Algebra I Semester 1

Syllabus:

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 the student 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
• State 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 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 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