Three fourths
Students work in groups of four. Each group will need 3 bananas, one plastic knife, four zip-lock bags, and some paper napkins or small paper plates. Two groups can share one scale, or, if there are enough scales, one scale can be used per group. (If the number of students is not divisible by 4, you may form one group of 3 with 2 bananas, or 1 or 2 groups of 5 with 3 or 4 bananas.)
Task.
Peel the bananas and share them equally among the members of your group. You cannot use the scales for this part of the task. But before you eat the bananas, you have to weigh and record all the portions in order to see how close you were to sharing them fairly.
Data from all groups should be written on the blackboard, and the methods of dividing the bananas that are used by different groups should be discussed.
Remarks.
There are some strategies that are supposed to guarantee that the shares are fair, without precise measurements. They are extensions of the simple "You divide, I choose" strategy. But this is not important in this task.
A peeled banana weighs around 4 ounces (100 grams), so you need rather good scales to detect differences between portions.
You may ask students how much each of them got. Don't be surprised if they are confused. Each one (from a group of 4) should get a portion that weighs 1/4 of the weight of the three bananas they are sharing. But many students will talk about the number of equal pieces instead.
The bananas do not have to be uniform in size. The task is more interesting if they are not.