The pilot reported he had departed from a paved runway in his amphibious airplane. After takeoff, he was momentarily distracted by communications with air traffic control and did not ensure the landing gear was retracted. After a short local flight, he prepared to make a water landing on a lake. However, he was unable to locate the water landing checklist in the airplane and completed the checklist from memory. During the process, he inadvertently "skipped over" verifying the landing gear was retracted. When the airplane touched down on the water, he was unable to prevent it from nosing over. Photographs of the airplane taken during recovery from the lake showed substantial damage to the fuselage and wings. The pilot reported no mechanical malfunctions or failures with the airplane that could have contributed to the accident.