What would you teach, how would you teach it, and why these ways?

I'd teach it in terms of translation, I've had success tutoring college algebra this way.

 

You just constantly cycle through the meanings of different notation until the student absolutely knows what it means, and once they can translate, they have power to see the numbers and what they're doing. I'd just simply translate notation into the context of practical application.

 

All the tests would be word problems the student would have to set up, that way they get a sense for practical application and importance.

 

Math is a language, I think it's best served to teach it as such.