I do this thing where my kids are divided up into groups on a daily basis. Most days it doesn't mean much, other than giving me an easy way to sub-divide warm ups. It comes in real handy when I want to do a partnering project and don't want to spend time thinking about who should work with who, the divisions already exist. My Pre-Calculus students always take to the concept moreso than my Algebra II kids, for whatever reason. It could be because the kind of students I get in Algebra II are far more diverse (anywhere from 9th to 12th graders) and their intrinsic feelings towards math are all over the map. Pre-Cal kids are in far narrower bands. They're the top performers from Algebra II, have lots of other classes with the same people, and are always close in age (it's pretty exclusive to 11th and 12th).
I also foster the group togetherness with a goofy points game we play. It's part of their grade, but contributes the teeniest fraction (by the time I type it in, it MAYBE nudges things a half point). But the kids love it because it's so public. So they get very heartbroken when I mention that seats will be changing. At the start of the year, it's alphabetical as I wait for rosters to settle down and I get to know the kids. Every year around Columbus Day I rearrange them based on ability, work habits, and compatibility.
I bounced the idea around in my head last year and actually followed through this year. In celebration of the good times they had with their new friends at the start of year, I offered up Pre-Cal Spirit Day. I left it free form, expressing the love of their color group in whatever way didn't violate dress code. The reward for sufficient spirit was maxing out their point total to 50 (the stated "goal" at the start of the game). The results:
Yes, one of the yellow teams brought bananas. Yes, one white team decided to deck themselves out in black. And yes, more than one shirt may have glowed in the dark.