Unit Plan 10 (Grade 8 Math): Solving Linear Equations—One Variable
8th graders derive the equation y = mx + b using similar triangles, then graph and interpret linear equations in context. Students learn how slope (m) and intercept (b) shape a line’s graph, explain constant rate of change, and distinguish linear from nonlinear functions.
Focus: Solve multi-step linear equations with rational coefficients, including cases with no solution and infinitely many solutions.
Grade Level: 8
Subject Area: Mathematics (Expressions & Equations)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week builds power and confidence with multi-step linear equations in one variable. Students will use properties of equality to distribute, combine like terms, clear fractions/decimals, and isolate the variable. They will also learn to classify solution types (one solution, no solution, infinitely many solutions) and verify results.
Essential Questions
- How do the properties of equality justify every step I take when solving an equation?
- When do linear equations have one, no, or infinitely many solutions—and how can I tell?
- What strategies help with fractions, decimals, and variables on both sides?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Solve multi-step linear equations with rational coefficients, including distribution, combining like terms, and variables on both sides.
- Classify equations as having one solution, no solution, or infinitely many solutions; verify by substitution or by analyzing structure.
- Handle fractions/decimals by clearing denominators or place value moves while keeping equations equivalent.
- Explain solution steps using precise language about properties (distributive, addition/subtraction, multiplication/division, combining like terms).
Standards Alignment — CCSS Grade 8
- 8.EE.7: Solve linear equations in one variable. Give examples of equations with one solution, no solution, or infinitely many solutions. Solve equations of the form px + q = r and p(x + q) = r, and equations requiring distribution and collection of like terms, including those with rational coefficients.
Success Criteria (student-friendly)
- I can solve equations like 3(x – 4) + 2 = 5x – 10 and check my solution.
- I can recognize and explain when steps lead to a true statement (identity → infinitely many solutions) or a false statement (contradiction → no solution).
- I can clear fractions correctly and keep the equation equivalent.
- I can justify each step using a named property of equality.