In the schools I'm familiar with, this isn't really a skill that's taught. The emphasis is on carrying out steps correctly on paper. Making a good estimate without showing work would definitely be frowned upon.
In Germany this was part of the physics curriculum.
It made sense since order-of-magnitude estimations constantly come up naturally in all fields of physics, whether you are asking "is this plausibly possible", "what kind of instrument do I need for this measurement" (and later "can we even measure this in this setup") or "are the results of my experiment plausible". There's a reason we joke that to the physicist g=10 and pi=3.
It's difficult to test this kind of thinking in a written test without turning it into something entirely different, but not everything in school has to be on a test. Typically half of our marks were made up from classroom participation.
Taking the steps multiple times (practicing) will make it fast and trustful.
Guessing may get you a part of the way if you're very good at it, but repeatability is what really hammers it into you. It also gets you out of trouble when for any reason your guessing instinct is not at full steam (when tired or otherwise incapacitated, anxious, etc) since you can usually relatively quickly rely on the steps you have drilled for.
It made sense since order-of-magnitude estimations constantly come up naturally in all fields of physics, whether you are asking "is this plausibly possible", "what kind of instrument do I need for this measurement" (and later "can we even measure this in this setup") or "are the results of my experiment plausible". There's a reason we joke that to the physicist g=10 and pi=3.
It's difficult to test this kind of thinking in a written test without turning it into something entirely different, but not everything in school has to be on a test. Typically half of our marks were made up from classroom participation.