1: The student will develop, analyze, communicate, and apply models to real-world situations using the language of mathematics and appropriate technology.

1.1: The student will model and interpret real-world situations, using the language of mathematics and appropriate technology.

1.1.1: The student will determine and interpret a linear function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

1.1.1.A: The majority of these items should be in context.

Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Linear Functions
Modeling Linear Systems - Activity A
Using Tables, Rules and Graphs

1.1.1.B: Essential characteristics are any points on the line, x- and y-intercepts, and slope.

Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Linear Functions
Modeling Linear Systems - Activity A
Slope - Activity B
Using Tables, Rules and Graphs

1.1.1.a: Given one or more of the following:

1.1.1.a.1: a verbal description

Linear Functions
Using Algebraic Equations
Using Algebraic Expressions

1.1.1.a.2: a graph

Linear Functions

1.1.1.a.3: a table of values

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Using Tables, Rules and Graphs

1.1.1.a.4: an equation

Linear Functions

1.1.1.a.5: two or more essential characteristics

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Using Tables, Rules and Graphs

1.1.1.a.6: an absolute value equation

Linear Functions

1.1.1.b: the student will be able to do each of the following:

1.1.1.b.1: write and/or solve an equation or an inequality that models the situation

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Linear Inequalities in Two Variables - Activity A
Modeling and Solving Two-Step Equations
Road Trip (Problem Solving)
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Using Algebraic Equations
Using Tables, Rules and Graphs

1.1.1.b.2: graph the function

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Using Tables, Rules and Graphs

1.1.1.b.3: find and/or interpret the meaning of any essential characteristics in the context of the problem.

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Using Tables, Rules and Graphs

1.1.1.c: Students should be able to perform these skills with and without the use of a graphing calculator.

Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Linear Functions
Modeling Linear Systems - Activity A
Using Tables, Rules and Graphs

1.1.2: The student will determine and interpret a quadratic function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

1.1.2.A: The majority of the items should be in context.

Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

1.1.2.B: Essential characteristics are zeros, vertex (maximum or minimum), y-intercept, increasing and decreasing behavior.

Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

1.1.2.C: A table of values must include rational zeros and at least one other point.

Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

1.1.2.D: All have real zeros.

Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

1.1.2.a: Given one or more of the following:

1.1.2.a.1: a verbal description

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

1.1.2.a.2: a graph

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

1.1.2.a.3: a table of values

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

1.1.2.a.4: a function in equation form

Quadratics in Factored Form
Roots of a Quadratic

1.1.2.b: the student will be able to do each of the following:

1.1.2.b.1: find one or more of the essential characteristics

Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

1.1.2.b.2: write the function in equation form

Quadratics in Factored Form
Roots of a Quadratic
Using Algebraic Equations

1.1.2.b.3: graph the function

Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

1.1.2.b.4: approximate the value of f(x) for a given number x

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

1.1.2.b.5: determine x for a given value of f(x).

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

1.1.2.0: The student will determine and interpret information from models of simple conic sections.

1.1.2.0.B: Ellipses and hyperbolas will have axes parallel to the x and y axes and centers at the origin.

Hyperbola - Activity A

1.1.2.1.1.2.02.a: Given its center and radius, the student will write an equation of a circle.

Circles

1.1.2.1.1.2.02.b: Given an equation of a circle, the student will find the center and radius of the circle.

Circles

1.1.2.1.1.2.02.d: The student will graph ellipses and hyperbolas.

Ellipse - Activity A
Hyperbola - Activity A

1.1.3: The student will determine and interpret an exponential function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

1.1.3.A: The majority of the items should be in context.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)

1.1.3.B: Essential characteristics are y-intercepts, asymptotes, increasing or decreasing.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)

1.1.3.C: For f(x) = ab to the x power, b > 0, a and b are rational numbers, b is not 1.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Function Machines 2 (Functions, Tables, and Graphs)
Half-life

1.1.3.D: The y-values for x =0 and x = 1 will be given.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)

1.1.3.a: Given one or more of the following:

1.1.3.a.1: a verbal description

Exponential Functions - Activity A

1.1.3.a.2: a graph

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)

1.1.3.a.3: a table of values

Exponential Functions - Activity A

1.1.3.a.4: a function in equation form

Exponential Functions - Activity A

1.1.3.b: the student will be able to do each of the following:

1.1.3.b.1: find one or more of the essential characteristics

Exponential Functions - Activity A

1.1.3.b.2: write the function in equation form

Exponential Functions - Activity A

1.1.3.b.3: graph the function

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)

1.1.3.b.4: approximate the value of f(x) for a given number x

Exponential Functions - Activity A

1.1.3.b.5: determine x for a given value of f(x).

