1. What does this represent?
By now, you are probably very good at working with basic division problems.  For example, you can easily find how many teams of 3 students could be formed from a class of 36 students.  You can probably calculate quickly how many eggs would be in each carton if 24 eggs were divided evenly into 2 cartons.  Most likely, you have also learned how to do more complicated division calculations such as  208 ÷ 16 or ÷ 10.25 using methods like long division. 
How are division problems like these related to dividing pieces of licorice evenly among several people?  Can your methods and thinking in one situation be used to find solutions in the other situations?  Think about the focus questions below as you work with your team on the problems in this lesson.
What does this represent?
How does this connect to what we already know how to do?
How can we apply this strategy?

2. 15.  When dividing licorice among her teammates, one of the students in Ms. Yu’s class exclaimed, “Whoa!  We divided 7 pieces of licorice among 5 people and each person got 1 whole piece and    of another.  That’s   of a whole.  Is this just a coincidence?”
What do you think?  Does it make sense that the answer to 7 divided by 5 is  ?
Ms. Yu’s students decided to explore this question using smaller numbers and asked, “What if 4 pieces of licorice were shared among 3 people?” 
Three different teams drew the diagrams shown below.
Team A Team B Team C
Work with your team to make sense of these diagrams.  Did each team get the same answer?  How was each team thinking about dividing the licorice?  Be prepared to share your ideas with the whole class.

3. 16. Teams D and E were thinking about the “4 pieces of licorice divided by 3” problem, but they drew the diagrams shown below. 
“Our diagram looks very different!” Team D said. “Our question was, ‘If each package holds 3 pieces, how many packages will we need?’” 
Work with your team to make sense of these new diagrams.  What problem were the teams working on?  What is the answer to Team D’s question?  Where can you see the answer in the diagrams?  Explain. 
17. Is there a connection between the operation of division and a fraction like the one Ms. Yu’s students found in problem 6-15? Discuss this with your team and be prepared to explain your ideas to the class

4. 18. Three methods to illustrate “7 divided by 5” are shown below
18. Three methods to illustrate “7 divided by 5” are shown below.  The work on the left uses long division.  The other two methods involve diagrams.  Work with your team to make sense of the methods by answering the questions that follow.
In the leftmost method above, what does the “1” written at the top of the division calculation represent when sharing 7 pieces of licorice with 5 people?  How can you see the same “1” in the middle diagram? 
What does the “1” written at the top of the division calculation represent when packaging 7 pieces of licorice into bags that each hold 5 pieces?  How can you see the same “1” in the diagram that is farthest to the right? 
What does the “2” written at the bottom of the division calculation represent?  How can you see the “2” in both of the other diagrams?
The next step of the division calculation is shown at right.  What is done in this step?  How can you see the same step in the diagram?  That is, where is the “20” and how is it created?  What does the “20” mean? 
Copy the long division problem and the diagrams on your paper.  Then complete them.  For each remaining step, explain the connections between the two methods.  How much licorice would each person get altogether?  (This is another way of asking how many boxes are needed.

5. 19. Lalo was thinking about the connections between division and fractions and said to his team, “Division problems often result in fractions.  Since all fractions represent division, I think we can write all division problems as fractions.”  Explore Lalo’s idea by answering the questions below.
With your team, discuss how you could use Lalo’s idea to write  as a division problem.  Then use long division to find the decimal that results from the division problem you wrote.  Express your answer as both a decimal and a fraction.
Follow the directions below to write each of the following fractions as decimals.
i ii.
First estimate the size of each number by marking its place on a number line. 
Write the division problem that the fraction could represent. 
Then use long division to find the decimal representation.  How close were your estimates?

6. 20. LEARNING LOG
What do you know now about how fractions, division, and decimals are related?
Discuss this with your team and then make up examples to show what you know. 
Record your examples in your Learning Log.  Title this entry “Fractions as Division” and label it with today’s date.

7. Tonight’s homework is…
Review & Preview, problems # 5-14
Show all work and justify your answers for full credit.