I got this idea from H. Mazzuto over at Art. Paper. Scissors. Glue! They shared some wonderful examples and a great how- to post for the process. The only thing I've changed is the color scheme and the collaborative aspect of the project.
I give each student 4 small squares of white paper, so that they can practice each of the folds. After this they work in quartets and fold more paper and create their radial symmetry design. How they split up the work is up to them. For example, they can each be responsible for a different type of fold or they can each be responsible for a different color. I emphasize that if a student has a good handle on one of the folds and a classmate is struggling with that same thing, be like a teacher and work with that student, so they get it.
Once all their folding is done, they plan and assemble the pieces on a larger black square. They then lock stuff down with their glue sticks.
The kids have had a blast with this one. Even though the vocabulary of shapes is limited to 4, there has been quite a lot of variety in the finished designs.