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

Lesson 6.14The Distributive Property

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
The Distributive PropertySpanish: La propiedad distributiva Multiply a factor by every term inside parentheses. 3(x + 4) = 3x + 12
Distributive PropertySpanish: Propiedad distributiva Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac. 3(4 + 5) = 3×4 + 3×5 = 12 + 15 = 27 — the 3 gets 'distributed' to both the 4 and the 5
FactorSpanish: Factor A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4. In 3(x + 2), the 3 is the factor outside the parentheses that multiplies each term inside
ExpandSpanish: Desarrollar To multiply out the parentheses in an expression. Expand 2(n + 6): multiply 2 × n = 2n and 2 × 6 = 12, so 2(n + 6) = 2n + 12
EquivalentSpanish: Equivalente Expressions that always have the same value. 3(x + 4) and 3x + 12 always give the same answer: when x = 2, both = 18; when x = 10, both = 42
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. In 6x + 15, the coefficient of x is 6 — it came from distributing in 3(2x + 5)

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Each bundle has a ticket ($15) and a snack ($5). For 3 bundles I can write 3(15 + 5).

  1. Way 1: add inside first. 15 + 5 = 20, then 3 × 20 = 60.
  2. Way 2: distribute the 3 to each part. 3 × 15 + 3 × 5.
  3. That is 45 + 15 = 60.
  4. Both ways give $60, so 3(15 + 5) = 3 × 15 + 3 × 5.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Let's expand 2(8 + 3). Where does the 2 go?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

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

Word bank The Distributive PropertyDistributive PropertyFactorExpandEquivalentCoefficientdistributemultiplyeach termfactorexpandequivalent

Watch outA common mistake

The most common mistake in The Distributive Property is multiplying the outside factor by only the FIRST term inside the parentheses and forgetting the second — for example, writing 3(x + 4) = 3x + 4 instead of 3x + 12. Before you submit, check: did the outside number reach BOTH terms inside the parentheses?

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

Lesson 6.14The Distributive Property

Version ASupported practice

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

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

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Use the distributive property to expand each expression.

    Factored FormExpanded Form
    2(x + 5)
    4(3 + 7)

    Hint Expand means: the outside number multiplies every term inside the parentheses.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Expand 6(n + 3) using the distributive property.

    1. A6n + 18
    2. B6n + 3
    3. C6n + 9
    4. Dn + 18

    Hint The 6 outside must visit BOTH terms inside the parentheses: the n and the 3.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    Expand 4(5 − 2) using the distributive property.

    1. A9
    2. B12
    3. C20 − 2
    4. D22

    Hint Even with subtraction inside, the 4 must multiply BOTH the 5 and the 2.

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Expand 3(x + 4) using the distributive property.

    1. A3x + 12
    2. B3x + 4
    3. C7x
    4. Dx + 12

    Hint The 3 outside multiplies each term inside — both the x and the 4.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    When using the distributive property with a(b + c), you must multiply 'a' by:

    1. AOnly b
    2. BOnly c
    3. Cb + c first, then multiply
    4. DBoth b and c

    Hint This asks about the RULE itself: where does the outside factor 'a' go?

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Expression4(n + 3)
    2. 2Distribute4 × n + 3
    3. 3Simplify4n + 3

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Did the 4 get multiplied by both n and 3, or only by the n?

    Correct work
    Correct answer:

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.

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

Version BCore practice

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

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

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Use the distributive property to expand each expression.

    Factored FormExpanded Form
    3(2x + 5)
    7(a − 4)
    2(3m + 8)
    5(6 − y)
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each factored form to its expanded form.

    1. 2(x + 9)
    2. 5(3n − 2)
    3. 4(a + 6)
    4. 3(7 − y)
    5. 6(2m + 1)
    6. 8(x − 3)
    • A2x + 18
    • B15n − 10
    • C4a + 24
    • D21 − 3y
    • E12m + 6
    • F8x − 24
  3. 3Write the name of the correct group on each line.

    Expand each expression, then sort by whether the expanded form has a constant greater than 15 or not.

    Groups: Constant > 15 Constant ≤ 15
    • 3(x + 7)
    • 2(n + 5)
    • 5(a + 4)
    • 4(y − 2)
    • 6(m + 3)
    • 2(3x + 1)
  4. 4Decide whether each pair balances. Check Yes or No, then explain.

    Both equal 32 when x = 5 — they are equivalent by the distributive property.

    Left sideRight sideBalanced?
    Explain your choice
Part 2Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Expression5(3x + 2)
    2. 2Distribute5 × 3x + 2
    3. 3Simplify15x + 2

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

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

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

ChallengeExtension

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

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

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Work backwards: factor each expanded expression into its factored form using the GCF.

    Expanded FormGCFFactored Form
    6x + 18
    10n − 15
    8a + 12
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Distributive Error

    1. 1Expression5(2x + 4)
    2. 2Distribute5 × 2x + 4
    3. 3Simplify10x + 4

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    Use the distributive property to explain why 6 × 98 can be calculated as 6 × 100 − 6 × 2 = 588. Then create your own example of using the distributive property to make multiplication easier.

    Write your answer

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

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help