Lesson 5: Number of Solutions
Duration of Days: 5
Lesson Objective
Students will be able to determine whether a linear equation in one variable has one solution, no solution, or infinitely many solutions by transforming the given equation into simpler forms.
How does simplifying a linear equation to the form a=a differ in meaning from an equation that simplifies to a=b (where a
does not = b)?
What structural features in an equation's variable terms and constant terms allow you to predict its number of solutions before solving it completely?
Why does an equation with infinitely many solutions remain true no matter what numerical value is substituted for the variable?
One Solution,
No Solution,
Infinitely Many Solutions,
Identity,
Constant,
Coefficient,
Linear Equation
8.EE.C.7: Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.C.7.A: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
Description: This lesson moves students beyond standard algorithmic calculation into structural analysis.
Purpose: To deepen conceptual understanding of algebraic equality.
DOK Level: 3 (Strategic Thinking / Complex Reasoning)
The x=0 Confusion: Students frequently mistake an equation that simplifies to x=0 as having "No Solution" rather than recognizing that zero is a single, valid numerical solution.
Variable Drop: When an equation simplifies to a constant statement like 4=4 or 4=7, students panic because the variable has disappeared, often assuming they made a computational error rather than interpreting the logic of the statement.
Graphic Organizer Classification Tables
Concrete Sorting Activities
Open ended tasks
Exit Tickets
Quiz