EA.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

EA.1.3: Apply algebraic methods to solve problems in real-world contexts.

Estimating Population Size

EA.1.5: Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

Correlation
Solving Equations on the Number Line
Square Roots
Stem-and-Leaf Plots
Using Algebraic Equations
Using Algebraic Expressions

EA.2: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

EA.2.1: Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers).

Rational Numbers, Opposites, and Absolute Values

EA.2.2: Apply the laws of exponents and roots to solve problems.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Radical Expressions

EA.2.3: Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

EA.2.4: Use dimensional analysis to convert units of measure within a system.

Unit Conversions

EA.2.5: Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

EA.2.7: Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

Addition of Polynomials
Dividing Polynomials Using Synthetic Division

EA.2.8: Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).

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

EA.2.9: Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication).

Translations

EA.3: The student will demonstrate through the mathematical processes an understanding of relationships and functions.

EA.3.1: Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph.

Introduction to Functions
Linear Functions
Points, Lines, and Equations

EA.3.3: Carry out a procedure to evaluate a function for a given element in the domain.

Introduction to Functions
Logarithmic Functions
Radical Functions

EA.3.5: Carry out a procedure to graph parent functions (including y = x, y = x², y = the square root of x, y = the absolute value of x, and y = 1/x).

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Exponential Functions
Linear Functions
Radical Functions
Translating and Scaling Functions

EA.3.6: Classify a variation as either direct or inverse.

Direct and Inverse Variation

EA.3.7: Carry out a procedure to solve literal equations for a specified variable.

Area of Triangles
Solving Formulas for any Variable

EA.3.8: Apply proportional reasoning to solve problems.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios

EA.4: The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.

EA.4.1: Carry out a procedure to write an equation of a line with a given slope and a y-intercept.

Point-Slope Form of a Line
Standard Form of a Line

EA.4.2: Carry out a procedure to write an equation of a line with a given slope passing through a given point.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

EA.4.3: Carry out a procedure to write an equation of a line passing through two given points.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Standard Form of a Line

EA.4.4: Use a procedure to write an equation of a trend line from a given scatterplot.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

EA.4.5: Analyze a scatterplot to make predictions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

EA.4.6: Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard).

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Linear Systems (Standard Form)
Standard Form of a Line

EA.4.7: Carry out procedures to solve linear equations for one variable algebraically.

Area of Triangles
Solving Formulas for any Variable

EA.4.8: Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution.

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

EA.4.9: Carry out a procedure to solve systems of two linear equations graphically.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

EA.4.10: Carry out a procedure to solve systems of two linear equations algebraically.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

EA.5: The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.

EA.5.1: Carry out a procedure to graph a line when given the equation of the line.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

EA.5.2: Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b.

Slope-Intercept Form of a Line

EA.5.3: Carry out a procedure to graph the line with a given slope and a y-intercept.

Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

EA.5.4: Carry out a procedure to graph the line with a given slope passing through a given point.

Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

EA.5.6: Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.

Cat and Mouse (Modeling with Linear Systems)
Slope
Slope-Intercept Form of a Line

EA.5.7: Apply the concept of slope as a rate of change to solve problems.

Cat and Mouse (Modeling with Linear Systems)
Distance-Time and Velocity-Time Graphs
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

EA.5.11: Analyze given information to write a system of linear equations that models a given problem situation.

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

EA.5.12: Analyze given information to write a linear inequality in one variable that models a given problem situation.

Systems of Linear Inequalities (Slope-intercept form)

EA.6: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

EA.6.1: Analyze the effects of changing the leading coefficient a on the graph of y = ax².

Zap It! Game

EA.6.2: Analyze the effects of changing the constant c on the graph of y = x² + c.

Zap It! Game

EA.6.3: Analyze the graph of a quadratic function to determine its equation.

Addition and Subtraction of Functions
Parabolas
Translating and Scaling Functions
Zap It! Game

EA.6.4: Carry out a procedure to solve quadratic equations by factoring.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

IA.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

IA.1.3: Apply algebraic methods to solve problems in real-world contexts.

Estimating Population Size

IA.1.5: Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

Solving Equations on the Number Line
Square Roots
Using Algebraic Equations
Using Algebraic Expressions

IA.2: The student will demonstrate through the mathematical processes an understanding of functions, systems of equations, and systems of linear inequalities.

IA.2.2: Carry out a procedure to solve a system of linear inequalities graphically.

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

IA.2.3: Analyze a problem situation to determine a system of linear inequalities that models the problem situation.

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

IA.2.4: Use linear programming to solve contextual problems involving a system of linear inequalities.

Linear Programming

IA.2.7: Carry out a procedure to graph translations of parent functions (including y = x, y = x², y = square root of x, y = absolute value of x, and y = 1/x).

