Virginia SOL 7.PFA.4.c
The Standard
Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number line.
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 solve linear inequalities with one variable and state the full set of possible values. They represent that set with inequality notation and a number-line graph.
What Mastery Looks Like
- Students correctly solve the inequality and write its solution using an inequality symbol. Their number-line graph has the correct endpoint, open or closed point, and shading direction.
Common Misconceptions
- Students often reverse the shading direction or confuse greater than with less than. They may use a closed point for < or >, or forget to reverse the inequality after dividing by a negative number.
How to Assess It
- Exit ticket: Solve 3x - 5 ≤ 10, write the solution algebraically, and graph it on a labeled number line.
Lesson moves
Ways to Teach It
Use floor tape to make a number line, then have students stand on all values that satisfy a given inequality.
Ask students to explain why x < 4 uses an open point while x ≤ 4 uses a closed point.
Run a card match with inequality, solution, and number-line graph cards, then have pairs justify each completed set.
Give a phone plan budget problem, then have students write an inequality and graph all possible numbers of data add-ons.
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Related Standards
- 6.PFA.4.b
Write a linear inequality in one variable to represent a given constraint or condition in context or given a graph on a number line.
- 8.PFA.5.b
Represent solutions to inequalities algebraically and graphically using a number line.
- 8.PFA.5.g
Interpret algebraic solutions in context to linear inequalities in one variable.
- 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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