Virginia SOL 6.PFA.4

6.PFA.4 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 6.PFA.4.a

  Given the graph of a linear inequality in one variable on a number line, represent the inequality in two equivalent ways (e.g., x < -5 or -5 > x) using symbols....

• 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.

• 6.PFA.4.c

  Given a linear inequality in one variable, create a corresponding contextual situation or create a number line graph.

• 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.

• 6.PFA.4.e

  Identify a numerical value(s) that is part of the solution set of a given inequality in one variable.

01

What Students Need to Do

Students translate a limit or condition into an inequality with one variable and graph its solutions on a number line. They rewrite the same relationship with the variable on either side. They substitute values or read a graph to decide which numbers are solutions.

02

What Mastery Looks Like

A student chooses the correct symbol for phrases such as “at least,” “more than,” and “no more than.” They place the boundary correctly, use an open or closed point, and shade in the right direction. They can write an equivalent reversed form, create a matching context, and justify a tested value.

03

Common Misconceptions

Students often read “at least” as > instead of ≥, or “no more than” as ≥ instead of ≤. They may use a closed point for < or >, or shade away from the actual solutions. When switching x < -5 to -5 > x, they may reverse the relationship incorrectly.

04

How to Assess It

Exit ticket: A backpack may weigh no more than 18 pounds; write two equivalent symbolic forms, graph the solution set, and test 18.5.

1. 01

   Give pairs inequality cards, number-line strips, and counters; students place the boundary, choose an open or closed point, and shade solutions.

2. 02

   Discuss the prompt, “A movie ticket costs less than $12”; students write two equivalent inequalities and explain the matching graph.

3. 03

   Run a card-match race using sets of context cards, symbolic inequalities, number-line graphs, and values labeled solution or not a solution.

4. 04

   Students use a $40 field-trip budget and an $8 admission fee to write, graph, and test possible lunch costs.

• 7.PFA.4

  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 t...

• 7.PFA.4.c

  Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number line.