(1) Make sure everyone knows the names of the students in your group. In addition to making for better interaction within your group, you will need to know the names of your fellow group members when you hand in your write-up at the end of class, and possibly in future classes.
(2) Have someone be in charge of keeping time -- so your group doesn't run out of time before completing the activity. Decide what is a reasonable amount of time for each part, or each section with several parts, of the activity. Make sure to leave time for write-up, and choose someone to write up your final results clearly and legibly, if it is an activity where the write-up is due at the end of class rather than at a future date.
Sometimes I may ``over-book'' an activity, and it is certainly better to hand in a well-thought-out report for only half of the activity than to hand in an activity which is ``completed'' but in a hasty, disorganized, poorly argued/explained, or illegible manner. On the other hand, don't let your group get bogged-down for too long on trying to figure out a detail or two in one part at the expense of being able to give the other parts of the activity a serious attempt (you should, of course, make sure that you do sort out those ``details,'' which you will be expected to understand for future material built upon them, as well as exams).
(3) Make sure everyone reads and understands all the directions. If you are not certain about something, ask your groupmates. The same holds for interpretation; it may be that everyone feels they understand what is expected of your group in the activity, but some have different interpretations than others as to what exactly that is. Try to arrive at a concrete consensus as to what are the goals to be met. If you are still uncertain, ask me when I come around to your group.
(4) Next -- and this will be even more important in the projects than in the in-class activities -- plan out, together, how you intend to accomplish the task at hand; for example, step-by-step, or a modular top-down/bottom-up approach. Decide which portions will be carried out together, which individually, and who will do what.
``First, let's brainstorm together what information we have about the function. Then, Beth will use that information to sketch the function while Chris factors the given polynomial, and Debra looks up the formula for the sine of a sum of two angles and plugs in the appropriate variables here, then works with Chris to decide behind which door the dragon most likely is hiding. Then together we use Beth's sketch and ... (other information) to design the hose to put out the fire-breathing dragon's flames, and the velocity vectors needed to use for the catapult for getting the Ben & Jerry's ice-cream pints to tumble down into our waiting hands.''
(5) Double-check your results. With several pairs of eyes at your disposal, there should be (virtually) no computational mistakes. Even more important than the calculations is to double-check your reasoning (the logic and arguments you have used to solve the problem) -- is there any gap or mistake? Your activity will be more highly valued if you hand it in with a note such as ``near the end, we realized that we were assuming the angle theta is positive, so we need to find a new proof, or to modify our method'' than if it is a ``complete'' report which glosses over key points.
(6) Write up your results, either individually, or collectively, depending on the assignment. If written up collectively, this means that you are handing in one copy. If one person is writing up the final solution/report (e.g. some activities), those responsible for parts of the solution are expected to work with the person writing up to make sure that they have everything they need. Or you may have each group member write/type/sketch parts of the final report (for example, on a project, if you so choose).
Write-ups should be neat and legible, of course. They also need to be well-argued. A string of formulas and equations without accompanying phrases, sentences, and sometimes even paragraphs is next to useless; you need to explicitly state what are the ``givens'' and your assumptions; what you are trying to prove; what you've proved so far; the reasoning as to why Step 3 justifies your opening claim in Step 4; what all the variables stand for; and so on.
If you have questions about write-up, especially for the projects, please ask! If reading through your report is cumbersome, your project will likely not reflect the full effort and understanding that went into it, and therefore may not receive as high an appraisal. This is just a fact of life, true outside the university class as much as within its confines.
Finally, be creative -- and have fun!