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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: Find 3 ÷ 1/4. Then explain why the answer is greater than 3. Rewrite 3 ÷ 1/4 as a multiplication. (3 × 4) What is the quotient? (3 × 4 = 12) Why is 12 greater than 3? (The pieces are smaller than 1 whole. Each whole holds 4 pieces, so 3 wholes hold 12.)

   Show your work
2. 2

   Warm restartWhich property is shown? 7 × 5 = 5 × 7

   1. AAssociative Property
   2. BIdentity Property
   3. CCommutative Property
   4. DDistributive Property

   How do you know?
3. 3

   Warm restartWhich property is shown? (2 + 9) + 1 = 2 + (9 + 1)

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

   How do you know?
4. 4

   Warm restartWhich grouping makes 4 × 25 × 7 easiest to multiply mentally?

   1. A(4 × 25) × 7
   2. B4 × (25 + 7)
   3. C(4 + 25) × 7
   4. D(25 × 7) × 4

   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 through10 ÷ 1/4 = ?

   1. A2.5
   2. B4
   3. C14
   4. D40

   Why is that the answer?
2. 6

   Think it throughWhat is the reciprocal of 1/4?

   1. A1/4
   2. B−1/4
   3. C1/2
   4. D4

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

   Think it throughA student answered 2.5. What did they do wrong?

   1. AThey multiplied by 4
   2. BThey added 1/4
   3. CThey used the wrong rope length
   4. DThey divided by 4 instead of by 1/4

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

   Back to the modelWhy does 3 ÷ 1/4 = 12? How does the number line show this?

Use the words

Fill each blank with a word from the bank.

• A counting number like 0, 1, 2, or 3 with no fraction or decimal part is a ___.
• A number that shows part of a whole, like 3/4, is a ___.
• The fraction you get by flipping a fraction upside down is its ___.
• To divide by a fraction, I ___: keep the first number, change ÷ to ×, and flip the second fraction.

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 Divide Whole Numbers by Fractions is doing 'Keep, Change' but skipping the 'Flip' — students multiply by the divisor as it is instead of by its reciprocal.
2. 10

   Say moreHow does 'Keep, Change, Flip' turn 6 ÷ 1/3 into a multiplication problem?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A STEM summer camp has a 3-hour afternoon session. Campers choose from afternoon activities that are each 45 minutes long.

   Show your work

Last check

These two come from Lesson 6.8. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — What is 9 ÷ 1/3?

   1. A1/27
   2. B3
   3. C9/3
   4. D27

   Explain your choice.
2. 13

   From Lesson 6.8Explain your thinking — Which property is shown? (8 + 5) + 2 = 8 + (5 + 2)

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

   How do you know?
3. 14

   From Lesson 6.8What is 4 × 17 × 25?

   1. A170
   2. B425
   3. C1,000
   4. D1,700

   How do you know?

Be honest — this tells your teacher what to do next