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Common Core Math6th GradeExpressions & Equations

6.EE.3: Generate Equivalent Expressions

Also written as 6.EE.A.3 and CCSS.MATH.CONTENT.6.EE.A.3 · Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.

Make a 6.EE.3 WorksheetAll 29 6th Grade Math Standards

The Official Wording

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Common Core State Standards, Grade 6, Expressions & Equations · Read it at the source · Checked October 14, 2026

What 6.EE.3 Means in Plain English

Sixth graders rewrite expressions without changing what they are worth. The distributive property turns 4(x + 5) into 4x + 20 and runs backward to factor 12a + 8b as 4(3a + 2b), and like terms collapse: n + n + n + 2n becomes 5n.

The properties are old friends from 3.OA.5, where 7 × 8 was split into 7 × 5 + 7 × 3. Now they move letters around. Sixth graders check their work with 6.EE.4 by substituting a value, and in 7th grade the coefficients turn negative and fractional (7.EE.1).

6.EE.3 I Can Statements

  • I can expand 4(x + 5) to 4x + 20.
  • I can factor 12a + 8b using the greatest common factor.
  • I can combine like terms, so n + n + 2n is 4n.

6.EE.3 Worked Example

A perimeter expression with a bracket and repeated terms, simplified twice over, then checked with a number.

Problem

A rectangle has length x + 3 and width x, so its perimeter is 2(x + 3) + x + x. Write the perimeter in its simplest equivalent form.

Simplifying 2(x + 3) + x + x
  1. Distribute the 2 over both terms inside the parentheses. Each term gets multiplied, not only the first.2(x + 3) = 2x + 6
  2. Rewrite the whole expression with the bracket gone.2x + 6 + x + x
  3. Collect the like terms. x means 1x, so 2x + 1x + 1x is 4x. The 6 has no partner.4x + 6
  4. Factor if you want the other equivalent form: both terms share a factor of 2.4x + 6 = 2(2x + 3)
Answer4x + 6, also written 2(2x + 3)

Check it: Substitute x = 5 into every version: 2(8) + 5 + 5 = 26, 4(5) + 6 = 26, 2(13) = 26. Same number, so they are equivalent.

Common Mistakes with 6.EE.3

Distributing to the first term only

3(2 + x) = 6 + x

Try this: Draw arrows from the 3 to each term inside. Two terms, two products: 3 × 2 and 3 × x, so 6 + 3x.

Combining unlike terms

4x + 6 = 10x

Try this: Sort the terms by what they are made of: x-terms with x-terms, plain numbers with plain numbers. 4x + 6 cannot shrink.

Factoring out too little

24x + 18y = 2(12x + 9y)

Try this: Find the greatest common factor of the coefficients before factoring. For 24 and 18 that is 6, giving 6(4x + 3y).

Where 6.EE.3 Fits

Comes Before3.OA.5Use the distributive property with numbers, like 7 × 8 = 7 × 5 + 7 × 3.6.NS.4Find the greatest common factor and use it to factor a sum, like 36 + 8 = 4(9 + 2).
Alongside6.EE.2Name the parts of an expression: terms, factors, coefficients.6.EE.4Check that two expressions are equivalent by substituting values.
Comes Next7.EE.1Expand and factor linear expressions with rational coefficients, like 0.5(x - 4).7.EE.2Rewrite an expression to shed light on a problem, like a + 0.05a = 1.05a.

Practice 6.EE.3

Math Worksheet GeneratorFree ToolExpand, factor and combine-like-terms pages with the answer key in simplest form, so students compare their last line to one target.Distributive propertyLike termsAnswer key
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Quick Check

  1. Expand 5(y + 4).
  2. Factor 18m + 30n using the greatest common factor.
  3. Simplify 3(a + 2) + 4a + a.

6.EE.3: Other Names

6.EE.36.EE.A.3CCSS.MATH.CONTENT.6.EE.A.3

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.