Modeling Proportions

Use 2 or more representations to solve each of the following problems.

1) Andrew has a recipe for cookies that calls for 3 cups of brown sugar to make 7 batches.

a) How many batches can Andrew make with one cup of sugar?
b) How many cups of brown sugar does Andrew need for one batch?

2) Erik is putting oil in his scooter. When he had 3/4 of a liter in the reservoir, he realized that the tank was 1/2 full. How many liters will the fully filled reservoir hold?

3) If a container holds 3/5 gallons of milk, how many containers will one gallon hold?

4) Ms. Cohen asked her students, “If 5/7 of a group gets 1 1/4, then how much should a whole group get?” One student came up with the following reasoning:

First, I shared 1 1/4 between the 5/7 to figure out that each 1/7 gets ¼.

To find out how much a whole group gets, I made 6 copies of 1/7 for a total of 7 copies to produce a whole. Then, I made 6 copies of the 1/4 so there would be 7 of those. Seven one-quarters equals 1 3/4, so the whole group gets 1¾.

Is the student’s reasoning correct? If so, explain the student’s reasoning in your own words. If not, explain why the student’s reasoning is incorrect.