C172 flight instructor reported overlooking the position of the carburetor heat control; allowing the engine to fail on approach to landing due to fuel starvation.

Narrative

My student and I decided to go out and practice landings VFR at ZZZ before low ceilings arrived later that evening. The temperature was around 40 degrees F and dew point spread about 4 degrees C. We taxied out to XXL and flew two right VFR patterns; each landing on XXR. I flew the first pattern to demonstrate and the student flew the second pattern. As we came in on final for the second pattern; the engine RPM dropped and the propeller came to a stop at the end of the ground roll of the second landing. We quickly used the momentum to exit XXR onto Runway XY and hold short of XXL. I stated to Tower that my engine just quit and the Tower Controller confirmed observing this over the Tower frequency. My student and I were immediately able to get the engine started on Runway XY to taxi back to the ramp.In hindsight; I realize what likely occurred; but it is speculation. As my student performed the run-up before I took off of XXL; I recall noticing a 200 RPM drop when the student tested the carburetor heat. Having flown a fuel injected C172 a couple times before this flight; I was not in the habit of turning the carb heat on. And I did forget to turn the carb heat on during my first pattern and mentioned this out loud to the student while on final for XXR during my demonstration. The student took the controls for the second pattern while on upwind for XXR. During the student's pattern; our downwind was extended for landing traffic and he also forgot to turn the carb heat on as he configured for landing. I noticed this; but with this flight being a pre-solo evaluation; I decided to make a note of this for later and did not correct it immediately. While on final for his landing; he pulled the throttle to idle for the entirety of final approach. As we continued the ground roll after his landing; the prop stopped turning about halfway down the runway. I do not recall hearing the engine quit; just that the RPM began to get pretty low. With the weather conditions the way they were; I strongly suspect carb icing. The engine didn't have time to warm up either after two patterns in these conditions.To prevent further occurrence; I will be more diligent when switching between aircraft with slightly different systems and identify the differences before beginning the flight. I also need to emphasize the landing checklist while on downwind for myself and my students. I also am fully aware of the consequences of not turning on the carb heat in conditions where carb icing is prevalent.