CCSS.Math.Content.6.EE.A.3
The standard
Apply the properties of operations to generate equivalent expressions.
Common Core State Standards for Mathematics · Expressions and Equations
What this standard means
Students need to rewrite expressions without changing their value. They should use the distributive property, combine like terms, and factor out common factors. They also need to explain why two expressions are equal, not just copy a rule.
Mastery looks like moving flexibly between forms, such as 4(x + 5), 4x + 20, and 2(2x + 10). Students often get stuck by distributing to only one term, combining unlike terms, or thinking expressions must look the same to be equal.
Ways to teach it
- Hands-on activity: Give students algebra tiles to build 3(x + 2), then rearrange the tiles to show 3x + 6.
- Discussion prompt: Ask, “Are 5a + 10 and 5(a + 2) always equal, sometimes equal, or never equal? Prove it.”
- Quick assessment: Write 6(2x + 3) and 12x + 18 on the board, then ask students to create one more equivalent expression.
- Real-world connection: Use a grocery receipt with 4 bags of apples at x dollars plus 4 coupons, then write two equivalent cost expressions.
Plan a lesson for CCSS.Math.Content.6.EE.A.3
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Related standards
- CCSS.Math.Content.7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- CCSS.Math.Content.HSA-SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- CCSS.Math.Content.8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- CCSS.Math.Content.7.EE.A
Use properties of operations to generate equivalent expressions.