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

Lesson 6.146.14 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use the distributive property to expand and factor expressions, explain why the method works, and use it on a problem I have not seen before.

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.

Expand 4(x + 3).

  1. Multiply 4 by the first term: 4 × x = 4x
  2. Multiply 4 by the second term: 4 × 3 = 12
  3. Add the two products: 4(x + 3) = 4x + 12
  4. 4(x + 3) is equivalent to 4x + 12.
  5. Factor 6x + 15 using the greatest common factor (GCF).
  6. Find the GCF of 6 and 15: 6 = 3 × 2 → 15 = 3 × 5 → GCF: 3
  7. Divide each term by 3: 6x ÷ 3 = 2x; 15 ÷ 3 = 5
  8. Write the GCF outside the parentheses: 3(2x + 5)
  9. Check by expanding: 3(2x + 5) = 6x + 15
  10. 6x + 15 is equivalent to 3(2x + 5).

Now you trySame steps, your turn

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

Use the distributive property to find 2(8 + 3). Then explain a common mistake.

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 6.146.14 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can use the distributive property to expand and factor expressions, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    y56??
    The 6 multiplies the y and the 5.

    Expand 6(y + 5).

    1. 1Multiply 6 by each term. Write the two products.
    2. 2What is 6 × 5?
    3. 3Write the expanded expression.
    Final answer:
  2. 2Complete each step, then write the final answer.
    ???12x18
    You know the parts. Find the side.

    Factor 12x + 18 using the greatest common factor (GCF).

    1. 1What is the GCF of 12 and 18?
    2. 2Divide each term by 6. Write the factored form.
    3. 3Why is 2(6x + 9) not finished?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Expand 4(3x + 5). Fill in the blank: 12x + ___.

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

    Factor 15x + 25 using the GCF. What number goes outside the parentheses?

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

    A store sells 8 shirts. Each shirt costs $20, with $3 off. Use 8(20 − 3) to find the total cost.

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

    Find the missing number so the expressions are equivalent: 4(x + ___) = 4x + 36.

    Show your work
    Final answer:

Explain your thinkingExpanding and factoring undo each other. How can you use one to check the other? Use 12x + 18 = 6(2x + 3).

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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