Virginia SOL 6.PFA.3.c
The Standard
Apply properties of real numbers and properties of equality to solve a one-step equation in one variable. Coefficients are limited to integers and unit fractions. Numeric terms are limited to integers.
Virginia Standards of Learning for Mathematics · 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 equation in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students choose an inverse operation to isolate the variable while keeping both sides equal. They solve equations with integer constants and integer or unit-fraction coefficients, then check each solution by substitution.
What Mastery Looks Like
- A student correctly solves equations such as 5x = -30, x/4 = 7, and x - 9 = -2. They show the same operation on both sides and verify the solution by substitution.
Common Misconceptions
- Students may change only one side of an equation or use the same operation instead of the inverse operation. They may mishandle negative signs or multiply by a unit fraction instead of its reciprocal.
How to Assess It
- Give this exit ticket: Solve (1/3)x = -5, name the operation used on both sides, and check the answer by substitution.
Lesson moves
Ways to Teach It
Use a balance mat and integer counters to model x - 4 = 7, then add four counters to both sides.
Compare 4x = -20 and x/4 = -20, then explain in writing why the inverse operations differ.
Match equation cards with solution cards, and require a substitution check before claiming each pair.
Use 6x = 42 to find the price of one notebook when six identical notebooks cost $42.
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