A flight Instructor conducting training for a single engine landing reported a prop strike and gear up landing resulting in a go around followed by a successful landing.

Narrative

In a routine pattern flight in Aircraft X; during our final landing; the aircraft endured ground contact without gear down. The student had requested practice in the pattern as recommended from her previous flight. We had completed our fifth landing and the it was time to bring it in for a full stop. On the last landing the student had completed a successful landing. On downwind; I failed the engine to simulate another landing. After the proper procedure for maintaining control of the aircraft; we flew a wide base into final. It is routine to not introduce gear as it depletes 20 knots of airspeed and can severely hinder aircraft control. During my final checks; I looked down and verified three green. On flare to land; I realized we were abnormally low; which was immediately followed by what felt like as tail strike. Noise from the tail.I was already guarding the throttles; and I immediately performed a go around. I did believe at the time that the props had not made contact with the ground as I had expected performance with no abnormal indications. I flew a short pattern and landed the aircraft safely. I taxied to the ramp and shutdown. Upon shut down; I realized that the props had made contact with the ground. I Immediately contacted to report what had occurred and that myself and the student were both safe. During the post flight walk around I found the tail tie down point and step had also sustained a small amount of damage as well. From other peoples experiences and the way I was taught; I always verify three greens on all segments of approach to land in a normal landing. During approach's due to task saturation; I verify them at least on base and final. I really did believe that that I saw three green on final; and the normal safeties in place to prevent potential gear up situations do not occur since it was an approach with simulated feathered engine.