Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.6Identify Equivalent Algebraic Expressions

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show that two expressions are equivalent by simplifying and combining like terms.

Why This Matters At the music studio, two producers wrote formulas for the cost of renting equipment. Producer A wrote 3x + 2x + 10, and Producer B wrote 5x + 10. They look different, but are they really? Let's check: if x = 4, Producer A gets 3(4) + 2(4) + 10 = 30, and Producer B gets 5(4) + 10 = 30. Same result — they're equivalent expressions!

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Equivalent ExpressionsSpanish: Expresiones equivalentes Expressions that look different but have the same value for every allowed variable value. 7c + 9 + 6c = 13c + 9
EquivalentSpanish: Equivalente Expressions that always have the same value. 2x + 4 and 2(x + 2): when x = 3, both = 10; when x = 7, both = 18 — always the same
SimplifySpanish: Simplificar To rewrite an expression in a shorter form that is still equal to the original. 7c + 9 + 6c → 13c + 9
Like TermsSpanish: Términos semejantes Terms with the same letter raised to the same power, like 2x and 5x. 7c and 6c
CombineSpanish: Combinar To add or subtract terms with the same letter into one. 7c + 6c = 13c
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. the 13 in 13c

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Simplify 7c + 9 + 6c. Is it equivalent to 13c + 9?

  1. Like terms: 7c and 6c.
  2. Combine: 7c + 6c = 13c. The 9 stays alone.
  3. 7c + 9 + 6c = 13c + 9.

Answer: 13c + 9; yes, equivalent

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Let's check 2x + 3x and 5x. Try x = 2.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The like terms are and because .
  • I combined them to get .
  • The constant stays by itself because .
  • The two expressions equivalent because .

Word bank equivalentlike termscombinesimplifycoefficientconstanttermvariablesame valuegroupaddcompare

Watch out!A common mistake

A common mistake in Equivalent Expressions is adding the exponents instead of the coefficients when combining like terms

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.6Identify Equivalent Algebraic Expressions

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Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show that two expressions are equivalent by simplifying and combining like terms.

Why This Matters At the music studio, two producers wrote formulas for the cost of renting equipment. Producer A wrote 3x + 2x + 10, and Producer B wrote 5x + 10. They look different, but are they really? Let's check: if x = 4, Producer A gets 3(4) + 2(4) + 10 = 30, and Producer B gets 5(4) + 10 = 30. Same result — they're equivalent expressions!

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Simplify 7c + 9 + 6c. Is it equivalent to 13c + 9?

  1. Like terms: 7c and 6c.
  2. Combine: 7c + 6c = 13c. The 9 stays alone.
  3. 7c + 9 + 6c = 13c + 9.

Answer: 13c + 9; yes, equivalent

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Which expression is equivalent to 4x + 3x?

    1. A7x
    2. B7x²
    3. C12x
    4. D43x
    Steps to try
    1. 4x and 3x share the exact same variable, x — that makes them like terms.
    2. Combine like terms by adding the coefficients (the number parts). The variable tags along unchanged.
    3. Add the coefficients: 4 + 3. Keep the x exactly as it is — no new exponent appears.
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which expression is equivalent to 2(m + 5)?

    1. A2m + 10
    2. B2m + 5
    3. C7m
    4. Dm + 10
    Steps to try
    1. The 2 outside the parentheses must multiply both the m and the 5.
    2. Distribute: write 2 × m and 2 × 5, then join the products with +.
    3. Start: 2 × m = 2m. Now multiply 2 × 5 and add that product on.
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Which property is shown: 3(x + 7) = 3x + 21?

    1. ACommutative
    2. BDistributive
    3. CAssociative
    4. DIdentity
    Steps to try
    1. Watch what happened to the 3: it multiplied the x AND the 7 across the parentheses.
    2. The order didn't change and the grouping didn't just move — a factor was handed out to each term. Which property does that?
    3. Check: 3 × x = 3x and 3 × 7 = 21 — both appear on the right. Name the property that multiplies across a sum.
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Simplify: 5n + 2n

    1. A7n
    2. B7n²
    3. C10n
    4. D52n
    Steps to try
    1. 5n and 2n both have the variable n — they're like terms, so they can combine.
    2. Add the number parts (coefficients) and keep n the same. Don't multiply them.
    3. Compute 5 + 2 for the new coefficient, then write it in front of n.
    Show your work

Explain your thinkingHow did you decide which expressions belong in the same group? What strategies did you use?

Sentence starter I knew ___ and ___ are equivalent because when I ___ the terms, I got the same expression.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help