Flight Instructor on training flight with student reported a gear up landing.

Narrative

After finishing training maneuvers northeast of the airport; the student and myself began a descent and approach to landing into ZZZ. Once up-beam the 1000 foot markings on Runway XX/XX in the downwind leg; I configured the aircraft for landing with the 'Landing Checklist' as the student was flying. While performing the duties as a flight instructor I was somewhat distracted and do not recall checking the three green lights that would verify the landing gear was down. After reducing power and flaring; we touched-down; at which point we started to slide down center line of the runway and I became aware that we had landed without gear down. We then drifted to the right side of the runway and into the grass; where I shutoff the fuel to the engine and removed both the student and myself from the aircraft. No occupants on-board were injured; and no public property was damaged. The lesson I've learned from this; and my new rule flying complex aircraft moving forward; is to never descend below the traffic pattern altitude until the landing checklist has been completed; meaning it is not completed until landing gear is down; and do not continue past the runway threshold with the intent to land unless the landing gear down has been verified again; otherwise go around. After speaking to experienced pilots who also have been in this type of situation; they have shared lessons they have learned and rules they place upon themselves now to never allow a gear-up landing to occur again.