Virginia SOL 8.PFA.4.e
The Standard
Solve problems in context that require the solution of a multistep linear equation.
Virginia Standards of Learning for Mathematics · The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equation in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the unknown and represent the situation with a linear equation. They solve using inverse operations, combining like terms or distributing when needed. They check the result in context and state the answer with units.
What Mastery Looks Like
- A student can define the variable, write an equation from the given details, and solve it accurately. They show balanced steps, check the solution by substitution, and report the answer with correct units.
Common Misconceptions
- Students may swap the fixed fee and the rate, or use the total as a coefficient. They may distribute incorrectly, perform an operation on only one side, or give a number without checking whether it fits the situation.
How to Assess It
- Exit ticket: Plan A costs $12 plus $4 per movie, and Plan B costs $30 plus $2 per movie. Write and solve an equation to find when the costs match, then verify your answer in both plans.
Lesson moves
Ways to Teach It
Use labeled cups and counters to model a ticket sale equation, then remove equal amounts from both sides to isolate the unknown.
Ask, "A taxi charges $4 plus $2 per mile for an $18 trip. What does each number mean in your equation?"
Run a card sort matching six situation cards to equations, worked solutions, and final answers with units.
Compare two streaming plans with different monthly fees and per-movie charges, then solve when their total costs are equal.
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Printable 8.PFA.4.e Worksheet
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Related Standards
- 8.PFA.5.e
Solve problems in context that require the solution of a multistep linear inequality in one variable.
- 7.PFA.3.f
Solve problems in context that require the solution of a two-step linear equation.
- 7.PFA.4.f
Solve problems in context that require the solution of a one- or two-step inequality.
- 8.PFA.4
The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equat...
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