Virginia SOL 8.PFA.5.f
The Standard
Identify a numerical value(s) that is part of the solution set of a given inequality.
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 test given numbers by substituting them for the variable in an inequality. They simplify both sides and decide which substitutions make a true statement.
What Mastery Looks Like
- A student substitutes each candidate value, simplifies both sides correctly, and decides whether the resulting statement is true. The student includes or excludes boundary values based on the inequality symbol.
Common Misconceptions
- Students may treat the inequality like an equation and look for only one answer. They may reverse the inequality sign without multiplying or dividing, or forget that a boundary value is excluded with < or >.
How to Assess It
- Exit ticket: For 3(2x - 1) ≤ 15, circle all solutions from -2, 0, 3, and 4. Show substitution for one choice.
Lesson moves
Ways to Teach It
Give students number cards to place on a true or false mat after substituting each number into a posted inequality.
Ask students to explain why a boundary number works for ≤ but not for < using one example.
Play Solution Sort, where teams sort candidate values into solution and not solution columns, then check each other’s work.
Present a $40 spending limit with a fixed fee and item cost, then test which item quantities stay within budget.
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Related Standards
- 6.PFA.4.e
Identify a numerical value(s) that is part of the solution set of a given inequality in one variable.
- 6.PFA.4.d
Use substitution or a number line graph to justify whether a given number in a specified set makes a linear inequality in one variable true.
- 7.PFA.4.f
Solve problems in context that require the solution of a one- or two-step inequality.
- 7.PFA.4.g
Identify a numerical value(s) that is part of the solution set of as given one- or two-step linear inequality in one variable.
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