What you provide as an example isn’t quite what is called an educated guess, more like the ability to subitize and estimate well. Those skills are more likely to be improved only with experience and the teacher would not be able to help hone them really.
With what you said about visualizing and feeling what an answer could be, I would expect there to be some form of synergy between your ability to grasp the formulae and the mentioned ability to estimate things. With this the teacher could have helped by teaching you properties and basics about different formulae, but the problem with that approach is that you will at some point stumble upon a limitation of what can be guessed and will likely not know about it.