Amatl/amate was made from the bark of a ficus tree. Amatl trees are still found in Mexico today. Here is a photo of the bark before it is processed. Here is a short video (in Spanish, with some English subtitles) that shows how amate paper is made in a family in a town called San Pablito.
Here is a modern narrative (in Spanish, with English translation) about the amatl tree with a beautiful work of art, suitable for use in classes.