No, you could focus on the applications of those rules, of which there are more in day to day life. If I see a car's speedometer moving, I don't need to be able

No, you could focus on the applications of those rules, of which there are more in day to day life. If I see a car's speedometer moving, I don't need to be able to figure out how long it would take to travel a certain distance. But dealing with infrequent events in a smarter way? Super useful. Teach it the way you suggest and it would just be another useless math class that people would tune out of instead of grounding it in their everyday life experiences. ("Deriving from first principles" isn't the interesting stuff about calculus, either. And we're not requiring quantum physics to derive gravity from first principles in high school...)