The flight instructor reported the purpose of the flight was to train the student pilot on landings and go-arounds. After completing one touch-and-go landing and two go-arounds without incident, the flight instructor recounted that the student pilot flew the airplane through the traffic pattern and final approach leg at the appropriate speeds, altitudes, and descent rates. During the landing, the student pilot flared high and the airplane subsequently impacted the runway hard and flat. This led to a short bounce resulting in the airplane touching down a second time in a side-loaded and nose-down attitude. Upon the second touchdown the nose landing gear collapsed, and the right wing struck the runway resulting in substantial damage to the right wing and lower fuselage. The flight instructor did not report any preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.