This should not be an aeronautical engineering degree lesson.
For PPL’s I think it is very important to keep things practical, so I like Photo’s observation that in general when fuel is tight slowing down will extend your range. This is the kind of simple practical lesson which should be part of basic flying instruction. The truth of it is easily demonstrated by reviewing the POH range charts.
The only thing I would add is to guard against the tendency to teach exercises in isolation. How not to get tight on fuel in the first place needs to be included in the discussion. So part of the practical “range” lesson means when you are teaching Nav you need to talk about how to decide how much contingency fuel should be added and emphasize the importance of monitoring your enroute fuel state so if things start looking tight you already have a plan B.
My personal opinion is that in general flight schools don’t do a good job of this because training flights are dispatched with much more fuel than they need so a student never has to worry about whether they have enough fuel to finish the lesson with sufficient reserves.
In the case of maximum endurance, the fact that propeller driven aircraft and jet aircraft have different relationships between fuel flow/thrust/power is the reason why your maximum endurance airspeed aerodynamic definition differs. I'd argue this is fairly important to understand as an instructor.
I agree the why and how matter, but the OP is someone working on his instructor rating so there is a lot of why and how he needs to know. Studying up on jet vs prop theory for range and endurance should only happen after he had mastered the basic theory and even then given the amount of knowledge you need to be an effective instructor, I don’t think it is the best way to spend the study time.
For this lesson “basic” theory means understanding and be able to explain in about 3 mins
the total drag and power required graphs in the FTM.
As a general rule flight training, especially initial flight training should be concentrated on the practical. If the information can’t be used in a practical way then it should probably not be part of the lesson
Most of the aerodynamic theory falls into this category, so I spend very little time on it, but I spend a lot of time on explaining how the aircraft systems work. Not understanding what the gauges are saying and what it means to the proper functioning of the system, not understanding what is happening when the knob is pulled or the switch flicked has real practical consequences.
BTW, I said in an earlier thread I had never flown a GA aircraft at endurance speed for real which is true. I did once fly a 96,000 lb transport category aircraft at max endurance. We had a sudden need to loiter for about 40 mins and not a lot of fuel. The solution was to go to the AFM and look up the max endurance power setting. That power setting was applied and resulted in us conserving enough fuel to finish the job
Now I am sure there was a lot of aeronautical engineering behind how that power setting was derived but I sure wasn’t going to over think it.