Exponential Functions - Activity A

1.1.4: The student will be able to use logarithms to solve problems that can be modeled using an exponential function.

1.1.4.A: The majority of the items should be in context.

Exponential Functions - Activity A

1.1.4.B: Properties used to solve problems may include the product, quotient, and/or power properties of logarithms.

Exponential Functions - Activity A

1.1.4.a: Given verbal descriptions and formulas in exponential form, the student will be able to use the properties of logarithms to solve problems such as exponential growth and decay.

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

1.2: Given an appropriate real-world situation, the student will choose an appropriate linear, quadratic, polynomial, absolute value, piecewise-defined, simple rational or exponential model and apply that model to solve the problem.

1.2.A: The majority of the items should include a verbal description of a real-world situation.

Drug Dosage
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

1.2.a: Given a scatter plot of approximately linear data, the student will write an equation of best fit and/or use that equation to find values for x or f(x) using a graphing calculator.

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Lines of Best Fit Using Least Squares - Activity A
Solving Using Trend Lines

1.2.b: Given a verbal description and/or a table of values of a function, the students will recognize that the function is linear, quadratic, polynomial, absolute value, piecewise-defined, simple rational or exponential and/or write the appropriate equation that models the situation.

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

1.3: The student will communicate the mathematical results in a meaningful manner.

1.3.0.1: The student will compute and interpret summary statistics for distributions of data including measures of center (mean, median, and mode) and spread (range, percentiles, variance, and standard deviation).

Describing Data Using Statistics
Mean, Median and Mode
Populations and Samples

2: The student will demonstrate the ability to analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

2.1: The student will be familiar with basic terminology and notation of functions.

2.1.1: The student will identify and use alternative representations of linear, piecewise-defined, quadratic, polynomial, simple rational and exponential functions.

2.1.1.A: These items are not in context.

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.a: Given one or more of the following:

2.1.1.a.1: a verbal description

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic
Using Algebraic Equations
Using Algebraic Expressions

2.1.1.a.2: a graph

Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.a.3: a table of values

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Linear Functions
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.a.4: an equation

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.a.5: two or more essential characteristics

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.b: the student will be able to do each of the following:

2.1.1.b.1: find a value for x or f(x)

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.b.2: find real roots

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.b.3: find maximum and/or minimum

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.b.4: find intervals on which the function is increasing and/or decreasing.

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.1.c: Given an absolute value function, the student will graph the function and/or calculate a numeric value of the function.

Function Machines 2 (Functions, Tables, and Graphs)
Translating and Scaling Functions

2.1.2: The student will identify the domain, range, the rule or other essential characteristics of a function.

2.1.2.A: Vertical and horizontal lines are included.

Functions Involving Square Roots

2.1.2.B: Functions with restricted domain and/or range are included.

Functions Involving Square Roots

2.1.2.D: Rational functions should have denominators that are:

2.1.2.D.1: linear

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Linear Functions
Rational Functions

2.1.2.D.2: quadratic

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.1.2.D.3: sum and/or difference of two cubes in factored form.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Rational Functions

2.1.2.E: Essential characteristics of a polynomial function include degree, intercepts, end behavior and symmetry of even or odd power functions.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

2.1.2.a: Given one or more of the following:

2.1.2.a.1: a graph of a linear or non-linear function or relation including polynomial functions

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)

2.1.2.a.2: an equation over a specified interval

Functions Involving Square Roots

2.1.2.a.3: a written description of a real-world situation with a restricted domain

Functions Involving Square Roots

2.1.2.a.4: a simple rational function

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Rational Functions

2.1.2.b: the student will be able to do each of the following:

2.1.2.b.3: describe the end behavior of a polynomial function

Arithmetic and Geometric Sequences
Cubic Function Activity
Finding Patterns
Fourth-Degree Polynomials - Activity A

2.1.2.b.4: describe the symmetry of even or odd power functions

Arithmetic and Geometric Sequences
Finding Patterns

2.1.2.b.5: describe the interrelationship between the degree of a polynomial function and the number of intercepts

Arithmetic and Geometric Sequences
Finding Patterns

2.1.2.c: Given the equation of a function, the student will produce the graph and describe the domain and range using inequalities.

