Unit Plan 17 (Grade 8 Math): Systems of Linear Equations—Graphing & Estimation
8th graders learn to solve systems of linear equations by graphing, identifying intersections as solutions, and estimating non-integer points. They interpret intersections in real contexts and recognize special cases visually.
Focus: Understand solution as intersection; solve by graphing; estimate solutions and interpret meaning.
Grade Level: 8
Subject Area: Mathematics (Expressions & Equations • Functions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week launches systems of linear equations through a visual lens. Students learn that a solution to a system is the point of intersection of two lines. They will graph both equations, find the intersection exactly when it lands on grid points, estimate when it doesn’t, and interpret what that point means in context (for example, a break-even quantity and cost). Special cases—no solution (parallel lines) and infinitely many solutions (same line)—are identified visually and by quick inspection.
Essential Questions
- What does it mean to be a solution of a system, and how do I see it on a graph?
- How can I estimate a solution when the intersection is not at integer coordinates?
- How do I recognize and explain no solution and infinitely many solutions from equations and graphs?
- What does the intersection mean in a real situation (units, reasonableness)?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Explain that the solution of a system of two linear equations is the ordered pair where both equations are true; on a graph, this is the point of intersection.
- Graph two linear equations (from slope–intercept form, two points, or intercepts) and find the exact intersection when possible; otherwise estimate coordinates from the grid and scale.
- Use quick inspection to identify special cases: same slope and different intercepts (no solution), same slope and same intercept (infinitely many solutions).
- Interpret the solution in context, including units, domain limits, and reasonableness of an estimate.
Standards Alignment — CCSS Grade 8
- 8.EE.8a: Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs.
- 8.EE.8b: Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations; solve simple cases by inspection. (Note: Algebraic methods are previewed via inspection here; full algebraic solving is developed in a later unit.)
Success Criteria (student-friendly)
- I can graph two lines and find where they meet; that point makes both equations true.
- I can estimate an intersection when it is not on grid points and report a sensible coordinate with units.
- I can recognize parallel lines (no solution) and overlapping lines (infinitely many solutions) from equations and graphs.
- I can explain what the intersection means in a real situation and check if my estimate is reasonable.