Instructor reported missing the final gear check and landing without the gear down.

Narrative

Began training flight with standard preflight actions and run up. Takeoff power was set and normal takeoff achieved. Student had difficulty maintaining pitch attitude while gear was retracted. Made crosswind turn and downwind turn. Achieved pattern altitude and Student set power to 16 inches manifold pressure. Missed downwind BGUMPS check. Student tried to extend flaps above the white arc. Instructor corrected Student action and advised student to first set MP to 12 inches. Student successfully reduced MP and deployed flaps. Turned base and noted that we were high. Student reduced power to idle. Turned final. And noted that we were still high on glide slope. Instructor coached Student in a forward slip maneuver to loose excess altitude. At this point both Student and Instructor were task saturated. We both missed our final gear check. When propeller began to strike the ground; Instructor took the controls and made a gear up landing. No gear warning horn was heard by the Student or Instructor. After the aircraft came to a stop Instructor went through a shutdown flow and both occupants evacuated the aircraft. Contributing factors were loss of situational awareness; task saturation; and lack of gear horn.