Absolute Value with Linear Functions
General Form of a Rational Function
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translations
Zap It! Game

IA.2.8: Carry out a procedure to graph transformations of parent functions (including y = x, y = x², and y = absolute value of x).

Absolute Value with Linear Functions
Exponential Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Translations
Zap It! Game

IA.2.9: Carry out a procedure to graph discontinuous functions (including piecewise and step functions).

Absolute Value with Linear Functions

IA.2.11: Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function).

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

IA.3: The student will demonstrate through the mathematical processes an understanding of quadratic equations and the complex number system.

IA.3.1: Carry out a procedure to simplify expressions involving powers of i.

Points in the Complex Plane

IA.3.2: Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division).

Points in the Complex Plane

IA.3.3: Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula).

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Roots of a Quadratic

IA.3.4: Use the discriminant to determine the number and type of solutions of a quadratic equation.

Roots of a Quadratic

IA.3.5: Analyze given information (including quadratic models) to solve contextual problems.

Addition and Subtraction of Functions
Quadratics in Polynomial Form

IA.3.6: Carry out a procedure to write an equation of a quadratic function when given its roots.

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form

IA.4: The student will demonstrate through the mathematical processes an understanding of algebraic expressions and nonlinear functions.

IA.4.1: Carry out a procedure to perform operations (including multiplication, exponentiation, and division) with polynomial expressions.

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Exponential Expressions
Dividing Polynomials Using Synthetic Division
Exponents and Power Rules
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions

IA.4.2: Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form

IA.4.9: Carry out a procedure to solve radical equations algebraically.

Operations with Radical Expressions
Radical Functions

IA.4.13: Carry out a procedure to graph logarithmic functions.

Logarithmic Functions

IA.4.14: Carry out a procedure to graph exponential functions.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

IA.5: The student will demonstrate through the mathematical processes an understanding of conic sections.

IA.5.1: Carry out a procedure to graph the circle whose equation is the form x² + y² = r².

Circles

IA.5.2: Carry out a procedure to write an equation of a circle centered at the origin when given its radius.

Circles

IA.5.3: Carry out a procedure to graph the ellipse whose equation is the form (x²/a²) + (y²/b²) = 1.

Ellipses

IA.5.4: Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices.

Ellipses

IA.5.5: Carry out a procedure to graph the hyperbola whose equation is the form (x²/a²) - (y²/b²) = 1.

Hyperbolas

IA.5.6: Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices.

Hyperbolas

IA.5.7: Match the equation of a conic section with its graph.

Circles
Ellipses
Hyperbolas
Parabolas

IA.6: The student will demonstrate through the mathematical processes an understanding of sequences and series.

IA.6.1: Categorize a sequence as arithmetic, geometric, or neither.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

IA.6.2: Carry out a procedure to write a specified term of an arithmetic or geometric sequence when given the nth term of the sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

IA.6.3: Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence.

Arithmetic Sequences
Geometric Sequences

IA.6.4: Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence.

Arithmetic Sequences
Geometric Sequences

IA.6.7: Carry out a procedure to determine consecutive terms of a sequence that is defined recursively.

Arithmetic Sequences
Geometric Sequences

IA.6.8: Carry out a procedure to define a sequence recursively when given four or more consecutive terms of the sequence.

Arithmetic Sequences
Geometric Sequences

IA.6.9: Translate between the explicit form and the recursive form of sequences.

Arithmetic Sequences
Geometric Sequences

G.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

G.1.3: Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement.

Biconditional Statements
Conditional Statements

G.1.10: Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices).

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

G.2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

G.2.2: Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems.

Constructing Congruent Segments and Angles
Parallel, Intersecting, and Skew Lines

G.2.3: Use the congruence of line segments and angles to solve problems.

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Proving Triangles Congruent
Triangle Angle Sum

G.2.5: Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line).

3D and Orthographic Views
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines
Segment and Angle Bisectors

G.2.6: Use scale factors to solve problems involving scale drawings and models.

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

G.2.7: Use geometric probability to solve problems.

Geometric Probability

G.3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

G.3.1: Carry out a procedure to compute the perimeter of a triangle.

Perimeters and Areas of Similar Figures

G.3.2: Carry out a procedure to compute the area of a triangle.

Area of Triangles
Perimeters and Areas of Similar Figures

G.3.4: Apply properties of isosceles and equilateral triangles to solve problems.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Triangle Inequalities

G.3.5: Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems.

Concurrent Lines, Medians, and Altitudes
Segment and Angle Bisectors
Similarity in Right Triangles
Triangle Angle Sum

G.3.6: Apply the triangle sum theorem to solve problems.

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

G.3.7: Apply the triangle inequality theorem to solve problems.

Triangle Inequalities

G.3.8: Apply congruence and similarity relationships among triangles to solve problems.

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

G.3.9: Apply theorems to prove that triangles are either similar or congruent.

