M.B.
What happened is what is commonly called "new tank syndrome".
Basically, when the fish poo, it builds up in the water until it poisons them. (The fish waste is eventually converted to ammonia.)
It is difficult to get a small tank set up to cycle, especially if you don't know that much about fish and water chemistry.
The drops you put into the water at first remove the chlorine from the water, making it safe for them.
If you want to try having fish in a classroom tank again, you need to remove about 10% of the water every week and replace it with freshly dechlorinated water. That will help keep the fish healthier.
Also, it depends on what kind of fish you have...... even though you see a BUNCH of fish in a smallish tank at the pet store, you really can't have very many fish in a tank...... and those tiny little goldfish you see? They can grow up to 20" in good conditions. (The goldfish in my water garden in my back yard are about 10" long..... and there are only about 6 in an 800 gallon pond.)
Anyway, here is an article that talks about setting up a new tank properly..... and explains the nitrogen cycle that is happening in a fish tank.
http://www.wikihow.com/Avoid-%27New-Tank%27-Syndrome