CCSS.Math.Content.6.EE.A.4
The standard
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
Common Core State Standards for Mathematics · Expressions and Equations
What this standard means
Students need to decide whether two algebraic expressions always have the same value, not just for one chosen number. They should use properties like the distributive property, combining like terms, and the meaning of repeated addition to explain why expressions match.
Mastery looks like students saying, for example, that 4(x + 2) and 4x + 8 are equivalent because distributing gives the same expression. Students often get stuck by testing only one value, mixing unlike terms, or treating 2x + 3 as 5x.
Ways to teach it
- Hands-on: Give students algebra tiles to build 3x + 6 and 3(x + 2), then compare the models side by side.
- Prompt: Ask, “Can two expressions be equal for one value but not equivalent?” Have students explain with a number example.
- Quick check: Show 5n + 10 and 5(n + 2), then ask students to prove equivalent using words or symbols.
- Real-world: Compare two phone plans, 20 + 5m and 5m + 20, and ask why the monthly cost is always the same.
Plan a lesson for CCSS.Math.Content.6.EE.A.4
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Related standards
- CCSS.Math.Content.3.NF.A.3a
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- 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.6.EE.A.3
Apply the properties of operations to generate equivalent expressions.
- CCSS.Math.Content.7.EE.A
Use properties of operations to generate equivalent expressions.