Teaching youngsters to ski?

So I took my nephew out today for a few hours, he's 8, and it went ok. He's still a beginner obviously and has only been out a few times on the bunny hill. I taught him how to stop using the pizza on flat ground while I pulled him and he did great. Taught him the stance he wants to be in and showed him how to carry his lunch tray. Told him that if he ever felt out of control and couldn't stop, just to fall to the side. He got all that although he tended to lean back until I gave him some poles to hold out front. Rode up with him once on the rope tow and after that he did it by himself with only a couple spills. He can even pick himself up most of the time with no problems. Once we got to the top of the bunny hill, he just wanted to go straight down. I explained that he needs to learn how to turn, went over the procedure with him and then showed him. Instead of following me through big turns, he just went straight down, repeatedly. So I took him back to the flat ground and practice stopping some more. Awesome! Back up the hill, straight down. He's going to be taking a two-hour group lesson monday with some kids his own age but they add up quickly at $40 a pop plus $15 to ski afterward for a couple hours. So I need some tips on teaching him to turn in between lessons. I know we've all been there, speed first learn how to stop later but seeing as I can only take him once a week at most I would like to get the most out of each venture. Any input would be appreciated.