THE CERTIFICATED FLIGHT INSTRUCTOR (CFI) STATED THAT THE FLIGHT WAS AN INTRODUCTION FLIGHT. HE STATED THAT AFTER THE PREFLIGHT, HE AND THE STUDENT SPENT SOME TIME TAXIING THE AIRPLANE AND PERFORMED SOME GROUND HANDLING EXERCISES. THE CFI STATED PRIOR TO TAKEOFF, TWO ENGINE RUN-UP'S WERE PERFORMED, AND NOTHING UNUSUAL WAS NOTED. THE CFI STATED THAT SHORTLY AFTER LIFTOFF THE ENGINE LOST PARTIAL POWER. HE STATED THAT A STRAIGHT AHEAD LANDING WAS NOT POSSIBLE DUE TO TREES AND HOMES, SO A LEFT TURN WAS MADE. THE CFI SAID HE CHECKED THE MAGNETOS, FUEL, AND APPLIED CARBURETOR HEAT. HE STATED THAT THE ENGINE CONTINUED TO LOSE POWER. THE CFI SAID HE EXECUTED AN OFF AIRPORT EMERGENCY LANDING AND SHORTLY AFTER TOUCHDOWN THE AIRPLANE'S LEFT WING STRUCK A TREE CAUSING SUBSTANTIAL DAMAGE. THE ON SCENE INVESTIGATION BY THE FAA REVEALED THE AIRPLANE WAS FUELED AND NO ENGINE ANOMALIES WERE FOUND. THE CFI REPORTED THE TEMPERATURE AT THE TIME OF THE ACCIDENT WAS 64 DEGREES F, AND THE DEW POINT WAS 63 DEGREES F.