Which three go together? Why do they go together?

A rectangular tile pattern with 2 rows of tiles. It has 2 blue tiles and then 3 yellow tiles on the bottom row and 3 yellow tiles then 2 blue tiles on the top row.

A rectangular tile pattern with 2 rows of blue and yellow tiles. It has 3 yellow, then 2 blue, then 3 yellow and 2 blue tiles on the bottom row and 2 blue, 3 yellow, 2 blue and 3 yellows on the top row. 

A rectangular tile pattern with 2 rows of tiles. It has 6 yellow tiles on the bottom row and 4 blue tiles on the top row

A rectangular tile pattern with 2 rows of tiles. It has 3 yellow tiles then 1 wide blue tile then 3 yellow tiles on the bottom row and 1 wide blue tile then 3 yellow tiles then 1 wide blue tile on the top row.

There are 100 centimeters (cm) in every meter (m).

1. Complete the tables.
2. For each table, find the constant of proportionality.
3. Describe the relationship between these two constants of proportionality.
4. For each table, write an equation for the proportional relationship. Let represent a length measured in meters and represent the same length measured in centimeters.

It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let be the number of gallons of water in the cooler after minutes.

1. Which of the following equations represent the relationship between and ? Select all that apply.

2. What does 1.6 tell you about the situation?

3. What does 0.625 tell you about the situation?

4. Priya changed the rate at which water flowed through the faucet. Write an equation that represents the relationship of and when it takes 3 minutes to fill the cooler with 1 gallon of water.

5. Was the cooler filling faster before or after Priya changed the rate of water flow? Explain how you know.

At an aquarium, a shrimp is fed gram of food each feeding and is fed 3 times each day. 

1. How much food does a shrimp get fed in 1 day?

2. Complete the table to show how many grams of food the shrimp is fed over different numbers of days.

   number of days	grams of food
   1
   7
   30

   

3. What is the constant of proportionality? What does it tell us about the situation?
4. If  the columns in the table were switched, what would be the constant of proportionality? Explain your reasoning
   
5. Use for number of days and for amount of food in grams that a shrimp is fed to write two equations that represent the relationship between  and .
6. At this rate, how much food does a shrimp get fed in 75 days?
   
7. At this rate, how many days would 75 grams of shrimp food last? Explain or show your reasoning.