The relationship between shutter speed, aperture and ISO (again?) .... now simplified

This might sound like a topic that has been hammered enough to not even bother to publish an article on, but I can see the confusion in the eyes of my students every time this comes up. Why do we have 3 (four if you count the flash!) different adjustments for exposure in a camera?

The usual explanation goes like: "...aperture controls the ammount of light entering the lens, but it also has effect on the depth of field in the image..". So this gets even more confusing as we bring another parameter into play! I seem to have much more success with a little twist that I have given to these well-known (for a photographer) concepts.

I try to explain what are the unique effects of each of the adjustments in the camera in terms that are not related to exposure and then add, "...but it also has a collateral effect of changing the exposure.." So here is the whole explanation:
Aperture affects the depth of field. The higher the "f-stop" number, the better the depth of field. The lower the number, the shallower the depth of field. Changing the aperture has the additional effect of changing the amount of light that gets into the camera. The higher the number, the more light is blocked.
Shutter speed affects how motion is recorded in the image. Increasing the shutter speed will stop motion. Slower shutter speeds will cause blur or will make the camera more prone to record camera shake. Shutter speed also affects how long the sensor is exposed to light. The higher the number, the faster the shutter, more light is kept out of the camera.
ISO is the sensor sensitivity and the lower it is, the less noise we have in the image. But the higher the number, the more sensible the sensor is to light.
So is clear now the function of each parameter, but it is also clear that if you want to get a certain (many times referred to as the "correct") exposure, when you move one of them, either one of the other two have to change accordingly to restore balance. If you are in any of the automatic exposure modes (Aperture priority, Shutter Speed priority), this will happen automatically.
This is proving to be a much more easier to understand approach as it assigns at first a unique effect to each control and then ties them together through exposure.
Shoot away...