Virginia SOL 7.PFA.2.b
The Standard
Represent equivalent algebraic expressions in one variable using concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles).
Virginia Standards of Learning for Mathematics · The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students build one-variable expressions with algebra tiles or colored chips, then sketch the models. They rearrange or group pieces to show why two expressions are equivalent without changing their value.
What Mastery Looks Like
- Given expressions such as 3(x + 2) and 3x + 6, a student builds or draws matching models and identifies each tile. The student can also write an equivalent expression from a model.
Common Misconceptions
- Students may combine an x-tile and unit tiles, incorrectly changing x + 3 into 4x. Some read x + x as x² rather than 2x. They may also remove positive and negative pieces without forming a complete zero pair.
How to Assess It
- Exit ticket: Draw algebra tiles for 2(x + 3) and 2x + 6, then explain in one sentence why the models match.
Lesson moves
Ways to Teach It
Give each pair algebra tiles to build 4(x + 1), regroup the tiles, and record the equivalent expression 4x + 4.
Ask, “How can two expressions look different but contain the same tiles?” Students write an example and explain their reasoning.
Play a matching game with expression cards and model cards, requiring students to justify each match before keeping the pair.
Model four identical ticket orders, each with one student ticket and a $2 fee, then compare 4(x + 2) with 4x + 8.
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Printable 7.PFA.2.b Worksheet
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