One of the places that stars are used for designs is in quilting. There are all-over designs that form a star and there are individual blocks that are stars. Layouts from the latter can be used to make greeting cards.
I found a collection of star patterns for quilters here.
If you want a printed copy, there is a pdf here. The image will be a little blurry, but clear enough to see the patterns.
I have also made a pdf of the basic underlying grids that the patterns are built on. You can download it here.
You can create your own variations using the grids provided.
This is an excellent way to use up small pieces of decorative paper. I used some paste papers made by Susan Kristoferson. If you really hate cutting and pasting (and I understand that some of you do), you can draw out your pattern and colour it in.
I imagine a creative teacher could also find a way to use these stars to introduce fractions or geometry to a class.