As beginners become high beginners, within about 3 hours of lessons, my Matrix begins to "zoom out" until it becomes what I call a Map of the language. The Map is a single page which shows you the complete tense/aspect matrix of the language, core verbs, an adverb timeline, questions words, pronouns, and a few other items at a glance.
Once the Map becomes in view, the potential for conversation multiplies into a variety of topics. At that point, it's time to begin choosing the most relevant topics to you, and begin to converse on those topics in a question-answer, question-answer format. At this point, lessons feel like playing a game of tennis...back and forth, practicing conversing freely, with our Map as the basis.
As the student becomes more and more comfortable in the "tennis game", I begin introducing techniques to better "serve", or ask questions, and better "return", or answer questions. There are defensive techniques, methods for understanding when you're not really understanding, and techniques for making the most out of what you have.
Around this time (about 5 or 6 hours in), I introduce listening exercises that train you to deal with different native speakers when different accents and styles speaking at different speeds, and again I teach strategies to deal with those situations.
When a student is rather advanced, the lesson becomes focused on "elective"-type material such as business, or whatever sort of subjects they need, and I just provide feedback/refinement within 5 categories, which are accent, pronunciation, structure, vocabulary, and colloquial language. Poetry and phonology is also of personal interest to me.
But no matter what the students' level, Katarina, my goal is also to impart to the student an understanding of the principles that underlie each stage, so that ultimately he or she will not have to rely on anyone or anything, including me, to improve in the language, but rather can continue to learn the language by simply living in the language, and let interacting with and in the language be the true, natural teacher.