First goal: Get together and share proofs (separate document). Make sure that all three of you fully understand each proof. Figure out a good way to write up each one and decide which of you should write up each one in elegant and neat form. These should be turned in all together on Feb. 16.
Safety valve: You may omit one proof. If you do so, the others must be extremely elegant and neat.
Next goal: Get together and share solutions to problems (another separate document) Same procedure with same safety valve. Turn in Feb. 28.
Third goal: Prepare a presentation for the rest of the class, to be made March 7, 9 or 12. One Pythagoras group should take the first half of class and treat proofs, the other the second and treat problems. You must discuss your plans with me by March 2 (so this probably overlaps with working on Goal 2).
First goal: Chapter 22, sections 1 and 2. You should work through the Activities together and discuss them. Then you should share solutions to as many of the Learning Exercises from both sections as you can. As a group, choose five problems from each section and write up careful, neat, well-written solutions. Make the set as representative as you can, and choose problems that are interesting and challenging. With each problem, include a sentence or two explaining why as a group you chose that problem. Turn in on Feb. 16.
Second goal: Same thing for sections 3 and 4. Due Feb. 28.
Third goal: Prepare a presentation for the rest of the class, to be made March 7, 9 or 12. Each group that has worked on Transformational Geometry should plan on spending one half of a class period presenting. You will need to negociate among yourselves to decide who presents what. You must discuss your plans with me by March 2 (so this probably overlaps with working on Goal 2).
My intention is that each group should be working closely together and as much on its own as a group as possible. On the other hand, I have no interest in making you bang your heads against a wall, even if your heads are close together when you do it. Josh and I will answer questions, with one proviso: if the question is on the mathematics (not on logistics or technicalities) then before we answer it you must convince us that you have worked on it as a group, and the question being posed is a group question.