Georgia 8.PAR.3.2
The Standard
Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Georgia's K-12 Mathematics Standards · Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real phenomena.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students simplify equations step by step while keeping both sides equal. They use the final result to tell whether one number works, every number works, or no number works.
What Mastery Looks Like
- Students keep both sides equivalent while simplifying and clearly show each step. They use the final statement to decide whether one value, every value, or no value makes the equation true.
Common Misconceptions
- Students may turn a true statement such as 6 = 6 into x = 6 instead of recognizing that every value works. They may treat a false statement such as 6 = 2 as a solution or lose signs when distributing and combining terms.
How to Assess It
- Exit ticket: Solve and classify 2(x + 3) = 10, 3(x + 2) = 3x + 6, and 4x + 5 = 4x - 2. Show each equivalent step and state what the final result means.
Lesson moves
Ways to Teach It
Use balance mats and algebra tiles to model 3(x + 2) = 3x + 6, then record why every value works.
Ask students to explain in writing why 5 = 5 and 5 = 2 lead to different solution sets.
Run a card sort matching equations, worked steps, final statements, and the correct solution description.
Compare two taxi fare rules, write an equation for equal costs, and interpret whether they match once, always, or never.
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Related Standards
- 8.PAR.3.5
Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical ...
- 8.FGR.7.4
Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.
- 8.PAR.3.3
Create and solve linear equations and inequalities in one variable within a relevant application.
- 8.PAR.3.4
Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.
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