Gamma and Delta classes, especially adults, spend inordinate amounts of time doing "patchy" little turns on half circles, in place. But once you start working on turns, especially once you've actually turned a few, you can start doing the fun stuff- moving across the ice and working toward those mysteriously effortless-looking transitions from forwards to backwards.
We started with a weight-shift warm up and then moved to turns on a Serpentine pattern (alternating half-circle lobes along a long axis). The trick to these patterns is to maintain flow (not necessarily speed) and to place the elements in the correct spot (push at the long axis, turns at the right place on the lobe, etc.)
Warm up: Forward wide-footed slaloms up the long axis, forward crossover to forward outside edge glide (or make it a spiral, if you like). Forward mohawk, repeat pattern backwards. Do this along a continuous axis, i.e. all the way around the rink.
Forward power 3 turns (from the Adult Bronze Moves in the Field test). Forward outside 3 turn on one side of the long axis, cross the long axis backwards, back crossover takes you around the lobe back to the long axis, step forward to outside edge and repeat. If you do a left 3-turn you do a right cross over. We then did this pattern substituting a Mohawk for the three turn (add an extra step after the forward outside edge-- instead of just a 3 turn, do forward inside edge, Mohawk).
Alternating three turns, inside and outside. Just what it sounds like, alternating 3-turns down a long axis.

Five-step Mohawk, another alternating pattern on a Serpentine along a long axis. Forward inside edge to mohawk, change feet to back outside edge, step forward to forward outside edge, slide chasse to forward inside edge; repeat on other foot on the other side of the long axis. You can fit five to seven lobes on a full size rink; if you can do this in four you're a superstar.

Adult Pre-Bronze inside-outside 3 turns. This one's a brain-freezer. Forward inside three turn from the long axis, step forward along the same lobe to forward outside three turn; back power cross over on the other side of the axis, step to forward inside edge, repeat from forward inside three turn (in other words, there's a cross over and a step on the second lobe, unlike the power 3- turn pattern, where you step into the three turn straight out of the cross over)
All of these patterns must be skated with as much confidence as you can muster-- make sure you are making these shapes, or it's easy to get lost.
These are not the only patterns you can do with turns. Make up your own, and see what combinations you can invent. If you have a cool one, share it here! I'll add it to the repertoire.
UPDATE: you can find all the Moves in the Fields patterns in pdf form at the US Figure Skating site.