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

Lesson 6.14The Distributive Property

Set B · Version ASecond form · supported practice

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

Learning target I can use the distributive property to expand and factor expressions.

Why This Matters You're selling concert bundles at the music studio. Each bundle includes a ticket ($15) and a snack ($5). If 3 people each buy a bundle, you can calculate the total as 3(15 + 5) OR as 3 × 15 + 3 × 5. Either way, the total is the same — $60! This is the distributive property.

RememberThe Distributive Property

The Distributive Property. Formula: a(b + c) = ab + ac | a(b − c) = ab − ac The distributive property means you can multiply a number by everything inside the parentheses, one piece at a time: a(b + c) = ab + ac.

  1. Expand: Multiply the outside factor by each term inside parentheses.
  2. Factor: Find the GCF of terms and pull it outside: ab + ac = a(b + c).
  3. Visual: Represent as the area of partitioned rectangles

Words: The Distributive Property (La propiedad distributiva)Distributive Property (Propiedad distributiva)Factor (Factor)Expand (Desarrollar)Equivalent (Equivalente)

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

    What is the prime factorization of 24?

    1. A2 × 2 × 2 × 3
    2. B2 × 12
    3. C3 × 8
    4. D4 × 6
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which number is prime?

    1. A19
    2. B21
    3. C27
    4. D33
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A factor tree for 36 ends with which prime factors?

    1. A2 × 2 × 3 × 3
    2. B2 × 18
    3. C3 × 12
    4. D6 × 6
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    In the prime factorization of 50, how many times does 5 appear?

    1. AOnce
    2. BThree times
    3. CTwice
    4. DNot at all
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A music studio is ordering supplies for 8 practice rooms. Each room needs a music stand ($12) and a stool ($9). The total cost can be written as 8(12 + 9). Distribute: 8(12 + 9) = ?

    1. A8 × 12 + 8 × 9
    2. B8 × 12 + 9
    3. C8 + 12 × 9
    4. D8 × 21 × 8
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A music studio is ordering supplies for 8 practice rooms. Each room needs a music stand ($12) and a stool ($9). The total cost can be written as 8(12 + 9). What is the total cost for 8 practice rooms?

    1. A$21
    2. B$96
    3. C$105
    4. D$168
    Show your work

Explain your thinkingWhat pattern do you see when you expand an expression using the distributive property?

Sentence starter When I distribute, I multiply the outside factor ___ by each term ___. The operation inside the parentheses ___ stays the same.

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 6.14The Distributive Property

Set B · Version BSecond form · core practice

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

Learning target I can use the distributive property to expand and factor expressions.

Why This Matters You're selling concert bundles at the music studio. Each bundle includes a ticket ($15) and a snack ($5). If 3 people each buy a bundle, you can calculate the total as 3(15 + 5) OR as 3 × 15 + 3 × 5. Either way, the total is the same — $60! This is the distributive property.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each a(b + c) light cue to its ab + ac expanded form.

    1. 2(b + c)
    2. 6(x + 2)
    3. 3(m + 5)
    4. 5(p + 1)
    • A2b + 2c
    • B6x + 12
    • C3m + 15
    • D5p + 5
  2. 2Write the name of the correct group on each line.

    Sort each light-cue expansion: was the factor distributed correctly to BOTH terms, or only to one?

    Groups: Distributed correctly Distributed incorrectly
    • 2(x + 6) = 2x + 12
    • 4(n + 3) = 4n + 3
    • 5(y + 2) = 5y + 10
    • 3(a + 7) = 3a + 7
    • 6(m + 1) = 6m + 6
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A music studio is ordering supplies for 8 practice rooms. Each room needs a music stand ($12) and a stool ($9). The total cost can be written as 8(12 + 9). A student wrote 8(12 + 9) = 8 × 12 + 9 = 105. What went wrong?

    1. AThey added instead of multiplying
    2. BThey used the wrong prices
    3. CThey forgot to multiply the 9 by 8 as well
    4. DThey distributed too many times
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Light Cue 1: Expand 3(x + 4) for the stage-light controller.

    1. A3x + 12
    2. B3x + 4
    3. C3x + 7
    4. Dx + 12
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Light Cue 2: Expand 5(2 + n) to set two spotlight banks.

    1. A7 + 5n
    2. B10 + 5n
    3. C10 + n
    4. D10 + 5
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    Light Cue 3: Expand 4(a + 2) for the back-row beam.

    1. A4a + 8
    2. B4a + 2
    3. C4a + 6
    4. Da + 8
    Show your work

Explain your thinkingWhat pattern do you see when you expand an expression using the distributive property?

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