Virginia SOL 7.PFA.3.a
The Standard
Represent and solve two-step linear equations in one variable using a variety of concrete materials and pictorial representations.
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 model equations such as 3x + 5 = 20 with algebra tiles, counters, balance drawings, or tape diagrams. They use inverse operations while keeping both sides equal to find the unknown value.
What Mastery Looks Like
- A student can build or draw an accurate model, use it to isolate the unknown, and find the correct value. The student keeps both sides equal and checks the result by substitution.
Common Misconceptions
- Students may remove a term from only one side or treat 3x as 3 + x. They may divide only some terms, mishandle negative tiles, or forget to check the solution in the original equation.
How to Assess It
- Give this exit ticket: Draw a tape diagram for 3x + 5 = 20, solve for x, and verify the answer by substitution.
Lesson moves
Ways to Teach It
In pairs, students use cups and counters to model 3x + 6 = 18, remove six equally, then split the remaining counters.
Show two tape diagrams for 4x - 3 = 13, then have students choose the accurate model and explain why in writing.
Play Equation Match by pairing equation cards with algebra-tile pictures, tape diagrams, solutions, and substitution checks.
Present a phone bill with a $7 fee, $3 per gigabyte, and a $22 total, then have students draw and solve.
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Printable 7.PFA.3.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...
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- 8.PFA.4.a
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- 7.PFA.4.c
Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number line.
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