Virginia SOL 8.PFA.4.a
The Standard
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 concrete materials and pictorial representations.
Virginia Standards of Learning for Mathematics · The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equation in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use algebra tiles, balance diagrams, or bar models to show an equation and its equal sides. They distribute, combine like terms, and use inverse operations to isolate the variable. They check the result by substitution.
What Mastery Looks Like
- A student can model and solve an equation with parentheses, like terms, and variables on both sides. The student keeps both sides equal, shows clear steps, and checks the solution by substitution.
Common Misconceptions
- Students may change a sign when moving a term without understanding that they are applying an inverse operation. They may distribute to only one term, combine unlike terms, or perform an operation on only one side.
How to Assess It
- Give this exit ticket: Draw a balance model for 3(x + 2) = 2x + 11, solve for x, and verify by substitution.
Lesson moves
Ways to Teach It
Use algebra tiles on a balance mat to model and solve 2(x + 3) + x = x + 10.
Ask students to explain why subtracting 2x from both sides keeps 5x - 7 = 2x + 8 balanced.
Play a card match connecting each equation with its correct first step, solution, and substitution check.
Compare class plans costing 15 + 8x dollars and 35 + 4x dollars, then find when the costs are equal.
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Printable 8.PFA.4.a Worksheet
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Related Standards
- 6.PFA.3.b
Represent and solve one-step linear equations in one variable, using a variety of concrete manipulatives and pictorial representations (e.g., colored chips, alg...
- 6.PFA.3.d
Confirm solutions to one-step linear equations in one variable using a variety of concrete manipulatives and pictorial representations (e.g., colored chips, alg...
- 7.PFA.3.a
Represent and solve two-step linear equations in one variable using a variety of concrete materials and pictorial representations.
- 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...
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