During the instructional flight, the flight instructor demonstrated each flight control to the student pilot at an altitude of 1 to 4 ft above the ground, and then allowed the student pilot to manipulate one flight control at a time. The student pilot manipulated the cyclic control several times with no issue but later allowed a slow drift to occur, which moved the helicopter away from its initial ground reference point. The flight instructor then took the flight controls and returned the helicopter to the reference point. During the student pilot’s last attempt at manipulating the cyclic control, the helicopter drifted to a dirt area, descended, and its skid contacted the ground. The helicopter rolled over and impacted terrain resulting in substantial damage to the fuselage, main rotor, and main rotor gearbox. The flight instructor stated he was too slow to take the controls from the student pilot, which resulted in the helicopter’s impact with terrain. The flight instructor stated there was no mechanical malfunction/failure of the helicopter that would have precluded normal operation. The Helicopter Instructor’s Handbook, FAA-H-8083-4, states in part, “…beginning the flight instruction at altitude is a good way to allow the student to manipulate all of the controls at one time and with a larger margin of error than beginning the flight instruction at a hover.”