Optional: To get kids started, have them divide a square into eighths. Next, have them make 1/2 (or 4/8) of their quilt colored. Then, 2/8 (or 1/4) striped. After they have their initial design, let them decide what direction they would like their design to go. They could have 1/16 of their quilt polka dot or so forth. If you want to explore symmetry, then guide children to make the quilt equal on both sides.
To integrate technology, you could have students create their design in Illustrator. If you're working with older kids, let them completely design their quilt with little to no instruction.