Unit Plan 11 (Grade 8 Math): Equations with Variables on Both Sides
8th graders solve linear equations with variables on both sides, using properties of equality to simplify efficiently and identify whether equations have one, none, or infinitely many solutions.
Focus: Strategically use properties of equality to isolate variables; analyze solution sets and structure.
Grade Level: 8
Subject Area: Mathematics (Expressions & Equations)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week sharpens strategy for solving linear equations with variables on both sides. Students will choose efficient paths (when to distribute, when to combine like terms, when to clear denominators), keep equations equivalent at every step, and analyze structure to predict whether an equation has one solution, no solution, or infinitely many solutions—before finishing the algebra. Connections to graphs (as intersections of two lines) reinforce meaning.
Essential Questions
- Which sequence of moves makes this equation simplest to solve—and why?
- How can I tell from the structure whether an equation has one, none, or infinitely many solutions?
- How do I check that each transformation keeps the equation equivalent?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Solve multi-step linear equations with variables on both sides, including distribution, combining like terms, and rational coefficients.
- Plan a solving path that minimizes complexity (for example, move the smaller variable term; clear denominators once).
- Classify solution sets (one, none, infinitely many) and justify using simplification or by graphing both sides.
- Explain and defend steps using properties of equality and the idea of equivalent equations.
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 choose a smart first move (distribute? combine? move a term?) and explain why it helps.
- I can solve equations like 3(x – 4) + 2 = 5x – 10 and (x/3) – (2/5) = (x/2) + 1.
- I can tell when an equation reduces to a true statement (infinitely many) or a false statement (no solution) and justify.
- I can check my solution by substitution and, when helpful, by graphing y = left side and y = right side.