Virginia SOL 8.PFA.4

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

• 8.PFA.4.a

  Represent and solve multistep linear equations in one variable with the variable on one or both sides of the equation (up to four steps) using a variety of conc...

• 8.PFA.4.b

  Apply properties of real numbers and properties of equality to solve multistep linear equations in one variable (up to four steps). Coefficients and numeric ter...

• 8.PFA.4.c

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

• 8.PFA.4.d

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

• 8.PFA.4.e

  Solve problems in context that require the solution of a multistep linear equation.

• 8.PFA.4.f

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

• 8.PFA.4.g

  Confirm algebraic solutions to linear equations in one variable.

01

What Students Need to Do

Students represent and solve linear equations with rational numbers and variables on one or both sides. They distribute, combine like terms, and use equality properties for up to four steps. They also write equations from situations, create matching situations, interpret answers, and check solutions by substitution.

02

What Mastery Looks Like

A student chooses valid steps, keeps both sides balanced, and reaches the correct value without losing signs or terms. The student can turn a short situation into an equation, explain what the solution means, and confirm it by substitution.

03

Common Misconceptions

Students often distribute to only one term, combine unlike terms, or drop a negative sign. They may change only one side of the equation or clear a denominator from only some terms. In context, they may define the variable poorly or give a bare number with no units or meaning.

04

How to Assess It

Exit ticket: Club A charges $5, gives two free sessions, then charges $3 per session; Club B charges $9 plus $2 per session. Write and solve an equation for equal cost, then verify the solution and state what it means.

1. 01

   Students model 2(x + 3) = x + 9 on balance mats, remove equal tiles, and record each matching algebra step.

2. 02

   Post one correct solution and one with 3(x - 2) written as 3x - 2; students explain which path preserves equality.

3. 03

   Prepare cards showing equations, shuffled solution steps, and answers; pairs race to build correct chains and verify them by substitution.

4. 04

   Give students two phone plan fee cards; they write an equation for equal cost, solve it, and explain whether the answer is reasonable.

• 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...

• 8.PFA.5

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

• 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...