RF.1.AII: Students will represent and analyze mathematical situations and properties using patterns, relations, functions and algebraic symbols.

RF.1.AII.1: Determine, with or without technology, the domain and range of a relation defined by a graph, a table of values, or a symbolic equation including those with restricted domains and whether a relation is a function

Introduction to Functions

RF.1.AII.2: Evaluate, add, subtract, multiply, and divide functions and give appropriate domain and range restrictions

Addition and Subtraction of Functions
Introduction to Functions
Logarithmic Functions
Radical Functions

RF.1.AII.3: Determine the inverse of a function (Graph, with and without appropriate technology, functions and their inverses)

Logarithmic Functions

RF.1.AII.4: Analyze and report, with and without appropriate technology, the effect of changing coefficients, exponents, and other parameters on functions and their graphs (linear, quadratic, and higher degree polynomial)

Absolute Value with Linear Functions
Graphs of Polynomial Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Translating and Scaling Functions
Zap It! Game

RF.1.AII.5: Graph, with and without appropriate technology, functions defined as piece-wise and step

Absolute Value with Linear Functions

RF.1.AII.6: Recognize periodic phenomena (sine or cosine functions such as sound waves, length of daylight, circular motion)

Translating and Scaling Sine and Cosine Functions

RF.1.AII.7: Investigate and identify key characteristics of period functions and their graphs (period, amplitude, maximum, and minimum)

Translating and Scaling Functions

LEI.2.AII: Students will analyze and apply various methods to model, graph and solve linear and absolute value equations and inequalities.

LEI.2.AII.1: Solve, with and without appropriate technology, absolute value equations and inequalities written in one or two variables, and graph solutions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Compound Inequalities

LEI.2.AII.2: Solve, with and without appropriate technology, systems of linear equations with two variables and graph the solution set

Solving Linear Systems (Standard Form)

LEI.2.AII.3: Develop and apply, with and without appropriate technology, the basic operations and properties of matrices (associative, commutative, identity, and inverse)

Translations

LEI.2.AII.5: Apply, with or without technology, the concepts of linear and absolute value equations and inequalities and systems of linear equations and inequalities to model real world situations including linear programming

Cat and Mouse (Modeling with Linear Systems)
Compound Inequalities
Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

QEF.3.AII: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve quadratic equations.

QEF.3.AII.1: Perform computations with radicals

QEF.3.AII.1.b: add, subtract, multiply and divide radicals

Operations with Radical Expressions

QEF.3.AII.1.c: rationalize denominators

Simplifying Radical Expressions

QEF.3.AII.1.d: solve equations that contain radicals or radical expressions

Operations with Radical Expressions
Radical Functions

QEF.3.AII.2: Extend the number system to include the complex numbers

QEF.3.AII.2.b: add, subtract, multiply, and divide complex numbers

Points in the Complex Plane

QEF.3.AII.3: Analyze and solve quadratic equations with and without appropriate technology by

QEF.3.AII.3.a: factoring

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

QEF.3.AII.3.b: graphing

Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

QEF.3.AII.3.d: completing the square

Roots of a Quadratic

QEF.3.AII.3.e: using the quadratic formula

Addition and Subtraction of Functions
Roots of a Quadratic
Translating and Scaling Functions

QEF.3.AII.4: Derive the quadratic formula and use it to solve equations

Roots of a Quadratic

QEF.3.AII.5: Develop and analyze, with and without appropriate technology, quadratic relations

QEF.3.AII.5.a: graph a parabolic relationship when given its equation

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

QEF.3.AII.5.b: write an equation when given its roots (zeros or solutions) or graph

Modeling the Factorization of x²+bx+c
Parabolas
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

QEF.3.AII.5.c: determine the nature of the solutions graphically and by evaluating the discriminant

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

QEF.3.AII.5.d: determine the maximum or minimum values and the axis of symmetry both graphically and algebraically

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

QEF.3.AII.6: Apply the concepts of quadratic equations and functions to model real world situations by using appropriate technology when needed

Addition and Subtraction of Functions
Quadratics in Polynomial Form

PRF.4.AII: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve polynomial and rational equations.

PRF.4.AII.1: Determine the factors of polynomials by

PRF.4.AII.1.a: using factoring techniques including grouping and the sum or difference of two cubes

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

PRF.4.AII.1.b: using long division

Dividing Polynomials Using Synthetic Division

PRF.4.AII.1.c: using synthetic division

Dividing Polynomials Using Synthetic Division

PRF.4.AII.2: Analyze and sketch, with and without appropriate technology, the graph of a given polynomial function, determining the characteristics of domain and range, maximum and minimum points, end behavior, zeros, multiplicity of zeros, y-intercept, and symmetry

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

PRF.4.AII.4: Identify the equation of a polynomial function given its graph or table

Graphs of Polynomial Functions
Quadratics in Factored Form
Quadratics in Vertex Form

ELF.5.AII: Students will graph exponential functions and relate them to logarithms. They will solve real world problems using exponential functions.

ELF.5.AII.1: Recognize the graphs of exponential functions distinguishing between growth and decay

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

ELF.5.AII.2: Graph exponential functions and identify key characteristics: domain, range, intercepts, asymptotes, and end behavior

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

ELF.5.AII.4: Recognize and solve problems that can be modeled using exponential functions

Exponential Functions
Introduction to Exponential Functions

ELF.5.AII.5: Establish the relationship between exponential and logarithmic functions

Logarithmic Functions

DAP.6.AII: Students will evaluate and interpret data, make predictions based on data, and apply basic understanding of probability to solve real world problems.

DAP.6.AII.1: Find regression line for scatter plot, using appropriate technology, and interpret the correlation coefficient

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

DAP.6.AII.2: Interpret and use the correlation coefficient to assess the strength of the linear relationship between two variables

Correlation

DAP.6.AII.3: Find the quadratic curve of best fit using appropriate technology

Zap It! Game

DAP.6.AII.4: Identify strengths and weaknesses of using regression equations to approximate data

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

DAP.6.AII.5: Compute and explain measures of spread (range, percentiles, variance, standard deviation)

Polling: City
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram

DAP.6.AII.6: Describe the characteristics of a Gaussian normal distribution

Polling: City
Populations and Samples