How to fill a jar with water?

3/12/2010

First of all, thanks to Smita who helped to teach today's class.

Wow! Today our 2nd grade math class solved the very difficult problem. I am still amazed that they did it.

There are 2 empty jars. The first jar can be filled with 5 ounces of water and the second jar with 3 ounces.
How do you fill the largest jar with 1 ounce of water? You can fill a jar or empty it, if necessary, and use any amount of water.

Before going to the class I asked several adults to solve the problem. Some adults found a solution within several minutes others spent hours. Before reading how to solve the problem try yourself. When preparing for the class I did not realize that the problem can be solved in more than one way.

We divided the class in two groups, so Smita worked with one and I with another. I brought 2 pairs of glasses. Each group were given 2 glasses: one glass represented the largest jar (5 oz) and another the smallest one (3 oz).

Kids started with running to the water fountain, filling glasses with water and pouring water from one glass to another. Some kids suggested to fill in the largest glass with 5 oz, pour water into the smallest glass leaving 2 oz in the largest one. However they realized that they could not get precisely 1 oz. Kids tried several ways, but nothing worked. They thought hard for about 10 minutes. Then we asked them to stop and we switched to other problems. We told them that this will be their homework...

Because kids finished all the problems that we prepared for them fast we had some time to work at 'jar' problem again.

Smita guided her group through the thinking process. I believe that their solution was the following.
Kids made 5 oz glass full . Then they poured 3 oz from the largest into the smallest glass. So they had 2 oz left in the largest glass. Because kids could see through the glass they took a marker and marked the level for 2 oz on the glass. Then they emptied the largest glass, poured 3 oz from the smallest to the largest. Afterward kids poured water from the largest into smallest glass up to the mark they put earlier. This way they ensured that they had only 1 oz in the smallest glass. Then the largest glass was emptied and they poured 1 oz from 3 oz glass into 5 oz glass. The problem is solved!

My group solved the problem by accident :) One kid suggested to make 3 oz glass full, pour water from that glass into 5 oz glass, and then repeat it one more time. He did not realize that he was so close to solving the problem. Then one girl said: Stop! If we put 3 oz of water from the smallest glass into the largest and repeat the same thing up to the point until 5 oz glass is full, then we would have exactly 1 oz in the smallest glass and we can put that 1 oz into the largest one afterward. The solution is found!

After the class one boy came to me and said: It was awesome!