use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles;

Arithmetic and Geometric Sequences
Classifying Triangles
Finding Patterns
Geometric Sequences

G.5.D: identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

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

G.6: The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

G.6.A: describe and draw the intersection of a given plane with various three-dimensional geometric figures;

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

G.6.B: use nets to represent and construct three-dimensional geometric figures; and

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.6.C: use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems.

3D and Orthographic Views - Activity A

G.7: The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

G.7.A: use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

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

G.7.B: use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons; and

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

G.7.C: derive and use formulas involving length, slope, and midpoint.

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

G.8: The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

G.8.A: find areas of regular polygons, circles, and composite figures;

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

G.8.B: find areas of sectors and arc lengths of circles using proportional reasoning;

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

G.8.C: derive, extend, and use the Pythagorean Theorem; and

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

G.8.D: find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

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.9: The student analyzes properties and describes relationships in geometric figures.

G.9.A: formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models;

Construct Parallel and Perpendicular Lines

G.9.C: formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models; and

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

G.10: The student applies the concept of congruence to justify properties of figures and solve problems.

G.10.A: use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane; and

Classifying Quadrilaterals - Activity B
Constructing Congruent Segments and Angles
Dilations
Parallelogram Conditions
Reflections
Rotations, Reflections and Translations
Special Quadrilaterals

G.10.B: justify and apply triangle congruence relationships.

Congruence in Right Triangles
Proving Triangles Congruent

G.11: The student applies the concepts of similarity to justify properties of figures and solve problems.

G.11.A: use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

Classifying Quadrilaterals - Activity B
Dilations
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons

G.11.B: use ratios to solve problems involving similar figures;

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

G.11.C: develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods; and

Cosine Function
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

G.11.D: describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

Area of Parallelograms - Activity A
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

P.1: The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigo

P.1.A: describe parent functions symbolically and graphically, including f(x) = x to the n power, f(x) = 1n x, f(x) = loga x, f(x) = 1/x, f(x) = e to the x power, f(x) = |x|, f(x) = a to the x power, f(x) = sin x, f(x) = arcsin x, etc.;

Cosine Function
Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

P.1.B: determine the domain and range of functions using graphs, tables, and symbols;

Functions Involving Square Roots
Introduction to Functions

P.1.D: recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function; and

Polynomials and Linear Factors
Roots of a Quadratic

P.2: The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems.

P.2.A: apply basic transformations, including a • f(x), f(x) + d, f(x - c), f(b • x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;

Inequalities Involving Absolute Values
Quadratic and Absolute Value Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

P.2.C: investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

P.3: The student uses functions and their properties, tools and technology, to model and solve meaningful problems.

P.3.A: investigate properties of trigonometric and polynomial functions;

Cosine Function
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Sine Function
Tangent Function

P.3.B: use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;

Cosine Function
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

P.3.C: use regression to determine the appropriateness of a linear function to model real-life data (including using technology to determine the correlation coefficient);

Correlation
Linear Functions
Solving Using Trend Lines

P.3.D: use properties of functions to analyze and solve problems and make predictions; and

Exponential Functions - Activity A
Logarithmic Functions: Translating and Scaling

P.3.E: solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

Riemann Sum

P.4: The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems.

P.4.A: represent patterns using arithmetic and geometric sequences and series;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

P.4.B: use arithmetic, geometric, and other sequences and series to solve real-life problems;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

P.5: The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations.

P.5.A: use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;

Hyperbola - Activity A

P.6: The student uses vectors to model physical situations.

P.6.A: use the concept of vectors to model situations defined by magnitude and direction; and

Vectors

P.6.B: analyze and solve vector problems generated by real-life situations.

Vectors

M.2: The student uses graphical and numerical techniques to study patterns and analyze data.

M.2.A: interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, line plots, stem and leaf plots, and box and whisker plots to draw conclusions from the data;

Box-and-Whisker Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

M.2.B: analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences;

Mean, Median and Mode

M.2.D: use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.

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

M.4: The student uses probability models to describe everyday situations involving chance.

M.4.A: compare theoretical and empirical probability; and

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

M.5: The student uses functional relationships to solve problems related to personal income.

M.5.A: use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions;

Direct Variation
Direct and Inverse Variation
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

M.7: The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning.

M.7.A: analyze types of savings options involving simple and compound interest and compare relative advantages of these options;

Exponential Functions - Activity A
Simple and Compound Interest

M.8: The student uses algebraic and geometric models to describe situations and solve problems.

M.8.B: use trigonometric ratios and functions available through technology to calculate distances and model periodic motion; and

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

M.8.C: use direct and inverse variation to describe physical laws such as Hook's, Newton's, and Boyle's laws.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

M.9: The student uses algebraic and geometric models to represent patterns and structures.

M.9.A: use geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and architecture; and

Dilations
Holiday Snowflake Designer
Reflections
Rotations, Reflections and Translations

M.9.B: use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music.

Dilations
Polling: Neighborhood
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons