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

Lesson 6.8Expanding and Factoring Expressions

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

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Learning target I can use the commutative, associative, and identity properties to rewrite expressions.

Remember6.8 · Part II

Properties of Operations

  1. Commutative Property: Order does not change sum or product
  2. Associative Property: Grouping does not change sum or product
  3. Identity Property: a + 0 = a; a · 1 = a

Words: Properties of Operations (Propiedades de las operaciones)Commutative Property (Propiedad conmutativa)Associative Property (Propiedad asociativa)Identity Property (Propiedad de identidad)Property (Propiedad)

  1. 1Complete each step, then write the final answer.

    Which property does 8 + 3 = 3 + 8 show? Type commutative or associative.

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

    Use properties to find 18 + 9 + 2. Add the friendly pair first.

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

    Rewrite 7 + x + 13 as x + ☐. What number goes in the box?

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

    A baker fills 5 trays. Each tray has 6 rows of 2 muffins. Find 5 × 6 × 2 by multiplying a friendly pair first.

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

    Mia rewrites (n + 8) + 12 as n + 20. Which property lets her group 8 and 12 together? Type commutative or associative.

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

    Use properties to find 0.5 × 37 × 4 × 1.

    Show your work
    Final answer:
  7. 7Circle the letter of the best answer. Show how you know.

    Which property is shown? 5 + 13 = 13 + 5

    1. ACommutative Property
    2. BAssociative Property
    3. CIdentity Property
    4. DDistributive Property
    Show your work
  8. 8Circle the letter of the best answer. Show how you know.

    Which property is shown? (6 × 3) × 2 = 6 × (3 × 2)

    1. ACommutative Property
    2. BIdentity Property
    3. CAssociative Property
    4. DDistributive Property
    Show your work
  9. 9Circle the letter of the best answer. Show how you know.

    Which property is shown? 47 + 0 = 47

    1. ACommutative Property
    2. BAssociative Property
    3. CDistributive Property
    4. DIdentity Property
    Show your work
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