Cessna 210 Centurion / Turbo Centurion 210C; 210D
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Flight Engineer; Flight Crew Flight Instructor
Flight Crew Last 90 Days 150; Flight Crew Total 41000; Flight Crew Type 200
Situational Awareness; Training / Qualification; Human-Machine Interface
Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Ground Event / Encounter Gear Up Landing
Human Factors
I checked us the pilots; weather; and airplane and did our normal tasks. We checked the NOTAMS and knew the ILS and radar were out of service.  We had no external pressures. Our mission was just to build some instrument time; and do a couple of IFR approaches and enjoy the world of aviation. We departed for ZZZ. There was a stratus ceiling which we enter at about 1;900 to 2;000 ft. and broke out at 4;000 ft. to a well-defined top and a beautiful blue sky above and leveled off at 5;000 ft. I teach normal operating procedures; flight standards; and the special areas of interest the FAA feels are important that cause pilots to fly airplanes into the ground. In instrument flying I teach the importance of not letting yourself get crowed.  That means getting the weather as soon as possible; building the approach; briefing the approach from the IAP to the holding pattern; and then checklist.  80 miles from ZZZ; we had received the ATIS information and a minute later he had built the RNAV approach to Runway XX. He briefed the approach.We left cruise altitude and descended to 2;000 ft. to begin the RNAV approach. We have two Garmin 430's WAAS equipped GPSs; a Garmin MX-20; a 2500 Aspen and were being vectored 120 degrees heading from the west to the Runway XX approach. We also have a three axis autopilot which was engaged HDG; and GPSS indicating that the autopilot is in NAV mode. It is not the greatest autopilot in the world; but still better than nothing. We had gone from enroute; to terminal on the Garmin and was looking for it to enter approach mode. We were 25 miles from ZZZ; the weather was VFR and I could see the airport. Pilot had the airplane slowing down and he was at approach speed and approach intercept altitude before we intercepted the final course inbound to the final approach fix. He had his NAV display correct to capture the approach course inbound. I cautioned that the autopilot is older and to be sure that it intercepts the final course approach.  I have seen it miss capturing before.  He knows you can assign tasks to your automatics and even your copilot; but you cannot assign the responsibility. This is where the adventure begins. Sure enough it is going to fly through the NAV course inbound; so I lifted up the right wing and told the student to just disconnect the autopilot and have fun and fly the approach. We picked up LPV on the Garmin and I looked down at the glass and we had no glideslope or LOC type information on the PFD; so I just asked the student to remove the view limiting glasses and fly the PAPI. I teach pilots to say positive rate after they rotate so gear up can be commanded; and if glide slope is alive to say 'gear down landing checklist'. At this point; the student is flying really well.  He is right on the center-line and on the PAPI; his manifold pressure was 17'; his airspeed was 80 kts.; and his pitch was -2.5 which was exactly what I would expect. I knew exactly where I was; but I had been distracted and had lost situational awareness and I didn't know it. I am actually impressed with how well [student] is flying.He is commanding his airplane and it is obeying him. When flying big airplanes your flaps will have a gate that restricts the pilot from going from a maneuvering flaps setting to a landing flaps setting. There is a reason for that.  It allows him to get the gear down before he puts out all the landing flaps. If this is overlooked he will get a very annoying gear warning horn. I tested the Cessna 210's landing gear warning horn before the trip and it worked.  It is not as annoying as a FAR 121 aircraft; but it worked. We did not hear a gear warning horn. Our Bose noise canceling headsets blocked the warning from us. [Aircraft landed with the gear up].
Cessna 210 instructor reported distraction during an approach that resulted in a gear up landing.