Virginia SOL 8.PFA.4.b
The Standard
Apply properties of real numbers and properties of equality to solve multistep linear equations in one variable (up to four steps). Coefficients and numeric terms will be rational. Equations may contain expressions that need to be expanded (using the distributive property) or require combining like terms to solve.
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 simplify each side by distributing and combining like terms. They use properties of equality to isolate the variable in no more than four steps. They also solve equations created from real situations and check solutions by substitution.
What Mastery Looks Like
- Students solve equations with rational numbers, parentheses, and like terms while showing valid steps. They can write an equation from a context, solve it, and explain what the answer means.
Common Misconceptions
- Students may distribute a negative or fraction to only the first term inside parentheses. They may combine unlike terms, change signs when moving terms, or apply an operation to only one side. Some stop after finding a value and do not check it in the original equation.
How to Assess It
- Give this exit ticket: Solve ¾(8x - 4) + 2 = 2x + 15, label each step, and check your answer by substitution.
Lesson moves
Ways to Teach It
Build ½(4x + 6) - 2 = x + 5 on a balance mat with paper x-cards and unit tiles, then solve.
Ask students to explain why subtracting 2x from both sides preserves equality and whether subtracting 6x would also work.
Run an equation relay where pairs expand, combine like terms, isolate the variable, and check the solution on separate cards.
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Printable 8.PFA.4.b Worksheet
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