How to make a glass half full?

03/26/2010


There are three glasses. The first glass can contain maximum 8 oz of water, the second 5 oz, and the third 3 oz. The first glass is full with water. How to make this glass half full?

This problem is similar to what we solved the other day with two jars (How to fill a jar with water) . See here.
For each sub-group I brought 3 cups : the first representing 8 oz, the second 5 oz, and the third 3 oz.

Kids went to the water fountain and filled in 8 oz cups full with water. Then we started thinking what we should do in order to make 8 oz cup filled with 4 oz of water. Somebody suggested to put 3 oz into 3 oz cup from the largest cup.

Kids thought about various alternatives: fill in 5 oz cup from 8 oz cup, pour 3 oz to 5 oz from 3 oz cup . I hinted that it might be a path to the actual solution. So they did it and continued discussing the next steps.

At that time I hinted them that if necessary they can pour some water out (not necessarily into another cup). Children continued deliberating. Somebody suggested fill 3 oz cup from 8 oz cup again. So at this point we had 2 oz in 8 oz cup.

We continued the discussion. With my hints they poured water from 3 oz cup into 5 oz to make 5 oz cup full. Then I told them that they can spill out 1 oz remaining in 3 oz cup.

So after that step they had 2 oz in 8 oz cup, 5 oz in 5 oz cup, and nothing in 3 oz cup.
I told kids that they should keep 2 oz in 8 oz cup and do something with 5 oz and 3 oz cups. So they filled 3 oz cup. I asked them: How much water in 5 oz cup now? 2 oz.
How to get 4 oz in 8 oz cup now? They realized that by pouring 2 oz into 8 oz cup they would solve the problem.

After that I asked everybody to repeat how to solve the problem. So they all went through the thought process again.