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

Lesson 6.146.14 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can use the distributive property to expand and factor expressions — one step at a time, with support.

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 $15 ticket and a $5 snack. Find the cost of 3 bundles: 3(15 + 5).

  1. Way 1: Add inside the parentheses first: 15 + 5 = 20 → 3 × 20 = 60
  2. Way 2: Multiply 3 by each part: 3 × 15 + 3 × 5
  3. Multiply, then add: 45 + 15 = 60
  4. Compare the two ways: 3(15 + 5) = 3 × 15 + 3 × 5
  5. 3 bundles cost $60. Both ways give the same total.

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).

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 1

Group 1Supported practice

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

Learning target With my small group, I can use the distributive property to expand and factor expressions — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    1245??
    The 5 multiplies the 12 and the 4.

    Each kit has a $12 ball and a $4 pump. Find the cost of 5 kits: 5(12 + 4).

    1. 1The 5 multiplies each part. Write the two products.
    2. 2Find each product.
    3. 3Add the products. What do 5 kits cost?
    Final answer:
  2. 2Complete each step, then write the final answer.
    x63??
    This time one part is a variable.

    Use the distributive property to expand 3(x + 6).

    1. 1The 3 multiplies each term. Write the two products.
    2. 2What is 3 × 6?
    3. 3Write the expanded expression.
    Final answer:
  3. 3Complete each step, then write the final answer.

    Use the distributive property to find 4(10 + 2).

    Show your work

    Hint Multiply 4 by 10 and 4 by 2. Then add the two products.

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

    Expand 6(x + 4). Fill in the blank: 6x + ___.

    Show your work

    Hint The 6 multiplies the x and the 4. What is 6 × 4?

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

    A class buys 4 lunches. Each lunch is a $7 sandwich and a $2 drink. Use 4(7 + 2) to find the total cost.

    Show your work

    Hint Find the cost of 4 sandwiches and 4 drinks. Then add.

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

    Ray says 3(9 + 5) = 3 × 9 + 5, so the value is 32. What mistake did he make? What is the correct value?

    Show your work

    Hint Did the 3 multiply both terms inside the parentheses?

    Final answer:

Explain your thinkingRay forgot one product. Why must the outside number multiply every term inside the parentheses?

Sentence starter The 3 multiplies both ___ and ___. · Ray's answer is too small because ___.

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