6.7.D
The Standard
generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite expressions while keeping the same value. They use operation rules to reorder, regroup, distribute, cancel opposites, and remove identity values.
What Mastery Looks Like
- Students can rewrite an expression without changing its value and explain each change. They can choose a useful property to simplify or reorganize an expression.
Common Misconceptions
- Students may write 3(x + 4) as 3x + 4 instead of 3x + 12. They may also switch terms in subtraction or division, or confuse identity values with inverse pairs.
How to Assess It
- Exit ticket: Rewrite 5(a + 2) + (−5a) + 0 as 10. Label the property used at each step.
Lesson moves
Ways to Teach It
Use algebra tiles to model 3(x + 2), rearrange them as 3x + 6, then sketch and label the change.
Ask students to compare 4(x + 3) and 4x + 3, then write why only one matches the original expression.
Play a card-matching game with equivalent expressions and property names, requiring students to explain one match before keeping the pair.
Model three identical meal orders with n + 2 dollars each, then compare 3(n + 2) with 3n + 6.
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Printable 6.7.D Worksheet
A ready-to-print activity worksheet aligned to 6.7.D, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 1.5.E
understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s)
- 6.7.A
generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization
- 6.7.C
determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations
- 7.3.B
apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers
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