Arithmetic and Geometric Sequences
Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots

2.2: The student will perform a variety of operations and geometrical transformations on functions.

2.2.1: The student will add, subtract, multiply, and divide functions.

2.2.1.A: Items involving factoring will be restricted to quadratics or the sum or difference of two cubes.

Addition and Subtraction of Polynomials
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

2.2.1.B: Long division is restricted to linear, binomial, or monomial terms in the denominator.

Linear Functions

2.2.2: The student will find the composition of two functions and determine algebraically and/or graphically if two functions are inverses.

2.2.2.A: Functions given in equation form can include linear, quadratic, exponential, logarithmic, or rational functions such as f(x) = (ax+b)/(cx+d).

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.2.2.a: Given a function in equation form, the student will find the inverse function in equation form.

Function Machines 3 (Functions and Problem Solving)

2.2.2.b: Given a one-to-one function as a graph, the student will graph the inverse of the function.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Translating and Scaling Functions

2.2.2.c: Given a function as a table of values, the student will determine the domain and/or range of the inverse of the function.

Function Machines 3 (Functions and Problem Solving)

2.2.3: The student will perform translations, reflections, and dilations on functions.

2.2.3.A: Translations are either vertical or horizontal shifts.

Translating and Scaling Functions

2.2.3.B: Dilations either shrink or stretch a function.

Translating and Scaling Functions

2.2.3.C: This indicator assesses recognition of translations, reflections, and dilations on functions.

Reflections of a Linear Function
Reflections of a Quadratic Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

2.2.3.D: Transformations for absolute value functions are restricted to translations and reflections. They do not include dilations.

Quadratic and Absolute Value Functions
Reflections of a Linear Function
Reflections of a Quadratic Function
Translating and Scaling Functions

2.2.3.E: Exponential functions are restricted to translations.

Exponential Functions - Activity A
Translating and Scaling Functions

2.2.3.a: The student will describe the effect that changes in the parameters of a linear, quadratic or exponential function have on the shape and position of its graph.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Roots of a Quadratic

2.2.3.b: Given a verbal description of a transformed linear, quadratic, or exponential function, the student will write the function in equation form.

Exponential Functions - Activity A
Quadratics in Factored Form
Roots of a Quadratic
Translating and Scaling Functions
Using Algebraic Equations
Using Algebraic Expressions

2.2.3.c: Given a transformed linear, quadratic, or exponential function in equation form, the student will give a verbal description of the transformation.

Exponential Functions - Activity A
Quadratics in Factored Form
Roots of a Quadratic
Translating and Scaling Functions
Using Algebraic Equations
Using Algebraic Expressions

2.3: The student will identify linear and nonlinear functions expressed numerically, algebraically, and graphically.

2.3.A: Functions can include linear, quadratic, exponential, logarithmic or functions such as f(x) = (ax + b)/(cx + d)

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.3.B: The items may have no real world context given.

Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

2.3.C: Graphs may include piece-wise functions.

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Using Tables, Rules and Graphs

2.3.a: Given one or more of the following:

2.3.a.1: a table of values

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.3.a.2: a graph

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

2.3.b: the student will be able to do each of the following:

2.3.b.1: choose the correct equation or graph from the same family of functions

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions

2.3.b.2: choose the correct equation or graph from a variety of families of functions.

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Using Tables, Rules and Graphs

2.4: The student will describe or graph notable features of a function using standard mathematical terminology and appropriate technology.

2.4.A: Essential characteristics of a linear, quadratic, or exponential function are those listed for 1.1.1, 1.1.2, and 1.1.3.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Polynomials and Linear Factors
Quadratics in Factored Form
Roots of a Quadratic
Slope - Activity B

2.4.B: Transformations for an absolute value function in one variable are restricted to translations and reflections. They do not include dilations.

