Send a muslin square to your favorite children's book authors. Ask them to sign the square and return it to you. Send a second square and ask them to have their illustrator sign a square as well.
Ask your students to illustrate squares with something that reminds them of the stories from the authors you have corresponded with. Fabric pens are great to use, or permanent markers (if you do not plan on washing the quilt).
Combine the squares from the class with the squares from the authors and illustrators into a pattern. Challenge the students to find the 'fatest' square possible with the number of squares available.
You can also do the same project using construction paper. Simply use the paper instead of muslin, and glue instead of sewing!