Really basic dressage/flatwork exercises?

Today was officially my first day of leasing Dakota! This is my first time ever leasing a horse, and it means I'll get to ride him 2 other times a week other than in my lesson. I'm not allowed to jump him outside of my lesson, so I'm going to really work on improving our flatwork and I thought you dressage riders might have some suggestions. :)

Dakota's a lesson horse, so he doesn't really know how to do anything fancy, and neither do I. But I thought I might be able to do some simple exercises in our flatwork sessions. I've already thought of circles, serpentines, and lead changes, but I can't think of anything else. If anybody knows some basic exercises like those that would help him or me or both, I'd love to hear them!

I've never really done this before, usually in my lessons the jumping is stressed and the flatwork is more like a "warmup." But, now that I'm leasing, I figure I might as well dive in! :P

Start on a 20m circle, or however big your arena is, slowly spiral the circle in to 15m or 10 whatever you want, then spiral out again

Ride a 'snowman' - A figure 8 with one circle smaller than the other

Leg yeilding

Transitions. The usual, Walk, trot, canter etc. Mix it up, walk to canter, halt to trot, halt to canter etc etc

Practice lengthening/shortening stides. You can use jump poles for this also.

Instead of riding a circle, ride a square.

Long and low

That's all I can think of right now

Figure eights!
You can vary the size of them from ten-meter to the whole arena. They're great for teaching smooth changes in bend, for capturing to horse's focus, and also for bringing a scared or excited horse back to reality. You can also add transitions to them, such as walk to trot or collected trot to medium trot.

Im not a 'dressage' person (nothing against it) but when were doing ring work, im constantly keeping him focused. This translates to lots of bending and flexing and tons of transitions. If you really mix them up, you wont get bored.

Do a 20m circle at each side of the arena, for example, A,E,B + C on both reins at trot. This is a really good warm up :)

ThatNinjaHorse suggested you do transitions, a great idea, but not walk-canter, halt-canter transitions. These are more advanced transitions and take time to develop.

Rein backs are good to, when you are just starting just do a few steps at a time. The same with leg yeilding, do a few steps, reward him by letting him walk out and then do a few more steps :) Once you've got leg-yeilding down pat at the walk and the trot, you can start incorperating it into your spirals.

Complete 1 20m circle, then legyeild onto a 15m circle, then onto a 12m circle - but remember, the smaller the circle the more work it is for your horse.

Play games! If you have a buddy to ride with and poles (as is the ones that stick up toward the sky) play bending games, etc, go trail riding, have fun!