Skip to main content
Common Core Math6th GradeExpressions & Equations

6.EE.4: Identify Equivalent Expressions

Also written as 6.EE.A.4 and CCSS.MATH.CONTENT.6.EE.A.4 · Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.

Make a 6.EE.4 WorksheetAll 29 6th Grade Math Standards

The Official Wording

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..

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

What 6.EE.4 Means in Plain English

Sixth graders decide whether two expressions are the same by asking one question: do they give the same number for every value of the letter? 2(n + 3) and 2n + 6 do. 2(n + 3) and 2n + 3 agree only at n = 0, which is not enough.

This is the test behind 6.EE.3: a rewrite is only legal if it passes it. Substituting one value can disprove equivalence, and the properties of operations are what prove it. Seventh graders use the same idea to rewrite expressions in useful forms (7.EE.2) and to solve multi-step equations (7.EE.4).

6.EE.4 I Can Statements

  • I can test two expressions by substituting the same value into both.
  • I can explain why y + y + y and 3y are equivalent.
  • I can show two expressions are not equivalent with one counterexample.

6.EE.4 Worked Example

Three expressions that look alike, two values plugged into each, and only one pair survives.

Problem

Two students rewrote 4(x + 2). Maya wrote 4x + 8 and Jon wrote 4x + 2. Which expression, if either, is equivalent to 4(x + 2)?

Which expressions are equivalent to 4(x + 2)?
  1. Pick an easy value and substitute it into all three. Try x = 1.4(1 + 2) = 12, 4(1) + 8 = 12, 4(1) + 2 = 6
  2. Jon’s expression already gives a different number, so one counterexample settles it: 4x + 2 is not equivalent.12 ≠ 6
  3. Maya’s matched once, but equivalent means every value. Try another, x = 5.4(5 + 2) = 28, 4(5) + 8 = 28
  4. Matching twice is evidence, not proof. The distributive property is the proof: 4 times x plus 4 times 2.4(x + 2) = 4 × x + 4 × 2 = 4x + 8
AnswerOnly 4x + 8 is equivalent to 4(x + 2)

Check it: Try x = 0, the sneaky case: 4(0 + 2) = 8 and 4(0) + 8 = 8, while 4(0) + 2 = 2. Still only Maya’s expression matches.

Common Mistakes with 6.EE.4

Testing one value and calling it proof

“x + x and x² are equivalent, because 2 + 2 = 4 and 2² = 4”

Try this: Push for a second value: at x = 3, x + x = 6 but x² = 9. One match is not every match.

Judging by looks

“3(x + 2) and 3x + 6 can’t be equivalent, they have different parentheses”

Try this: Substitute before deciding. At x = 4 both give 18, and the distributive property explains why they always will.

Treating 3y and y³ as the same

y + y + y = y³

Try this: Say the operations aloud: y + y + y is three y’s added, which is 3y. y³ is three y’s multiplied.

Where 6.EE.4 Fits

Comes Before5.OA.2Interpret a numerical expression without evaluating it, like seeing 3 × (18 + 7) as three times a sum.6.EE.2Read and evaluate expressions with letters by substitution.
Alongside6.EE.3Use the properties of operations to produce equivalent expressions.6.EE.5Use substitution to decide whether a value makes an equation true.
Comes Next7.EE.2Rewrite expressions in equivalent forms to understand a problem.7.EE.4Solve multi-step equations, where every line must stay equivalent to the last.

Practice 6.EE.4

Math Worksheet GeneratorFree ToolPairs of expressions to mark equivalent or not, with substitution tables underneath so the reason is on the page.Equivalent expressionsSubstitutionAnswer key
Make a Worksheet

Quick Check

  1. Are 5n and n + n + n + n + n equivalent? Why?
  2. Show that 2(x + 1) and 2x + 1 are not equivalent.
  3. Which is equivalent to 6a + 9: 3(2a + 3) or 3(2a + 6)?

6.EE.4: Other Names

6.EE.46.EE.A.4CCSS.MATH.CONTENT.6.EE.A.4

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.