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

Lesson 6.6Identify Equivalent Algebraic Expressions

Set B · Version ASecond form · supported practice

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!

RememberIdentify Equivalent Algebraic Expressions

Equivalent Algebraic Expressions Two expressions are equivalent when they always give the same value, no matter what number you put in for the variable. They can look different but mean the same thing.

  1. Equivalent expressions produce the same value for any substitution of the variable.
  2. Simplify expressions using algebraic properties (Distributive, Commutative, Associative).
  3. Test equivalence by substituting two different test numbers

Words: Equivalent Expressions (Expresiones equivalentes)Equivalent (Equivalente)Simplify (Simplificar)Like Terms (Términos semejantes)Combine (Combinar)

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

    Which expression means '7 more than a number x'?

    1. Ax + 7
    2. B7x
    3. Cx − 7
    4. D7 − x
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    A ticket costs $9. Which expression gives the cost of t tickets?

    1. A9t
    2. Bt + 9
    3. C9 + t
    4. Dt ÷ 9
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Evaluate 4n + 3 when n = 5.

    1. A23
    2. B27
    3. C35
    4. D45
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  2. 4Circle the letter of the best answer. Show how you know.

    Evaluate 30 − 4y when y = 6.

    1. A6
    2. B20
    3. C24
    4. D156
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  3. 5Circle the letter of the best answer. Show how you know.

    A music studio charges different clients using different formulas. Client A pays 4h + 2h + 30 for h hours. Client B pays 6h + 30. A new client asks if the pricing is fair. Simplify 4h + 2h + 30.

    1. A4h + 32
    2. B6h + 30
    3. C6h + 30h
    4. D36h
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    A music studio charges different clients using different formulas. Client A pays 4h + 2h + 30 for h hours. Client B pays 6h + 30. A new client asks if the pricing is fair. Are the two pricing formulas equivalent?

    1. AYes — 4h + 2h + 30 simplifies to exactly 6h + 30
    2. BNo — Client A pays more
    3. CNo — Client B pays more
    4. DOnly when h = 0
    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
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.6Identify Equivalent Algebraic Expressions

Set B · Version BSecond form · core practice

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!

  1. 1Circle the letter of the best answer. Show how you know.

    A music studio charges different clients using different formulas. Client A pays 4h + 2h + 30 for h hours. Client B pays 6h + 30. A new client asks if the pricing is fair. Test it: what does each expression equal when h = 5?

    1. AA = 50 and B = 60
    2. BBoth equal 60
    3. CA = 60 and B = 55
    4. DBoth equal 90
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Producer A wrote 2(x + 3) for a beat's cost. Which expression is equivalent?

    1. A2x + 6
    2. B2x + 3
    3. C2x + 5
    4. Dx + 6
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A track stacks 3x and then one more x. Which expression is equivalent to 3x + x?

    1. A3x²
    2. B3x
    3. C4x
    4. D4
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Producer B flipped a formula to 5 + 2x. Which expression is equivalent?

    1. A2x + 5
    2. B5x + 2
    3. C7x
    4. D10x
    Show your work
  5. 5Write the name of the correct group on each line.

    The target beat formula is 4x + 6. Spin each expression onto the deck where it belongs: equivalent to 4x + 6, or NOT equivalent.

    Groups: Equivalent to 4x + 6 NOT Equivalent
    • 2(2x + 3)
    • 4x + 3 + 3
    • x + x + x + x + 6
    • 4x + 10
    • 10x
    • 4(x + 6)
  6. 6Write the letter of the matching item on each line.

    Match each studio beat formula to its equivalent remix.

    1. 3(x + 4)
    2. 7y + y
    3. 6 + 5n
    4. 2(4a − 1)
    5. 9m − 3m
    • A3x + 12
    • B8y
    • C5n + 6
    • D8a − 2
    • E6m

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

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