Juice Containers

Part 1.
Pretend not to know any algorithms for computing with fractions and explain how to use a model to answer the following questions.

a. If 7 containers hold 4 gallons of juice, how many gallons does 1 container hold?
b. I have 4 gallons of juice. If a container holds 7 gallons, how many containers can I fill?
c. If 7 containers hold 1/4 gallons of juice, how many gallons does 1 container hold?
d. I have  gallon of juice. If a container holds 7 gallons, how many containers can I fill?
e. If 7 containers hold 3/4 gallons of juice, how many gallons does 1 container hold?
f. I have 3/4 gallon of juice. If a container holds 7 gallons, how many containers can I fill?

What are the similarities and differences between the problems?

Part 2.
Using a different context, write word problems for the following division expressions and then use a model to demonstrate the process of finding the correct answer.

a. 5 ÷ 2

b. 5 ÷ 1/2

c. 5 ÷ 3/2

Extension:
Notice that the numbers used above were relatively prime. What happens to the process when the numbers are no longer relatively prime? Create a sequence of 3 word problems and use a model to explore the process of finding correct answers.