The certified flight instructor did not visually inspect the fuel tanks prior to departure, but the fuel gauge was just below the full mark and the student pilot told him the fuel tanks were full. Based on his experience in the airplane, the instructor estimated a total of 4 hours of fuel on board and then departed on an instructional flight that included numerous practice take offs and landings. Approximately 3 hours into the flight, as they were returning to their home airport, the engine lost power. The instructor was unable to re-start the engine and made a forced landing to a grass field where the right wing hit a tree causing substantial damage to the strut. The nose gear separated from the airframe and both wing tips, the engine cowling, and wheel fairings were damaged. A Federal Aviation Administration inspector drained both fuel tanks and reported that approximately 3/4 of a gallon of fuel was drained from the right wing tank and 1/2 of a gallon of fuel was drained from the left wing tank. The fuel line to the carburetor was removed and some fuel was found in the line. The gascolator was removed and approximately 7 to 8 ounces of fuel (absent of debris) was recovered. The carburetor was removed and disassembled and approximately 2 ounces of fuel (absent of debris)was found in the bowl. No mechanical deficiencies were noted with the airplane or engine.