Georgia 7.PAR.2.1
The Standard
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Georgia's K-12 Mathematics Standards · Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant contextual situations.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students add and subtract linear expressions, distribute rational coefficients, combine like terms, and factor common factors. They use operation properties to explain why each rewritten expression remains equivalent.
What Mastery Looks Like
- A student can accurately add, subtract, expand, simplify, and factor linear expressions with integer, fraction, decimal, and negative coefficients. They can show that two forms are equivalent and name the property used in each step.
Common Misconceptions
- Students often distribute a coefficient to only the first term or lose a negative sign when subtracting an expression. They may combine unlike terms, such as 3x + 2 as 5x, or calculate fraction coefficients incorrectly. When factoring, they may divide only one term or fail to check by expanding.
How to Assess It
- Exit ticket: Rewrite 1/2(6x - 10) - (3/4x - 2) in simplest expanded form, then factor the result. Name one property you used.
Lesson moves
Ways to Teach It
Use algebra tiles labeled x, 1, 1/2x, and 1/2 to model an expression, then regroup tiles into an equivalent form.
Ask students to explain in writing why subtracting (2x - 3) changes both signs, using the distributive property.
Run an equivalent-expression card sort with expanded, simplified, and factored forms, including fraction and decimal coefficients.
Compare two phone plans by expanding each monthly cost expression, then identify which form shows fees and rates most clearly.
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Printable 7.PAR.2.1 Worksheet
A ready-to-print activity worksheet aligned to 7.PAR.2.1, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 1.NR.2.7
Apply properties of operations as strategies to solve addition and subtraction problem situations within 20.
- 6.PAR.6.5
Apply the properties of operations to identify and generate equivalent expressions.
- 7.NR.1.5
Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
- 7.NR.1.9
Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
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