Virginia SOL 7.PFA.3.f
The Standard
Solve problems in context that require the solution of a two-step linear equation.
Virginia Standards of Learning for Mathematics · 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 equation in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a real situation into an equation with one unknown, a fixed amount, and a changing amount. They solve using inverse operations and interpret the result with correct units.
What Mastery Looks Like
- Students identify the unknown, fixed amount, rate, and total in a word problem. They write and solve an accurate equation, then check that the answer makes sense in context.
Common Misconceptions
- Students may confuse the fixed amount with the rate or combine unlike quantities. They may undo operations in the wrong order, lose a negative sign, or give an unlabeled answer that does not fit the situation.
How to Assess It
- Use this exit ticket: “A skating rink charges $6 admission plus $3 per skate rental. If the total is $24, how many rentals were purchased?” Ask students to write an equation, solve it, and label the answer.
Lesson moves
Ways to Teach It
Give pairs cups and counters to model a fixed fee plus equal groups, then have them write and solve the matching equation.
Ask students to explain how they know which number is the fixed amount and which number multiplies the unknown.
Play equation match cards, pairing each short word problem with its equation, solution steps, and labeled answer.
Use a phone plan with a monthly fee and per-gigabyte charge, then find the usage from a given bill total.
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Printable 7.PFA.3.f Worksheet
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Related Standards
- 8.PFA.5.e
Solve problems in context that require the solution of a multistep linear inequality in one variable.
- 8.PFA.4.e
Solve problems in context that require the solution of a multistep linear equation.
- 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...
- 7.PFA.4.f
Solve problems in context that require the solution of a one- or two-step inequality.
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