Part I of this activity is called Crown Transformations,which I have tried many times in my Geometry classes. It is always a big hit. I usually have students fold a colored sheet of computer paper into eighths, and show the work on the paper. You can use this graphic organizer if preferred. We use colors to graph the different transformations of the crowns, which helps me assess understanding both during and after the activity. My finished product is below, and I will project this and call on students at random to tell what type of transformation was performed on the original crown (in red) to get to on of the other crowns. This activity will take about one 45-50 minute class period.
Parts II and IIIhttps://drive.google.com/file/d/0B8lXOcLLfHgvTF9KaXRWYjgySlU/edit?usp=sharing of this activity are new, and I haven't tried this yet with students. Follow the directions in the worksheet to learn how to transform points using GeoGebra, then turn on the trace function and create diagrams like the one below. Depending on student familiarity with GeoGebra, this activity with the final product should be doable during a 90 minute class period. I would ask for students to upload their diagram to Edmodo so that I could use the diagrams at a later time for review. Plus I like to fill my walls with student art.
Unfamiliar with GeoGebra? This tool can be used for teacher demonstration and student practice.