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

Lesson 6.6Testing Equivalence by Substituting

Apply Day · Set BSecond form · new problems, same idea

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

Remember6.6 · Part II

Equivalent Algebraic Expressions

  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.

    A gym fee is 2(x + 6) dollars for x months. Which expression is equivalent?

    1. A2x + 12
    2. B2x + 6
    3. Cx + 12
    4. D8x
    Show your work
  2. 2Circle 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
    Show your work
  3. 3Circle 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
    Show your work
Part 2Apply itreal-world problems
  1. 4Complete each step, then write the final answer.

    Fill in the box so the expressions are equivalent: 5x + 4x + 3 and ☐x + 3. What number goes in the box?

    Show your work
    Final answer:
  2. 5Complete each step, then write the final answer.

    Simplify 6x + 9 + 3x. Then find its value when x = 4.

    Show your work
    Final answer:
  3. 6Complete each step, then write the final answer.

    Kim says 6x + 2 and 8x are equivalent. They match at x = 1. Test x = 4. What is 6x + 2 when x = 4?

    Show your work
    Final answer:
  4. 7Complete each step, then write the final answer.

    A gym writes the cost of x classes as 3x + x + 10 dollars. This is equivalent to ☐x + 10. What number goes in the box?

    Show your work
    Final answer:
  5. 8Complete each step, then write the final answer.

    What number goes in the box so that 3(x + ☐) is equivalent to 3x + 21? Check your answer with x = 2.

    Show your work
    Final answer:
  6. 9Circle 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
    Show your work
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help