Virginia SOL 7.PFA.3.b
The Standard
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.
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 undo addition or subtraction, then multiplication or division, to isolate the variable in equations with fractions and decimals. They justify each move by applying the same operation to both sides and check solutions by substitution.
What Mastery Looks Like
- A student keeps both sides balanced, computes with rational numbers accurately, and records equivalent equations in a logical order. The student substitutes the result into the original equation and confirms both sides have the same value.
Common Misconceptions
- Students may change a sign when moving a term instead of showing the same operation on both sides. They may divide only one term on a side or mishandle negative fractions and decimals. Some stop after finding a value and do not check it in the original equation.
How to Assess It
- Give this exit ticket: Solve -3/4x + 2.5 = 8.5, name the property used at each step, and check the solution by substitution.
Lesson moves
Ways to Teach It
Place equation and operation cards on a balance mat, then have students apply matching operations to both sides until the variable is isolated.
Compare two worked solutions for 0.5x - 3 = 7, and explain why multiplying every term by 2 is allowed.
Run an equation relay: pairs draw a rational-number equation card, write one legal balancing step, then pass it for the next step.
Give a taxi receipt with a $4 fee and $2.50 per mile totaling $21.50; students write, solve, and verify the mileage equation.
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