The flight instructor was working with the private pilot on his flight review. Prior to the flight, the pilot checked the fuel and observed that the fuel level in both fuel tanks was below the tabs, and that the right fuel tank had less fuel in it then the left fuel tank. After departing, maneuvering in the local area, the pilot and the flight instructor returned to the airport, landed, then taxied back for another takeoff. After completing two traffic pattern circuits, on the third takeoff the engine stopped producing power at 800 ft. msl, on the upwind leg of the traffic pattern. The private pilot lowered the airplane's nose and the engine started running again. The flight instructor then took over control of the airplane as they started on the right crosswind leg for the runway, and at 900 ft. msl, the engine lost power again. After deciding that the airplane did not have enough altitude, to make the runway, she advised the air traffic control tower that they were going to attempt a landing in a field near the airport. She then checked the mixture, throttle, and ignition, without result, but neither she nor the private pilot, attempted to switch from the right fuel tank to the left fuel tank.During the off-airport landing, the airplane went through an electric fence, spun around about 180 degrees. The nose landing gear sheared off, resulting in substantial damage to the airframe. Examination of the engine revealed no evidence of any preimpact mechanical failures or malfunctions that would have precluded normal operation. Examination and draining of the fuel system, revealed that the fuel strainer bowl, the line from the fuel strainer to the carburetor, and the carburetor float bowl were absent of fuel. The right fuel tank also contained only about 1 pint of fuel, while the left fuel tank contained about 3 gallons of fuel. Review of flight school records revealed that the airplane had flown 4.7 hours since it was last refueled. When asked, the flight instructor advised that she had not observed the private pilot as he performed his preflight inspection, did not know when the airplane had last been refueled, and did not remember asking the private pilot about the fuel quantity before they departed.