A classic activity is to cover a 1-inch-side dodecagon with pattern blocks. This provides a great context to discuss symmetry (see Geometry Labs 5.6.) Here is one way to do it:
See many others, found by Simon Gregg’s students.
In the past few days, I’ve had fun making a double-size, quadruple-area dodecagon:
You too, and your students, can play this game! Download the big dodecagon, and get started!
–Henri
PS: Visit my Pattern Blocks home page!
…and my new Dodecagons page! (More images, and some math questions for your students to ponder.)
Henri's Math Education Blog 