Virginia SOL 7.PFA.3

7.PFA.3 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 7.PFA.3.a

  Represent and solve two-step linear equations in one variable using a variety of concrete materials and pictorial representations.

• 7.PFA.3.b

  Apply properties of real numbers and properties of equality to solve two-step linear equations in one variable. Coefficients and numeric terms will be rational.

• 7.PFA.3.c

  Confirm algebraic solutions to linear equations in one variable.

• 7.PFA.3.d

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

• 7.PFA.3.e

  Create a verbal situation in context given a two-step linear equation in one variable.

• 7.PFA.3.f

  Solve problems in context that require the solution of a two-step linear equation.

01

What Students Need to Do

Students translate situations into equations with one unknown and two operations. They solve using inverse operations and equality properties, then substitute the answer to check it.

02

What Mastery Looks Like

A student isolates the variable correctly when coefficients and constants are fractions, decimals, or integers. The student models the equation, explains each step, checks by substitution, and interprets the answer in context.

03

Common Misconceptions

Students may reverse the operation order or change only one side of an equation. They may confuse a fixed starting amount with a rate when writing an equation. Some stop after solving and do not check whether the answer fits the equation or context.

04

How to Assess It

Give this exit ticket: “A bike rental costs $6 plus $3.50 per hour. The total is $23.50. Write an equation, solve, and check by substitution.”

1. 01

   Use algebra tiles on balance mats to model 3x + 4 = 19, removing equal amounts before splitting the variable tiles.

2. 02

   Ask students to explain why subtracting 4 from only one side of 3x + 4 = 19 breaks equality.

3. 03

   Run an equation relay where teams match situation cards, equation cards, solution cards, and substitution checks.

4. 04

   Use a taxi receipt with a $4 fee and $2.25 per mile, then find miles traveled from a $17.50 fare.

• 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...

• 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...