If you can't find a cheap one to buy, I suggest that you go to a local carpet store in your area and tell them that you are a teacher and that you are in need of a carpet for your reading area. I did so a few years ago, and they gave me a piece that was a scrap, but was brand new. It was a tax write-off for them as well. When they found out my classroom theme was frogs, they even cut the carpet into a lily pad shape and bound it for me for free. Perhaps you will be as lucky, or maybe you will have a small be to have the edges bound, but it is worth a shot. Good luck from a fellow third grade teacher!
So sorry- I replied to the carpet post on yours by mistake. My daughter woke up with a nightmare in her room, and when I returned, I guess I confused the posts. (Late night blunder!) :)