I've been through you exact problem, also with a youngster i started myself. To calm my hyper little boy down, i did a lot of things in a random order.
I'd ask him to trot, then walk, then trot again, then do a circle, change rein, circle smaller, centre line, walk, circle, halt, rein change etc. i'd just keep him very busy so he had to listen because he had no idea what was coming next.
As he got more attentive, i'd ask for a canter and do one circle, then go back to a trot and work again as above. once he was settled, i'd ask for the canter on the other rein, and then go back to working his brain.
he learned to settle and focus incredibly fast, and also became more attentive and responsive. Also: don't forget to give him some 'space out' time. My youngster got lots of walking breaks on a long rein between exercises.
i also made it a point to take him out on a hack before he got frustrated at being cooped up in the arena all the time. but even on hacks, i'd ask for lots of transitions and square halts and generally just keep him thinking.