Reflections
Rotations, Reflections and Translations
Translating and Scaling Functions
Translations

2.4.a: Given one or more of the essential characteristics of a function, the student will graph the function.

Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots

2.4.b: Given the equation form of a linear, quadratic, or exponential function, the student will find one or more required essential characteristic and/or graph the function.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Roots of a Quadratic

2.5: The student will use numerical, algebraic, and graphical representations to solve equations and inequalities.

2.5.A: Equations may be in one or two variables.

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

2.5.B: Quadratic equations and inequalities are included.

Modeling and Solving Two-Step Equations
Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Using Tables, Rules and Graphs

2.5.C: Higher-order polynomial equations will be factorable.

Dividing Polynomials Using Synthetic Division
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

2.5.D: Absolute value equations and inequalities are single variable and may be linear or quadratic.

Inequalities Involving Absolute Values
Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

2.5.G: Simple rational inequalities will lead to a linear inequality.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

2.5.H: Exponential equations are either of the form f(x) = ab to the x power, b > 0, a and b are rational numbers, b is not 1 or the form c to the power (nx+d) = g to the power (mx + f), where c and g are powers of the same base.

Exponential Growth and Decay - Activity B
Translating and Scaling Functions

2.5.a: Given an equation or inequality, the student will find the solution and express the solution algebraically and graphically. For constructed response items the student will also justify their method and/or solution.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Modeling and Solving Two-Step Equations
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

2.6: The student will solve systems of linear equations and inequalities.

2.6.A: Systems of linear equations will be 2 x 2 or simple 3 x 3 that do not take too much time to solve without a calculator.

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

2.6.B: Systems of linear inequalities will be 2 x 2.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

2.6.a: Algebraically and graphically solve 2 x 2 systems of linear equations and algebraically solve simple 3 x 3 systems of linear equations.

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

2.6.b: Solve systems of two linear inequalities in two variables and graph the solution set.

Inequalities Involving Absolute Values
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

2.6.c: Interpret the solution(s) to systems of equations and inequalities in terms of the context of the problem.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

2.7: The student will use the appropriate skills to assist in the analysis of functions.

2.7.1: The student will add, subtract, multiply, and divide polynomial expressions.

2.7.1.A: Rational expressions may include monomials, quadratics, and the sum and difference of two cubes.

Addition of Polynomials - Activity A
Dividing Exponential Expressions
Dividing Polynomials Using Synthetic Division

2.7.2: The student will perform operations on complex numbers.

2.7.2.a: The student will represent the square root of a negative number in the form bi, where b is real; simplify powers of pure imaginary numbers.

Simplifying Radicals - Activity A
Square Roots

2.7.2.c: The student will simplify rational expressions containing complex numbers in the denominator.

Points in the Complex Plane - Activity A

2.7.3: The student will determine the nature of the roots of a quadratic equation and solve quadratic equations of the form y = ax² + bx + c by factoring and the quadratic formula.

2.7.3.A: The solutions may be real or complex numbers.

Factoring Special Products
Roots of a Quadratic

2.7.5: The student will perform operations on radical and exponential forms of numerical and algebraic expressions.

2.7.5.a: The student will convert between and among radical and exponential forms of expressions.

Simplifying Radicals - Activity A

2.7.5.A: Denominators in problems requiring rationalizing the denominator are restricted to square roots.

Square Roots

2.7.5.d: Radicals containing a numerical coefficient are restricted to square roots and cube roots.

Operations with Radical Expressions
Square Roots

2.7.6: The student will simplify and evaluate expressions and solve equations using properties of logarithms.

2.7.6.A: Properties of logarithms include the Change of Base Formula, property of equality for logarithmic functions, and the product, quotient, and power properties of logarithms.

Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

2.8: The student will use literal equations and formulas to extract information.

2.8.A: Problems may include addition/subtraction and multiplication/division properties of equality, factoring a common factor, and terms that are rational.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

2.9.0.1: The student will represent the general term of an arithmetic or geometric sequence and use it to determine the value of any particular term.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

2.9.0.2: The student will represent partial sums of an arithmetic or geometric sequence and determine the value of a particular partial sum.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

2.9.0.4: The student will recognize and solve problems that can be modeled using a finite arithmetic or geometric series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences