The flight instructor of the amphibious float-equipped airplane reported that after an instructional lesson, while returning to the airport, the student pilot was too low "while turning base leg" of the traffic pattern so the student pilot moved the throttle forward to add power, but the engine did not respond. The flight instructor further reported that he took control of the airplane and made an off airport landing. During the landing, the airplane impacted a low hanging tree limb. The airplane sustained substantial damage to the right wing. A postaccident examination by the Federal Aviation Administration aviation safety inspector revealed that the fuel tanks contained less than one gallon of fuel on board the airplane. The pilot reported that there were no preimpact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.