My fiber art students (at the homeschool co-op where I teach) have just finished weaving their drawstring tapestry bags. They had a lot of fun with the color combinations of their stripes, and the bags all came out beautifully.
The project is from a wonderful book, Kids Weaving, by Sarah Swett. All you need is a piece of cardboard cut to the size that you want your bag. The best thing about the project is that the bag is woven all in one piece around the cardboard, and the drawstring slits are woven in--so there's no sewing or finishing needed besides tucking in loose tails of yarn. The book has a lot of other great beginner weaving projects too.
This bag is almost done, she's just beginning to make the slits for the drawstring to pass through. The students much preferred using a tapestry needle to weave, rather than just their fingers. Several girls have already started making another bag at home, they enjoyed it so much.