Georgia 6.PAR.6.5
The Standard
Apply the properties of operations to identify and generate equivalent expressions.
Georgia's K-12 Mathematics Standards · Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant situations.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite algebraic expressions without changing their value. They use the distributive, commutative, and associative properties, combine like terms, and explain why two forms are equivalent.
What Mastery Looks Like
- A student can rewrite 3(x + 4) + 2x as 5x + 12 and explain each step. The student can test two expressions with a chosen value and use properties to justify equivalence.
Common Misconceptions
- Students may distribute a factor to only the first term, writing 3(x + 4) as 3x + 4. They may combine unlike terms or think changing the order of terms changes the expression's value.
How to Assess It
- Exit ticket: Rewrite 4(2x + 3) + x in simplest form, name the properties used, and verify equivalence when x = 2.
Lesson moves
Ways to Teach It
Use algebra tiles to build 3(x + 2), rearrange the tiles into 3x + 6, and record the matching expressions.
Ask students to explain in writing why 2(x + 5) and 2x + 5 are not equivalent.
Run a card sort matching expanded, factored, and simplified forms of the same expression.
Model four movie tickets costing t dollars plus a $3 fee each, then compare 4(t + 3) with 4t + 12.
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Printable 6.PAR.6.5 Worksheet
A ready-to-print activity worksheet aligned to 6.PAR.6.5, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 3.PAR.3.4
Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication are equivalent.
- 8.NR.2.1
Apply the properties of integer exponents to generate equivalent numerical expressions.
- 7.PAR.2.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.PAR.2
Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant contextual situations.
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