In order to bring the subject some meaningful context, I think it would be useful to begin a topic by first reviewing its utility. After that I would run through some basic cases. I have to stress that there are no silly questions, anything to help a tutee's comprehension is crucial. After I have actually gone through a couple of examples, I want to have the student gone through their personal example, talking to me as if they were the tutor and I was the student.
Many studies have actually revealed that aiming to explain an idea you have a little while ago learned helps profoundly in memorisation as well as understanding. If I'm satisfied with their teaching, I want to evaluate their critical thinking by setting a problem based on whatever discovered in the lesson, yet with refined modifications that need the tutee to actively involve with the work, rather than be on "auto-pilot".
Homework will be set on the topic discussed (absolutely nothing too extreme), and also further lessons will certainly be carried on addressing exam-styled enquiries before proceeding to the following topic.
Throughout lessons I want to encourage a fairly informal, pleasant atmosphere. I have fun training, and also I really hope students enjoy my training sessions, as well as an unwinded mind is better at studying.