Virginia SOL 8.PFA.5.c
The Standard
Write multistep linear inequalities in one variable to represent a verbal situation, including those in context.
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 turn a verbal situation into an inequality with one variable. They identify fixed amounts, changing amounts, grouping, and phrases that signal <, >, ≤, or ≥.
What Mastery Looks Like
- Students identify the unknown, fixed amount, rate, and limit in a situation. They write a correct inequality and explain how each term and the inequality symbol match the context.
Common Misconceptions
- Students often switch “at least” and “at most,” leading to the wrong inequality symbol. They may omit a fixed fee, misuse parentheses, or confuse a total amount with a rate. Some write an equation instead of an inequality.
How to Assess It
- Use this exit ticket: “A gym charges $25 to join and $18 per month. You can spend no more than $133. Write an inequality for m months.”
Lesson moves
Ways to Teach It
Give students cards showing fees, rates, limits, variables, and symbols, then have them arrange the cards into matching inequalities.
Ask students to explain why “no more than $80” uses ≤ and create a situation represented by 12 + 4x ≤ 80.
Play inequality match-up with context cards and inequality cards, awarding a point only when partners justify every term and symbol.
Use a class party budget with a room fee and per-person food cost, then write an inequality for the number of guests.
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Related Standards
- 7.PFA.4.e
Create a verbal situation in context given a one or two-step linear inequality in one variable.
- 8.PFA.5.d
Create a verbal situation in context given a multistep linear inequality in one variable.
- 8.PFA.4.c
Write a multistep linear equation in one variable to represent a verbal situation, including those in context.
- 7.PFA.4.d
Write one- or two-step linear inequalities in one variable to represent a verbal situation, including those in context.
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