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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.

   Let's try together: 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.

   My first step is ___ , because the problem asks for ___ .

   Show your work
2. 2

   Warm restartWhat is the GCF of 18 and 24?

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

   Warm restartWhat is the LCM of 4 and 6?

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

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?

   I chose ___ because ___ .
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?

   I chose ___ because ___ .
3. 7

   Think it throughWhat is 4 × 17 × 25?

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

   Explain your thinking.

   I chose ___ because ___ .
4. 8

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

   The ___ property changes the ___, while the ___ property changes the ___. I can tell by looking at whether the ___ moved or the ___ changed.

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.

   The ___ property changes the order, like 6 + 9 = 9 + 6.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   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 knowQuick check — you've got this: 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.

   I know it is ___ because ___ .
2. 13

   From Lesson 6.7Quick check — you've got this: 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
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

Be honest — this tells your teacher what to do next