Virginia SOL 8.PFA.5

8.PFA.5 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 8.PFA.5.a

  Apply properties of real numbers and properties of inequality to solve multistep linear inequalities (up to four steps) in one variable with the variable on one...

• 8.PFA.5.b

  Represent solutions to inequalities algebraically and graphically using a number line.

• 8.PFA.5.c

  Write multistep linear inequalities in one variable to represent a verbal situation, including those in context.

• 8.PFA.5.d

  Create a verbal situation in context given a multistep linear inequality in one variable.

• 8.PFA.5.e

  Solve problems in context that require the solution of a multistep linear inequality in one variable.

• 8.PFA.5.f

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

• 8.PFA.5.g

  Interpret algebraic solutions in context to linear inequalities in one variable.

01

What Students Need to Do

Students write and solve inequalities with rational numbers, including expressions that need distribution or combining like terms. They handle variables on one or both sides and show solutions with symbols and number-line graphs. They also connect inequalities to situations and decide whether given values fit the solution set.

02

What Mastery Looks Like

Students simplify expressions, collect variable terms, isolate the variable, and reverse the inequality sign when needed. They write the solution with a symbol and graph it correctly on a number line. They can explain what the solution means in a given situation.

03

Common Misconceptions

Students often forget to reverse the inequality sign when multiplying or dividing by a negative number. They may distribute incorrectly, combine unlike terms, or graph the endpoint with the wrong circle. Some treat the answer as one value instead of a set of values.

04

How to Assess It

Exit ticket: Solve and graph 3(2x - 1) ≤ 4x + 7. Then state whether x = 5 and x = 6 belong to the solution set.

1. 01

   Give students algebra tiles and inequality cards to model 2(x + 3) > x + 8, then solve and graph the result.

2. 02

   Ask students to write a shopping situation represented by 12 + 4x ≤ 40 and explain what each term means.

3. 03

   Play an error-analysis relay where teams correct distributed terms, combined terms, reversed signs, and number-line graphs on four posted problems.

4. 04

   Have students write and solve an inequality comparing two phone plans with different monthly fees and per-gigabyte charges.

• 6.PFA.3

  The student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equatio...

• 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.3

  The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equati...

• 8.PFA.4

  The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equat...