Algebra I (Credit Recovery)

Required Materials:

• Graphing paper
• Graphing Calculator (such as TI -83 or other)
• Online graphing tools such as Desmos, Geogebra, or other tools. (Free usage. Students need not purchase an account).

Syllabus:

Semester 1

Section 1: Algebra Basics

This section reviews the basic concepts of algebra including the understanding of essential vocabulary and simplifying and solving equations and inequalities.

After this section you will be able to:

• Recognize the contributions of historical mathematicians to the study of Algebra
• Recognize the applications of Algebra in today's world
• Know and apply algebraic vocabulary
• Know and apply the properties of equality
• Apply the order of operations to simplify expressions
• Evaluate algebraic expressions
• Write algebraic expressions and equations from given information
• Solve one and two-step equations
• Solve and graph one and two-step inequalities

Lessons:

• Algebra Past and Present
• Essential Vocabulary
• Expressions and Equations
• Solving Equations and Inequalities

Section 2: Linear Equations and Inequalities

This section is the study of linear equations and inequalities. Solutions to complex equations and inequalities will be found using a variety of methods.

After this section the student will be able to:

• Solve multi-step equations and inequalities for a given variable with rational coefficients
• Solve compound inequalities
• Write solutions to compound inequalities using interval notation
• Solve literal equations for a given variable
• Determine if an ordered pair is a solution to a given linear equation
• tate solutions when given an equation or graph
• Model the solutions to a linear equation with a graph
• Determine if an ordered pair is a solution to a given linear inequality
• State solutions when given an inequality or a graph
• Model the solutions to a linear inequality with a graph

Lessons:

• Multi-Step Solutions
• Solve Compound Inequalities
• Literal Equations
• Two-Variable Linear Equations
• Two-Variable Inequalities

Section 3: Systems of Equations and Inequalities

This Section continues the study of linear systems of equations and inequalities. Graphs and algebraic methods are used to find solutions to systems. Applications to real-world situations are emphasized.

After this section the student will be able to:

• Determine the number of solutions for a given system of equations
• Analyze graphs of linear and non-linear systems to estimate solutions.
• Determine if a point is a solution to a given system
• Find the solution(s) to a given system of equation by graphing
• Solve a system of linear equations using the substitution method
• Solve linear systems of equations by elimination
• Discern the best method to use to solve problems
• Determine if a given point is a solution to a system of inequalities
• Model the solution to a system of inequalities by graphing
• Apply solving systems to real-world problems

Lessons:

• Solutions to Systems
• Solve by Graphing
• Solve by Substitution
• Solve by Elimination
• Systems of Inequalities

Section 4: Introduction to Functions

This section introduces students to the concepts of relations and functions. Function notation is introduced and used to evaluate functions for a given domain. Functions are analyzed for a reasonable domain and range. Mathematical operations are performed on polynomial functions.

After this section the student will be able to:

• Represent relations in multiple ways
• Determine if a relation is a function
• State the domain and range of a relation
• Describe functions by analyzing key features
• Evaluate a function using function notation
• Interpret the value of a function in context
• Perform operations on polynomial functions
• Write functions to model real-world situations
• State a reasonable domain and range of a function
• Graph functions with restricted domains

Lessons:

• Relations and Functions
• Analyzing Functions
• Operations on Functions
• Modeling with Functions

Section 5: Linear Functions

This section focuses on modeling with linear functions. Transformations of the parent linear function are discussed. Arithmetic sequences are presented as a form of linear functions. Writing and graphing recursive and explicit equations for sequence is emphasized.

After this section the student will be able to:

• Determine if a function is linear
• Calculate and interpret the average rate of change
• Graph linear functions given in a variety of forms
• Write linear functions from given information
• Compare linear functions represented in different ways
• Identify, write, and graph direct variations
• Describe translations of linear functions
• identify an arithmetic sequence
• Write the functions that model an arithmetic sequence
• Graph an arithmetic sequence as a discrete linear function

Lessons:

• Modeling Linear Functions
• Writing Linear Functions
• Translations
• Arithmetic Sequences

Section 6: Piecewise Functions

This section addresses the concept of graphing, evaluating and writing piecewise functions. Absolute functions are identified as special piecewise functions consisting of two linear functions with opposite slopes and intersecting at the vertex. Graphing and solving absolute value equations and inequalities is presented.

