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

Lesson 6.8Expanding and Factoring Expressions

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

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

WordWhat it meansExample
Properties of OperationsSpanish: Propiedades de las operaciones Rules that let you reorder or regroup numbers without changing an expression's value. 3 + 5 = 5 + 3 (commutative property).
Commutative PropertySpanish: Propiedad conmutativa You can change the order and get the same answer. 3 + 7 = 7 + 3 = 10 both ways; 4 × 5 = 5 × 4 = 20 both ways — order does not matter
Associative PropertySpanish: Propiedad asociativa You can change the grouping and get the same answer. (2 + 3) + 4 = 5 + 4 = 9 and 2 + (3 + 4) = 2 + 7 = 9 — same answer, different grouping
Identity PropertySpanish: Propiedad de identidad Adding 0 or multiplying by 1 keeps the same value. 9 + 0 = 9 (zero is the identity for addition); 6 × 1 = 6 (one is the identity for multiplication)
PropertySpanish: Propiedad A rule that is always true in math. Commutative works for + and ×, but NOT for − or ÷ (since 5 − 3 = 2 but 3 − 5 = −2)
Distributive PropertySpanish: Propiedad distributiva Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac. a(b + c) = ab + ac

How it worksWorked example

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

Factor 18x + 27 using the GCF.

  1. The GCF of 18 and 27 is 9.
  2. Divide each term: 18x ÷ 9 = 2x and 27 ÷ 9 = 3.
  3. Expand to check: 9 × 2x + 9 × 3 = 18x + 27.

Answer: 9(2x + 3)

Say it and write itSentence starters

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

  • The greatest common factor of the terms is .
  • Factored, the expression becomes .
  • Expanded, the expression becomes .
  • I checked my work by , and I got back .

Word bank Distributive Propertyexpandfactorgreatest common factorGCFtermproductparenthesesmultiplydividecheckequivalent

Watch out!A common mistake

A common mistake in Properties of Operations is applying the commutative property where it does not belong, or confusing it with the associative property. Students often assume 15 − 8 = 8 − 15 (it does not: 7 ≠ −7

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

Lesson 6.8Expanding and Factoring Expressions

Apply Day · Version ASupported 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.

  1. 1Complete each step, then write the final answer.

    Use properties to find 6 + 8 + 4. Add the friendly pair first.

    Show your work

    Hint 6 and 4 make a ten.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Which property does 5 × 9 = 9 × 5 show? Type commutative or associative.

    Show your work

    Hint Did the order change, or only the parentheses?

    Final answer:
  3. 3Complete each step, then write the final answer.

    Use properties to find 5 × 8 × 2.

    Show your work

    Hint 5 × 2 makes 10. Multiply that pair first.

    Final answer:
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 6.8Expanding and Factoring Expressions

Apply Day · Version BCore 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.

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

    Which equation shows the Identity Property?

    1. A9 × 1 = 9
    2. B9 × 0 = 0
    3. C9 + 1 = 1 + 9
    4. D(9 + 1) + 2 = 9 + (1 + 2)
    Show your work
  2. 2Complete each step, then write the final answer.

    Use properties to find 2 × 17 × 50.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Use properties to find 7 + 16 + 3. Add the friendly pair first.

    Show your work
    Final answer:
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 6.8Expanding and Factoring Expressions

Apply Day · ChallengeExtension

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

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

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

    Which property of operations is shown by the equation (7 + 4) + 6 = 7 + (4 + 6)?

    1. ACommutative Property of Addition
    2. BIdentity Property of Addition
    3. CDistributive Property
    4. DAssociative Property of Addition
    Show your work
  2. 2Complete each step, then write the final answer.

    Eli says 12 ÷ 4 and 4 ÷ 12 have the same value, because the Commutative Property lets you switch the order. What is 12 ÷ 4?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Use properties to find 25 × 11 × 4.

    Show your work
    Final answer:
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