Virginia SOL 8.PFA.5.g
The Standard
Interpret algebraic solutions in context to linear inequalities in one variable.
Virginia Standards of Learning for Mathematics · The student will write and solve multistep linear inequalities in one variable, including problems in context that require the solution of a multistep linear inequality in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect an algebraic solution, such as x ≤ 12, to the situation it represents. They explain the boundary, allowed values, units, and any whole-number or nonnegative limits.
What Mastery Looks Like
- Students explain a solution using correct comparison words, units, and variable meaning. They identify whether the boundary is included and limit answers to values that make sense in the situation.
Common Misconceptions
- Students treat the solution as one value instead of a set of values. They confuse “at least” with “at most,” overlook endpoint inclusion, or report negative and fractional answers that do not fit the situation.
How to Assess It
- Give this exit ticket: “A club’s budget leads to n ≤ 12, where n is the number of students attending. Explain the solution in context.”
Lesson moves
Ways to Teach It
Give pairs context cards and number-line strips, then have them mark each solution set and write its meaning below the strip.
Ask students to explain why “x ≥ 8” means “at least 8” rather than “no more than 8” in a given situation.
Play a matching game with sets of inequality solutions, shaded number lines, context statements, and written interpretations.
Have students use a phone-plan or ticket-budget inequality to decide which whole-number choices are possible and explain the boundary value.
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Related Standards
- 8.PFA.4.g
Confirm algebraic solutions to linear equations in one variable.
- 8.PFA.4.f
Interpret algebraic solutions in context to linear equations in one variable.
- 7.PFA.4.c
Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number line.
- 7.PFA.3.c
Confirm algebraic solutions to linear equations in one variable.
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