My kids do Pony Club and it's a lot of learning about horses on and off. Today the instructor had the kids warm up by walking their horses around the arena and each one had to name a suppling exercise to warm themselves up (like dropping stirrups and doing ankle rolls, toe points, windmills with their arms, shoulder rolls, neck rolls, poll stretches, dock stretches), then she asked them parts of their tack and they had to put their hand on it like cantle, pommel, knee roll, stirrup, etc.
To get the more timid kids to learn to move from a slower trot or canter into a faster trot or gallop, she has them all maintaining that gait in pairs, one in front of the other. She tells the back one to pass and they have to speed up to pass, then they leap frog. My kids who are afraid of "galloping" really seemed to forget that it was a gallop when they had a goal in mind, to pass the other ride.
To teach them to ride in the arena with other rides, they go in opposite directions and work on verbalizing whether they are taking the inside or outside track to prevent collisions in that warm-up ring someday!
To improve balance and steering using your legs, we give them a tennis ball to balance on a racket or a golf ball in a spoon. Amazing how many kids can't steer without both hands but it gets better!
Sometimes we do turtle and fox races where all the kids start at one end of the arena and when you say Go, they have to move forward and whomever is the slowest at the gait you indicate is the winner but they can't stop, circl or break that gait. Canter is obviously the hardest!