The fifteen/ten exercise is a simple one.  All you do is ride large in the ring and at each at certain points do a fifteen meter circle, and then a ten meter circle inside the fifteen, then you ride large.  This asks the horse to bend and to travel true on the fifteen circle then uses that to ask the horse for more in the ten meter circle.  This is a good exercise for horses who tend to get bored in training  because you are not just riding down the side of the ring, for those who like to get fast down the long side, horse's who are stiff, lock their jaw, or have trouble doing smaller circles.