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

Lesson 6.86.8 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can use the commutative, associative, and identity properties to rewrite 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
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. a + b = b + a
Associative PropertySpanish: Propiedad asociativa You can change the grouping and get the same answer. (a + b) + c = a + (b + c)
Identity PropertySpanish: Propiedad de identidad Adding 0 or multiplying by 1 keeps the same value. a + 0 = a · a × 1 = a
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 examplerewriting an expression with properties

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

Write an expression equivalent to 6(y + 3) + 9y in simplest form.

  1. Distribute the 6 to each term inside. 6(y + 3) = 6y + 18
  2. Rewrite the whole expression. 6y + 18 + 9y
  3. Reorder so like terms sit together. 6y + 9y + 18
  4. Combine like terms. 15y + 18

Answer: 6(y + 3) + 9y is equivalent to 15y + 18.

Now you trySame steps, your turn

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

Write an expression equivalent to 4(m + 7) + 3m in simplest form.

  1. Distribute the 4 to each term inside. 4(m + 7) = +
  2. Rewrite the whole expression.
  3. Reorder so like terms sit together.
  4. Combine like terms.
Answer:equivalent expression in simplest form

Say it and write itSentence starters

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

  • I used the Property so that I could .
  • After distributing, the expression became .
  • The like terms and combine to make .
  • My rewritten expression is equivalent because .

Word bank CommutativeAssociativeIdentityDistributivepropertyequivalentreorderregroupdistributecombinelike termsvalue

Watch outA 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 — commutative only works for addition and multiplication), or they see parentheses move and call it "associative" even when the numbers inside just swapped places, like (2 + 3) + 4 = (3 + 2) + 4 (that is commutative — the order inside the parentheses changed, not the grouping). Before you label a property, ask: did only the order change (commutative), did only the grouping change (associative), or was a 0 or 1 involved (identity)?

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

Lesson 6.86.8 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 commutative, associative, and identity properties to rewrite expressions — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    4 + 7 + 64 + 6 + 7=
    Compare the two sides.

    A team has 4 runners, 7 jumpers and 6 throwers. Add 4 + 7 + 6. Then add 4 + 6 + 7. Which property does this show?

    1. 1What is 4 + 7 + 6?
    2. 2What is 4 + 6 + 7?
    3. 3What changed: the order or the grouping?
    4. 4Which property is this?
    Final answer:
  2. 2Complete each step, then write the final answer.
    (2 × 5) × 72 × (5 × 7)=
    Compare the two sides.

    Find (2 × 5) × 7 and 2 × (5 × 7). Do they give the same product? Which property does this show?

    1. 1Multiply 2 × 5 first. Then multiply by 7. What do you get?
    2. 2Multiply 5 × 7 first. Then multiply by 2. What do you get?
    3. 3Did the order change, or only the parentheses?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Which property does 8 + 3 = 3 + 8 show? Type commutative or associative.

    Show your work

    Hint Look at the numbers. Did their order change, or the parentheses?

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

    Use properties to find 18 + 9 + 2. Add the friendly pair first.

    Show your work

    Hint Which two numbers make a ten? Move them next to each other.

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

    A band sells 25 tickets on Friday, 13 on Saturday and 75 on Sunday. Use properties to find the total number of tickets.

    Show your work

    Hint 25 and 75 make a friendly number. Add them first.

    Final answer:
  6. 6Circle 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)

    Hint The Identity Property keeps a number the same. Look for × 1 or + 0.

    Show your work

Explain your thinkingHow can you tell the Commutative Property from the Associative Property? Use (2 × 5) × 7 = 2 × (5 × 7) to explain.

Sentence starter The Commutative Property changes the ___. · The Associative Property changes the ___ but keeps the ___.

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