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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Look at 6 + 9 and 9 + 6. Do they give the same total? 6 + 9 = 15 and 9 + 6 = 15. Yes, the same. Only the order changed, so this shows the Commutative Property. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhat is the GCF of 18 and 24?

   1. A6
   2. B3
   3. C2
   4. D72

   How do you know?
3. 3

   Warm restartWhat is the LCM of 4 and 6?

   1. A12
   2. B24
   3. C2
   4. D10

   How do you know?
4. 4

   Warm restartOne bell rings every 8 minutes and another every 12 minutes. They just rang together. After how many minutes will they ring together again?

   1. A24 minutes
   2. B4 minutes
   3. C20 minutes
   4. D96 minutes

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhich property lets you change the ORDER of the factors?

   1. ACommutative
   2. BAssociative
   3. CDistributive
   4. DIdentity

   Why is that the answer?
2. 6

   Think it throughWhich property lets you change the GROUPING of the factors?

   1. AAssociative
   2. BCommutative
   3. CDistributive
   4. DIdentity

   How do you know? Give a second reason as well.
3. 7

   Think it throughWhat is 4 × 17 × 25?

   1. A1,700
   2. B170
   3. C425
   4. D1,000

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelHow can you tell the difference between the commutative and associative properties? What clue helps you decide?

Use the words

Fill each blank with a word from the bank.

• Rules that let you reorder or regroup without changing the ___.
• The rule that order does not change a sum or product, like a + b = b + a, is the ___.
• The rule that grouping does not change a sum or product, like (a + b) + c = a + (b + c), is the ___.
• The rule that adding 0 or multiplying by 1 keeps a number the same is the ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The 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.
2. 10

   Say moreHow can you tell the commutative property from the associative property? Use 6 + 9 = 9 + 6 and (3 + 5) + 2 = 3 + (5 + 2) to explain.
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A sound engineer adds up the volume levels of three mixing-board channels: guitar at 15, bass at 22, and drums at 8. She writes the sum four ways: 15 + 22 + 8, 8 + 15 + 22, (15 + 22) + 8, and 15 + (22 + 8).

   Show your work

Last check

These two come from Lesson 6.7. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which property is shown? (8 + 5) + 2 = 8 + (5 + 2)

   1. AAssociative Property
   2. BCommutative Property
   3. CIdentity Property
   4. DDistributive Property

   Explain your choice.
2. 13

   From Lesson 6.7Explain your thinking — Two supply runs repeat every 6 weeks and every 8 weeks, and both happen this week. When will they next happen in the same week?

   1. AWeek 24, the least common multiple of 6 and 8
   2. BWeek 2, the greatest common factor of 6 and 8
   3. CWeek 48, because 6 × 8 = 48
   4. DWeek 14, because 6 + 8 = 14

   How do you know?
3. 14

   From Lesson 6.7A problem asks when two repeating schedules meet again. Which do you use?

   1. AThe least common multiple
   2. BThe greatest common factor
   3. CEither one works
   4. DNeither — you list factors

   How do you know?

Be honest — this tells your teacher what to do next