• ## Course 3, Module 3: Modeling with Linear Equations

In this module, students build on their experiences of solving two-step equations and graphing linear equations. They will apply number properties as strategies to write equations in equivalent forms and explore strategies for solving equations with variables on both sides of the equals sign. Students will write and solve equations to answer questions about real-world situations. They will also use systems of linear equations to solve real-world problems.

Topic 1: Solving Linear Equations

• In this topic, students increase the range of one-variable linear equations they can solve. To build fluency with solving linear equations with variables on both sides of the equals sign, students play a game in which they use given expressions to form equations with no solution, one solution, and infinite solutions.
• MATHia Workspaces (16)
• Exploring Two-Step Equations
• Solving Multi-Step Equations
• Solving by Combining Like Variable Terms and a Constant with Integers (No Type In)
• Solving by Combining Like Variable Terms and a Constant with Integers (Type In)
• Solving by Combining Like Variable Terms and a Constant with Decimals (No Type In)
• Solving by Combining Lke Variable Terms and a Constant with Decimals (Type In)
• Analyzing Models of Linear Relationships Involving the Distributive Property
• Modeling Linear Rates of Change
• Modeling Fractional Rates of Change
• Modeling using the Distributive Property over Division
• Solving with the Distributive Property over Division
• Solving with Integers (No Type In)
• Solving with Integers (Type In)
• Solving Equations with One Solution, Infinite, and No Solutions
• Sorting Equations by Number of Solutions

Topic 2: Systems of Linear Equations

• In this topic, students analyze and solve pairs of simultaneaus linear equations. They'll use slope-intercept and standard forms of linear equations to write systems of equations that represent scenarios and solve systems algebraically using substitution, including systems with no solution or infinite solutions.
• MATHIA Workspaces (4)
• Introduction to Systems of Linear Equations
• Modeling Linear Systems Involving Integers
• Modeling Linear Systems Involving Decimals
• Solving Linear Systems Using Substitution