Georgia 8.PAR.3.4
The Standard
Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.
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 solve linear equations and inequalities and explain why each step is valid. They use named properties and reverse the inequality sign when multiplying or dividing by a negative number.
What Mastery Looks Like
- Students solve one-variable equations and inequalities while labeling steps with properties such as distribution, combining like terms, and division. They explain why each step keeps an equivalent equation or inequality.
Common Misconceptions
- Students may perform an operation on only one side or combine terms that are not like terms. They often forget to reverse an inequality sign after multiplying or dividing by a negative number. Some can solve correctly but cannot name the property that supports each step.
How to Assess It
- Give students 4x − 7 = 21 and ask them to solve it, naming the property used at each step. Include one incorrect step for them to identify and correct.
Lesson moves
Ways to Teach It
Use algebra tiles and a balance mat to solve 3x + 5 = 20, recording the property behind each move.
Discuss: Why does multiplying both sides of −2x < 8 by −1 change the inequality sign?
Play a card match that pairs equation steps with property names, then have students explain each match to a partner.
Model a phone plan cost with a linear equation, solve it, and justify every step using named properties.
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Printable 8.PAR.3.4 Worksheet
A ready-to-print activity worksheet aligned to 8.PAR.3.4, with an answer key for the teacher on its own page. No account needed.
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Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.
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Create and solve linear equations and inequalities in one variable within a relevant application.
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