Course Overview:
Algebra I is a critical foundation to secondary mathematics education. Topics introduced in Algebra I provide a strong base for success in future high school mathematics. This course emphasizes the students to expand their critical thinking and problem-solving skills. Algebra I is the first step in helping students transition from concrete mathematical knowledge to more abstract algebraic generalizations.
Semester 2 extends the study of functions to include exponential, quadratic, rational, and radical functions. Students will simplify, graph, and solve functions using a variety of methods. Students will also analyze data using two-way tables, one-variable statistics, and bivariate statistics.
Note: This course is not designed for ELL (English Language Learners) students. ELL students may enroll in this course ONLY if they have adequate mentor support at their home school and are able to fulfill all course requirements.
Prerequisites:
Required Materials:
- Graphing paper
- Graphing Calculator (such as TI-83)
- Access to online graphing tools (such as Desmos)
Syllabus:
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 covers graphing 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
