Week 1: Order of Operations, Expressions, and Equations As students begin the course, this week sets a foundation for the course by presenting expectations, modeling some of the different activities that students will see throughout the course and clarifying communication tools. Virtual introductions will help begin to build a reflective and safe community of learners. This week, students will explore the order of operations in order to simplify expressions. In addition, they will work with equations to solve for an unknown. Ultimately, students will compare expressions and equations.
This week’s activities will focus on the following objectives:
- Identify the rules and policies of the course
- Meet classmates and get comfortable navigating the course
- Identify and apply the order of operations
- Translate verbal sentences into expressions and equations
- Use expressions and equations to represent specific real-world applications
Week 2: Functions
This week, students will be focusing on identifying and writing functions. Students will specifically look at functions through rules, tables, and as graphs. This will allow students to understand the meaning of a function in many different forms. During the week, students will practice working with functions in many ways. For example, they will write a function rule that illustrates a situation as well as construct a function rule that represents a particular graph.
This week’s activities will focus on the following objectives:- Define a function
- Represent a function numerically
- Identify the domain and range of a function
- Write a function rule for a graph
Week 3: Solving Equations
This week, students will further explore equations and how to solve them. Students will explore one-step and multi-step equations and how to solve them. They will learn how to solve equations by applying inverse operations to isolate the unknown. Later in the week, students will explore ratios and proportions. Most importantly, students will learn how to write equations and proportions that represent real world situations and solve them.
This week’s activities will focus on the following objectives:- Use inverse operations to solve one-step equations
- Solve multi-step equations using various mathematical properties
- Write an equation to represent a real-world problem and solve it
- Identify and write a ratio
- Identify and solve a proportion
- Write a proportion to represent a real-world problem and solve it
Week 4: Slope and Linear Equations
This week, students will be introduced to slope and linear equations. Students will first learn how to calculate slope and interpret it in context of a real-world problem. Later in the week, students will focus on linear equations. Specifically, they will explore the various forms of linear equations. In addition, they will learn to write linear equations in each of these forms as well as graph linear equations on the coordinate plane.
This week’s activities will focus on the following objectives:- Identify and interpret the slope of a real-world problem
- Identify the slope and y-intercept on any linear form
- Write and graph linear equations and functions of real-world problems
- Write linear equations given two points
- Write linear equations given the slope and a point on the line
- Determine if lines are parallel or perpendicular
Week 5: Inequalities
This week, students will begin exploring inequalities. Students will first explore basic inequality statements where they will learn to write and graph these statements. Students will use some of their knowledge from equations to solve one-step and multi-step inequalities. They will also explore linear inequalities in two variables as well as their graphs. Finally, students will use their knowledge of inequalities to solve real-world problems.
This week’s activities will focus on the following objectives:- Write and graph one-step and multi-step inequalities
- Write and solve inequalities that model real-world problems
- Solve absolute value equations and inequalities
- Solve and interpret absolute value equations and inequalities that model real-world problems
- Graph linear inequalities in two variables
- Solve, graph, and interpret linear inequalities in two variables that model real-world problems
Week 6: Solving Systems of Linear Equations This week, students will explore systems of linear equations. Students will explore the graphical and algebraic methods to solve systems of linear equations: graphical method, elimination method, and the substitution method. Students will learn to determine the intersection point on a graph and what it means to a system of linear equations. Students will also practice solving systems of linear equations by elimination and substitution.
This week’s activities will focus on the following objectives:- Graph equations to determine intersection point
- Solve linear systems using the substitution method
- Solve linear systems using the elimination method
- Write and solve a linear system that models a real-world problem
Week 7: Exponents, Polynomials, and Factoring During this week, students will begin the week exploring exponents and their properties. They will also explore exponential equations that represent real-world problems. Later in the week, students will be introduced to polynomials. They will learn how to perform operations with polynomials as well as learn various factoring methods. Students will use their knowledge of polynomials and factoring to solve various applications.
This week’s activities will focus on the following objectives:- Identify and apply properties of exponents
- Solve exponential growth and decay functions that model real-world applications
- Identify, classify, and operate polynomials
- Identify special products
- Identify and apply factoring methods
- Use factoring techniques to solve polynomial equations
Week 8: Quadratic Equations In this final week, students will be introduced to quadratic equations. Students will be introduced to the various properties of quadratic equations and also explore their graphs. Students will learn to graph these equations, identify special properties and solve equations. They will also explore quadratic equations representing real-world applications. Students will also complete some wrap-activities as well as complete their final exam.
This week’s activities will focus on the following objectives:- Graph simple quadratic equations and identify patterns
- Identify properties and special features of quadratic equations
- Solve quadratic equations graphically and algebraically
- Solve and interpret quadratic equations in real-world applications
- Complete final exam