After this section the student will be able to:

• Graph transformations of absolute value graphs
• Solve absolute value equations and relate the solution to the graph
• Solve absolute value inequalities and relate the solution to the graph
• Graph a piecewise function
• Evaluate a piecewise function given a graph or an equation
• Write the function for a piecewise function from a description or graph
• Recognize absolute value graphs as a piecewise function

Lessons:

• Absolute Value Graphs
• Absolute value Equations and Inequalities
• More Piecewise Functions

Semester 2

Section 1: Exponential Functions

This section introduces the rule of exponents, graphing and solving exponential functions as well as exploring geometric sequences.

After this section the student will be able to:

• Apply the property of exponents to simplify exponential expressions 
• Graph exponential functions and their transformations
• Apply exponential growth and decay to real-world problems
• Compare linear and exponential functions
• Write an exponential function from given information 
• State the next terms in a geometric sequence 
• Recognize a geometric sequence as a discrete exponential function 
• Write the recursive function for a geometric sequence 
• Write the explicit function for a geometric sequence

Lessons:

• Properties of Exponents
• Graphing exponential Functions
• Writing Exponential Functions
• Geometric Sequences

Section 2: Graphing Quadratic Functions

This section graphs the quadratic parent function and its transformations. How to convert between the forms of quadratic functions is explored. Quadratic functions are used to model data.

After this section the student will be able to:

• Determine if a set of data can be modeled by a quadratic function 
• Graph quadratic functions using key features of the graph 
• Calculate the average rate of change over an interval
• Describe and graph transformations of the parent function 
• State the domain and range of a transformed function
• Convert between standard form, vertex form, and factored form 
• Write the function that is modeled by a graph or a verbal description
• Determine if data is linear, exponential, or quadratic 
• Model real-world situations using the appropriate function

Lessons:

• Introduction to Quadratic Functions
• Transformations of Quadratic Functions
• Writing Quadratic Functions
• Modeling with Quadratic Functions

Section 3: Solving Quadratic Equations

This section continues the study of quadratic equations. Solving quadratic equations by a variety of methods is emphasized. Solving nonlinear systems is presented.

After this section the student will be able to:

• Use the discriminant to state the number and type of solutions to a quadratic equation.
• Factor quadratic functions.
• Solve quadratic functions by graphing, factoring, completing the square and the quadratic formula.
• Recognize that the quadratic formula is derived from completing the square. 
• Solve systems of equations that contain a linear and a quadratic function by graphing. 
• Solve a system of equations that contain a linear and quadratic function by substitution.

Lessons:

• Solve by Graphing
• Solve by Factoring
• Solve by Square Root Method
• Quadratic Formula
• Solve Nonlinear Systems

Section 4: Radical Functions

This section introduces radical functions. Methods to simplify, apply mathematical operations, and solve radical equations are presented.

After this section the student will be able to:

• State the domain and range of a radical function. 
• Describe the transformation of a radical function. 
• Graph a translated radical function.
• Simplify radical expressions by adding, subtracting, multiplying, and dividing.
• Rationalize the denominator of a ratio.
• Solve radical equations and recognize extraneous solutions. 
• Apply solving radical equations to real-world situations.

Lessons:

• Graphing Radical Functions
• Combining Radical Expressions
• Multiply and Divide Radical Expressions
• Solve Radical Equations

Section 5: Rational Expressions

This section focuses on rational expressions. Mathematical operations on rational functions are presented. Solving rational functions is explored.

After this section the student will be able to:

• Explain closure of the rational set of numbers.
• Simplify rational expression State excluded values of the domain 
• Applying rational expressions to real-world situations.
• Multiply rational expression and apply mathematical operations on like and unlike rational expressions.
• Solve rational equations by cross products and cleaning denominators.
• Apply solving rational equations to real-world situations.

Lessons:

• Simplify Rational Expressions
• Multiply and Divide Rational Expressions
• Add and Subtract Rational Expressions
• Solve Rational Equations

Section 6: Data Analysis

This section analyzes a variety of data sets. Two-way tables, center and spread of one-variable data sets and finding regression models are analyzed. The difference between correlation and causation are discussed.

After this section the student will be able to:

• Create a two-way frequency table. 
• Find joint relative, marginal relative frequencies, and conditional relative frequencies.
• Recognize trends and associations in the data set.
• Create dot plots, histograms, and box plots.
• Analyze distribution and spread of a data set.
• Compare distribution and spread between two data sets.
• Discuss the effects of outliers on the center and spread.
• Find and interpret the correlation coefficient of data sets using technology.
• Model data on a scatter plot and find the curve of best fit using technology.
• Distinguish between correlation and causation.

Lessons:

• Categorical Data
• Univariate Statistics
• Bivariate Data