Congruence in Right Triangles
Proving Triangles Congruent
Similar Figures

G.3.10: Use the Pythagorean theorem and its converse to solve problems.

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

G.3.11: Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.

Cosine Function
Sine Function
Tangent Function

G.3.12: Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

G.4: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them.

G.4.1: Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures.

Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures

G.4.2: Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures

G.4.3: Apply procedures to compute measures of interior and exterior angles of polygons.

Polygon Angle Sum
Triangle Angle Sum

G.4.4: Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons.

Perimeter and Area of Rectangles

G.4.5: Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems.

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

G.4.6: Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems.

Constructing Congruent Segments and Angles
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Similarity in Right Triangles

G.5: The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments.

G.5.1: Carry out a procedure to compute the circumference of circles.

Circumference and Area of Circles

G.5.2: Carry out a procedure to compute the area of circles.

Circumference and Area of Circles

G.5.4: Carry out a procedure to compute the length of an arc or the area of a sector of a circle.

Inscribed Angles

G.5.5: Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

Chords and Arcs
Circles
Inscribed Angles

G.5.7: Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems.

Chords and Arcs
Inscribed Angles

G.6: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors.

G.6.1: Use the distance formula to solve problems.

Circles
Distance Formula

G.6.2: Use the midpoint formula to solve problems.

Circles

G.6.3: Apply transformations-translation, reflection, rotation, and dilation-to figures in the coordinate plane by using sketches and coordinates.

Dilations
Rotations, Reflections, and Translations
Translations

G.6.4: Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices.

Dilations
Translations

G.6.5: Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.

Adding Vectors

G.6.6: Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement.

Adding Vectors
Vectors

G.6.8: Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement.

Adding Vectors
Vectors

G.7: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

G.7.1: Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres).

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

G.7.2: Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects).

Prisms and Cylinders
Pyramids and Cones

G.7.4: Apply congruence and similarity relationships among geometric objects to solve problems.

Circles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures

G.7.5: Apply a procedure to draw a top view, front view, and side view of a three-dimensional object.

3D and Orthographic Views

G.7.6: Apply a procedure to draw an isometric view of a three-dimensional object.

3D and Orthographic Views

PC.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

PC.1.1: Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

Cosine Function
Sine Function

PC.1.5: Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

Function Machines 1 (Functions and Tables)
Points, Lines, and Equations
Square Roots
Using Algebraic Equations
Using Algebraic Expressions

PC.1.6: Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios

PC.1.7: Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

PC.2: The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions.

PC.2.1: Carry out a procedure to graph parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Point-Slope Form of a Line
Rational Functions
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions

PC.2.2: Carry out a procedure to graph transformations (including -f(x), a * f(x), f(x) + d, f(x - c), f(-x), f(b * x), |f(x)|, and f(|x|)) of parent functions and combinations of transformations.

Translating and Scaling Sine and Cosine Functions

PC.2.3: Analyze a graph to describe the transformation (including -f(x), a * f(x), f(x) + d, f(x - c), f(-x), f(b * x), |f(x)|, and f(|x|)) of parent functions.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

PC.2.4: Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

Exponential Functions

PC.2.5: Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

Exponential Functions
Logarithmic Functions

PC.2.7: Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.

Polynomials and Linear Factors

PC.2.8: Carry out a procedure to determine whether the inverse of a function exists.

Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions

PC.3: The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions.

PC.3.1: Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.

Addition and Subtraction of Functions
Exponential Functions
Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Translating and Scaling Functions
Zap It! Game

PC.3.3: Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form

PC.3.4: Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

General Form of a Rational Function
Rational Functions

PC.3.5: Analyze given information to write a polynomial function that models a given problem situation.

Polynomials and Linear Factors

PC.4: The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions.

PC.4.1: Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

PC.4.2: Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.

Logarithmic Functions

PC.4.3: Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

PC.4.4: Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).

Logarithmic Functions

PC.4.6: Analyze given information to write an exponential function that models a given problem situation.

Exponential Functions
Introduction to Exponential Functions

PC.4.8: Carry out a procedure to solve exponential equations algebraically.

Exponential Functions

PC.4.9: Carry out a procedure to solve exponential equations graphically.

Exponential Functions

PC.5: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions.

PC.5.1: Understand how angles are measured in either degrees or radians.

Triangle Angle Sum

PC.5.2: Carry out a procedure to convert between degree and radian measures.

Cosine Function
Sine Function
Tangent Function

PC.5.4: Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

PC.5.14: Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

Cosine Function
Simplifying Trigonometric Expressions
Sine Function
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine
Tangent Function

PC.6: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.

PC.6.1: Carry out a procedure to graph the circle whose equation is the form (x-h)² + (y-k)² = r².

Circles

PC.6.2: Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

Circles

PC.6.4: Carry out a procedure to graph the ellipse whose equation is the form (((x-h)²)/a²) + (((y-k)²)/b²) = 1.

