On January 17, 1997, at 1259 mountain standard time, N739QE, a Cessna 172N, was substantially damaged when it collided with power lines during descent near Steamboat Springs, Colorado. The flight instructor, private pilot receiving instruction, and passenger were not injured. Visual meteorological conditions prevailed, and no flight plan was filed for the instructional flight conducted under Title 14 CFR Part 91. The flight originated at Steamboat Springs approximately 1200. According to the flight instructor's written statement and verbal statements he gave to the Routt County Sheriff's Office, he had given the pilot a mountain flying checkout and they were returning to Steamboat Springs, flying at 11,500 feet msl (mean sea level). The pilot said he had never flown close to the mountains, so the instructor suggested that he fly down a wide canyon that led back to the airport. They descended to 7,200 feet msl and the pilot remarked that they would have to watch for wires. The instructor became preoccupied watching elk and did not see the power lines. He heard "a loud scraping noise" and felt the airplane decelerate and shudder. It then fell into a clump of aspen trees in the Mad Creek drainage. Written statements submitted by the two pilots to the Routt County Sheriff's Office (attached) and a witness'statement (also attached) corroborated the above. Help was summoned by use of a cellular telephone.