CHA TRACON Controller Instructor reported an MVA violation during a training session.

Narrative

We were conducting training on radar. I was the OJTI. When we took the position we knew it was going to be busy just based on the amount of strips that were already in the bay. The traffic was picking up right as this loss happened. Aircraft X came from the SW and was given a vector for the VOR Runway 33 approach. Aircraft Y came from the NW and was being set up for a visual approach. Several miles in front of Aircraft Y was Aircraft Z who was on a 220 heading at 3000. Based on altitudes and location of the aircraft I thought my trainees sequence was different than what he actually did. Aircraft X was level at 6000 and my trainee turned and cleared him for the VOR with Aircraft Y to the NE level at 5000. Since he had the other arrivals lower and closer to the airport I did not anticipate Aircraft X was going to be the first aircraft to the field. Because of that my focus was on Aircraft Z that was level at 3;000 about to enter a 3;100 MVA and without a turn would have eventually entered a 3;600 MVA. Right about the time he was clearing Aircraft X for the approach I had keyed up to turn Aircraft Z to avoid that MVA. I missed hearing that Aircraft X had indeed heard approach clearance instructions. By the time I saw Aircraft X had descended and was already at 5;400 and through Aircraft Y flight path. I immediately took over the position from the trainee. We did not have a radar data assisting and the OS was sitting behind the desk doing paperwork not monitoring.My recommendation is to implement our new SOP procedures. We have briefed everyone but still need to run sims. The ATM also wants it done but in order to do that there will need to be some overtime to get controllers off the boards. We are too busy for one controller to work the entire airspace with only a radar data. It's extremely unsafe. Our management also needs to be aware when it is unsafe to train when the traffic will be a lot for even a CPC to work alone. They are so focused on the ridiculous NTI [National Training Initiative] that we've now had multiple deals while training. I understand the intent of the NTI but when management is so focused on getting those 12 hours it puts OJTI in these positions. My trainee is not ready for this level of traffic and was told to continue training even after this incident where I had to take over again because it was too much. I've had multiple discussions with the ATM about safety over training. He agrees but feels having a radar data should be enough. It's not and these losses will continue to happen if we are not utilizing all of our resources.