Ellipses

PC.6.5: Carry out a procedure to graph the hyperbola whose equation is the form (((x-h)²)/a²) - (((y-k)²)/b²) = 1.

Hyperbolas

PC.6.6: Carry out a procedure to graph the parabola whose equation is the form y-k = a(x-h)².

Parabolas

DA.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

DA.1.1: Execute procedures to conduct simple probability experiments and collect data by using manipulatives (including spinners, dice, cards, and coins).

Binomial Probabilities
Geometric Probability
Independent and Dependent Events

DA.1.2: Execute procedures to find measures of probability and statistics by using tools such as handheld computing devices, spreadsheets, and statistical software.

Probability Simulations
Theoretical and Experimental Probability

DA.1.4: Design and conduct a statistical research project and produce a report that summarizes the findings.

Box-and-Whisker Plots
Describing Data Using Statistics
Stem-and-Leaf Plots

DA.1.5: Apply the principles of probability and statistics to solve problems in real-world contexts.

Estimating Population Size
Theoretical and Experimental Probability

DA.1.6: Communicate a knowledge of data analysis and probability by using mathematical terminology appropriately.

Polling: City
Probability Simulations
Theoretical and Experimental Probability

DA.2: The student will demonstrate through the mathematical processes an understanding of the design of a statistical study.

DA.2.1: Classify a data-collection procedure as a survey, an observational study, or a controlled experiment.

Correlation
Describing Data Using Statistics
Polling: City
Polling: Neighborhood

DA.2.2: Compare various random sampling techniques (including simple, stratified, cluster, and systematic).

Polling: Neighborhood
Populations and Samples

DA.2.3: Analyze a data-collection procedure to classify the technique used as either simple cluster, systematic, or convenience sampling.

Describing Data Using Statistics

DA.2.5: Judge which of two or more possible experimental designs will best answer a given research question.

Real-Time Histogram

DA.2.6: Generate a research question and design a statistical study to answer a given research question.

Correlation
Polling: Neighborhood

DA.3: The student will demonstrate through the mathematical processes an understanding of the methodology for collecting, organizing, displaying, and interpreting data.

DA.3.1: Use manipulatives, random number tables, and technology to collect data and conduct experiments and simulations.

Binomial Probabilities
Describing Data Using Statistics
Geometric Probability
Independent and Dependent Events

DA.3.2: Organize and interpret data by using pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Forest Ecosystem
Histograms
Least-Squares Best Fit Lines
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

DA.3.3: Select appropriate graphic display(s) from among pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots when given a data set or problem situation.

Box-and-Whisker Plots
Forest Ecosystem
Histograms
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

DA.3.4: Represent frequency distributions by using displays such as categorical frequency distributions/Pareto charts, histograms, frequency polygons, and cumulative frequency distributions/ogives.

Histograms
Polling: City
Populations and Samples
Real-Time Histogram

DA.3.6: Classify graphically and analytically the correlation between two variables as either positive, negative, or zero.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

DA.3.7: Carry out a procedure to determine an equation of a trend line for a scatterplot exhibiting a linear pattern by using visual approximation.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

DA.3.8: Carry out a procedure using technology to determine a line of best fit for a scatterplot exhibiting a linear pattern.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

DA.3.9: Explain the meaning of the correlation coefficient r.

Correlation

DA.4: The student will demonstrate through the mathematical processes an understanding of basic statistical methods of analyzing data.

DA.4.4: Use procedures and/or technology to find measures of central tendency (mean, median, and mode) for given data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

DA.4.6: Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

DA.4.7: Use procedures and/or technology to find measures of position (including median, quartiles, percentiles, and standard scores) for given data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

DA.4.10: Use a knowledge of the empirical rule to solve problems involving data that are distributed normally.

Populations and Samples
Real-Time Histogram

DA.5: The student will demonstrate through the mathematical processes an understanding of the basic concepts of probability.

DA.5.1: Construct a sample space for an experiment and represent it as a list, chart, picture, or tree diagram.

Binomial Probabilities
Permutations and Combinations

DA.5.2: Use counting techniques to determine the number of possible outcomes for an event.

Binomial Probabilities

DA.5.3: Classify events as either dependent or independent.

Independent and Dependent Events

DA.5.6: Use the binomial probability distribution to solve problems.

Binomial Probabilities

DA.5.7: Carry out a procedure to compute simple probabilities and compound probabilities (including conditional probabilities).

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

DA.5.8: Use a procedure to find geometric probability in real-world contexts.

Geometric Probability

DA.5.9: Compare theoretical and experimental probabilities.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

DA.5.10: Construct and compare theoretical and experimental probability distributions.

Geometric Probability
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

DA.5.12: Understand the law of large numbers.

Theoretical and Experimental Probability