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

Lesson 6.86.8 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use the commutative, associative, and identity properties to rewrite expressions, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 6.8. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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 example

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

Simplify 4(m + 2) + 3m.

  1. Distribute the 4: 4m + 8 + 3m.
  2. Move like terms together: 4m + 3m + 8.
  3. Combine: 7m + 8. Test m = 1: 4(3) + 3 = 15 and 7 + 8 = 15.

Answer: 7m + 8

Now you trySame steps, your turn

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

Look at 6 + 9 and 9 + 6. Do they give the same total? Explain why.

Answer:

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 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 6.86.8 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 6.8. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    20 × 7 × 5(20 × 5) × 7=
    Both sides have the same value.

    Find 20 × 7 × 5 without a calculator. Use properties to make the work easier.

    1. 1Switch the order of 7 and 5. Which property is this?
    2. 2Group the friendly pair. What is 20 × 5?
    3. 3Multiply by 7. What is the product?
    Final answer:
  2. 2Complete each step, then write the final answer.
    ExpressionValue
    (24 ÷ 4) ÷ 2?
    24 ÷ (4 ÷ 2)?
    Find each value. Compare them.

    Does the Associative Property work for division? Compare (24 ÷ 4) ÷ 2 and 24 ÷ (4 ÷ 2).

    1. 1Find (24 ÷ 4) ÷ 2.
    2. 2Find 24 ÷ (4 ÷ 2).
    3. 3Why can you not move the parentheses in division?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Use properties to find 2 × 17 × 50.

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

    Rewrite 7 + x + 13 as x + ☐. What number goes in the box?

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

    A store sells 46 shirts, 38 hats and 54 jackets. Use properties to find the total number of items.

    Show your work
    Final answer:
  6. 6Complete 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:

Explain your thinkingWhen can you change the order or the grouping of numbers? When can you not? Give one example of each.

ChallengeWrite your own problem

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

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