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

Lesson 6.8Generate Equivalent Expressions

Set B · Version ASecond form · supported practice

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

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

Why This Matters You're a band director arranging musicians on stage. You have 3 guitarists, 5 drummers, and 2 keyboard players. Whether you seat the guitarists first or the drummers first, you still have 3 + 5 + 2 = 10 musicians. The order you arrange them doesn't change the total!

RememberGenerate Equivalent Expressions

Properties of Operations. Formula: Commutative: a + b = b + a | Associative: (a + b) + c = a + (b + c) Properties are math rules that are always true. The Commutative Property lets you change the order. The Associative Property lets you change the grouping (the parentheses).

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

    What is the GCF of 18 and 24?

    1. A2
    2. B3
    3. C6
    4. D72
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    What is the LCM of 4 and 6?

    1. A2
    2. B10
    3. C12
    4. D24
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    One bell rings every 8 minutes and another every 12 minutes. They just rang together. After how many minutes will they ring together again?

    1. A4 minutes
    2. B20 minutes
    3. C24 minutes
    4. D96 minutes
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    You have 30 pencils and 45 erasers to split into identical kits with nothing left over. What is the greatest number of kits?

    1. A3 kits
    2. B5 kits
    3. C15 kits
    4. D90 kits
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A sound engineer needs to calculate 4 × 17 × 25 mentally to find the total cost of audio cables. Using the associative and commutative properties, she rearranges: 4 × 25 × 17 = 100 × 17. Which property lets you change the ORDER of the factors?

    1. ACommutative
    2. BAssociative
    3. CDistributive
    4. DIdentity
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A sound engineer needs to calculate 4 × 17 × 25 mentally to find the total cost of audio cables. Using the associative and commutative properties, she rearranges: 4 × 25 × 17 = 100 × 17. Which property lets you change the GROUPING of the factors?

    1. ACommutative
    2. BDistributive
    3. CIdentity
    4. DAssociative
    Show your work

Explain your thinkingHow can you tell the difference between the commutative and associative properties? What clue helps you decide?

Sentence starter The ___ property changes the ___, while the ___ property changes the ___. I can tell by looking at whether the ___ moved or the ___ changed.

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 6.8Generate Equivalent Expressions

Set B · Version BSecond form · core practice

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

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

Why This Matters You're a band director arranging musicians on stage. You have 3 guitarists, 5 drummers, and 2 keyboard players. Whether you seat the guitarists first or the drummers first, you still have 3 + 5 + 2 = 10 musicians. The order you arrange them doesn't change the total!

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Drag each track on the playlist into the property of operations it shows. Ask yourself: did the order change, the grouping change, or did a 0 or 1 keep the value the same?

    Groups: Commutative Property Associative Property Distributive Property Identity Property
    • 2 + 5 = 5 + 2
    • 5 × 9 = 9 × 5
    • (2 + 6) + 4 = 2 + (6 + 4)
    • (3 × 2) × 5 = 3 × (2 × 5)
    • 5(7 + 2) = 5 × 7 + 5 × 2
    • 2(x + 5) = 2x + 10
    • 11 + 0 = 11
    • 6 × 1 = 6
  2. 2Write the letter of the matching item on each line.

    Match each playlist track to the property it plays.

    1. 8 × 6 = 6 × 8
    2. (4 × 2) × 3 = 4 × (2 × 3)
    3. 6(2 + 3) = 6 × 2 + 6 × 3
    4. 10 × 1 = 10
    5. 0 + 19 = 19
    6. 9 + 5 = 5 + 9
    • ACommutative (Multiplication)
    • BAssociative (Multiplication)
    • CDistributive
    • DIdentity (Multiplication)
    • EIdentity (Addition)
    • FCommutative (Addition)
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A sound engineer needs to calculate 4 × 17 × 25 mentally to find the total cost of audio cables. Using the associative and commutative properties, she rearranges: 4 × 25 × 17 = 100 × 17. What is 4 × 17 × 25?

    1. A170
    2. B425
    3. C1,000
    4. D1,700
    Show each partial product, then add them
  2. 4Circle the letter of the best answer. Show how you know.

    Track 2 on the playlist plays 5(7 + 2) = 5 × 7 + 5 × 2. Which property is this?

    1. ACommutative Property
    2. BAssociative Property
    3. CIdentity Property
    4. DDistributive Property
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Track 3 plays (7 + 3) + 5 = 7 + (3 + 5). Only the parentheses moved. Which property is this?

    1. ACommutative Property
    2. BDistributive Property
    3. CAssociative Property
    4. DIdentity Property
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    Track 4 plays 1 × y = y. Which property is this?

    1. ADistributive Property
    2. BCommutative Property
    3. CAssociative Property
    4. DIdentity Property
    Show your work

Explain your thinkingHow can you tell the difference between the commutative and associative properties? What clue helps you decide?

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