Proportion Reasoning from Susan J. Lamon's Representing and Presenting

Natasa's comments on the article by Sue Lamon were telling enough to get me read this carefully. She talked about the research using 6 classrooms where 1 class was taught fractions traditionally and the other 5 were all taught/learned fractions through some other method than parts of a whole. The 5 non-traditional classes all performed better on an assessment of their proportional reasoning than the control class. While I have been able to reason out problems from my own grasp, I was challenged by how unfluent I was in describing the other methods. I'm going to publish a few of problems they pose as an example of this thinking.

1.) Does the shaded area show 1 (3/8 pie), 3 (1/8 pies), or 1 1/2 (1/4 pies)? Does it matter?
[the shaded region was 3 sectors of a circle divided into 8 equal sectors]
2.) You have 16 candies. You divide them into 4 groups, select one group, and make it three times its size. What single operation would have accomplished the same result?
4.) If it takes 9 people 1 1/2 hours to do a job, how long will it take 6 people to do it?
5.) Without using common denominators, name three fractions between 7/9 and 7/8
6.) Yesterday Alicia jogged 2 lapps around the track in 5 minutes, and today she jogged 3 laps around the track in 8 minutes. On her faster day, assuming that she could maintain her pace, how long would it have taken her to run 5 laps?
7.) Here are the dimensions of some photos: (a) 9 cm x 10 cm, (b) 10 cm x 12 cm, (c) 6 cm x 8 cm, (d) 5 cm x 6.5 cm, and (e) 8 cm x 9.6 cm. Which one might be an enlargement of which other one?

Think of the nuances these represent?
My grade 8 classes this year have really exposed the gaps in this understanding:

For example: One case contains 8 cans. How many cans are in 3 cases? How many cans are in 2 3/4 cases?

Most could do the first question correctly. A common answer for the second question expectedly was 19 but some had answers of 40??? Clearly, I hadn't created learning in this area. The next period I had them again draw out the cases showing the cans in the cases. This simple improvement with a concrete example made it possible for the students to do much harder examples successfully.