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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: Let's try 2 ÷ 1/3. The question it asks is: how many 1/3-size pieces fit into 2 wholes? How many thirds are in 1 whole? Three. We have 2 wholes, so 2 × 3 = 6. That means 2 ÷ 1/3 = 6. The answer is bigger than the 2 we started with, because each piece is smaller than one whole. 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 4.8 ÷ 2?

   1. A2.4
   2. B24
   3. C0.24
   4. D2.6

   How do you know?
3. 3

   Warm restartWhat is 8.4 ÷ 0.7?

   1. A1.2
   2. B120
   3. C12
   4. D0.12

   How do you know?
4. 4

   Warm restartWhat is 14.4 ÷ 1.2?

   1. A1.2
   2. B12
   3. C120
   4. D0.12

   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 through6 ÷ 1/3 = ?

   1. A2
   2. B18
   3. C6
   4. D3

   Why is that the answer?
2. 6

   Think it throughWhy is the answer bigger than 6?

   1. ABecause the pieces are smaller than a whole yard, so many of them fit
   2. BBecause dividing always makes numbers bigger
   3. CBecause 1/3 is negative
   4. DBecause 6 × 3 is multiplication, not division

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

   Think it throughIf each section were 1/2 yard instead, how many sections?

   1. A3
   2. B12
   3. C18
   4. D24

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

   Back to the modelWhy does dividing by a unit fraction always give a number larger than the dividend?

Use the words

Fill each blank with a word from the bank.

• Dividing asks how many groups of one ___ fit inside another amount.
• In 6 ÷ 1/2, the number 6 being divided is the ___.
• In 6 ÷ 1/2, the number 1/2 we divide by is the ___.
• The answer to a division problem 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 Interpret Division of Fractions is assuming that dividing always makes the answer smaller.
2. 10

   Say moreWhat does 3 ÷ 1/4 actually mean? Show your partner with the bar model.
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Agent Reyes has a 3-foot strip of evidence tape. For the lab she needs to cut it into sections that are each 1/4 foot long.

   Show your work

Last check

These two come from Lesson 5.10. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — What does 5 ÷ 1/4 mean, and what is the quotient?

   1. AHow many 1/4-size pieces fit into 5; quotient is 20
   2. B5 groups of 1/4; quotient is 5/4
   3. C1/4 of 5; quotient is 5/4
   4. D5 minus 1/4; quotient is 4 3/4

   Explain your choice.
2. 13

   From Lesson 5.10Explain your thinking — A rectangular prism has l = 7 ft, w = 2 ft, h = 3 ft. What is the volume?

   1. A42 ft³
   2. B24 ft³
   3. C42 ft²
   4. D12 ft³

   How do you know?
3. 14

   From Lesson 5.10Why divide by 231 instead of multiplying?

   1. ABecause you are finding how many 231-in³ gallons fit inside the tank
   2. BBecause dividing always makes numbers smaller
   3. CBecause 231 is bigger than 24
   4. DBecause gallons are bigger than inches

   How do you know?

Be honest — this tells your teacher what to do next