Virginia SOL 7.PFA.4.f
The Standard
Solve problems in context that require the solution of a one- or two-step inequality.
Virginia Standards of Learning for Mathematics · The student will write and solve one- and two-step linear inequalities in one variable, including problems in context, that require the solution of a one- and two-step linear inequality in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the unknown and translate limits such as “at most” or “more than” into an inequality. They solve using inverse operations, graph or describe the solution, and interpret reasonable values for the situation.
What Mastery Looks Like
- Students choose a variable, write an inequality, and solve it with clear inverse-operation steps. They check the boundary value and state what the solution means in the situation, including any whole-number limit.
Common Misconceptions
- Students may use an equation when the situation describes a limit or range. They may reverse the inequality during addition or subtraction, or forget to reverse it when multiplying or dividing by a negative. They may report a decimal answer when the context requires a whole number.
How to Assess It
- Give this exit ticket: “A club has $80, pays a $20 fee, and buys shirts for $12 each. Write and solve an inequality to find the greatest number of shirts.”
Lesson moves
Ways to Teach It
Model 3x + 5 ≤ 20 with algebra tiles, remove five tiles, divide the remaining tiles into three equal groups, and record each step.
Discuss: “Why does dividing by a negative reverse the inequality sign?” Students write an example and explain it with two tested values.
Run a card sort matching situation cards, inequalities, number-line graphs, and written conclusions, then have pairs justify each completed set.
Plan a class party with a fixed room fee and per-person food cost, then calculate how many people can attend within a budget.
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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.4.e
Create a verbal situation in context given a one or two-step linear inequality in one variable.
- 7.PFA.3.f
Solve problems in context that require the solution of a two-step linear equation.
- 8.PFA.4.e
Solve problems in context that require the solution of a multistep linear equation.
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