In order to bring the subject some meaningful context, I think it would work to begin a topic by first reviewing its utility. Then I would run through some basic examples. I must emphasise that there are no stupid enquiries, anything to aid a student's understanding is essential. After I have actually run through a couple of cases, I would like to have the student run through their own instance, talking to me pretending they were the tutor and I was the tutee.
Lots of researches have actually revealed that attempting to explain a principle you have a little while ago found out helps exceptionally in retention and comprehension. If I'm satisfied with their teaching, I want to check their critical thinking by giving them an issue based on whatever discovered in the lesson, but with refined modifications that require the tutee to proactively involve with the work, instead of be on "auto-pilot".
Home task will certainly be set on the material talked about (nothing extra extreme), and further lessons will be spent responding to exam-styled enquiries before moving on to the following theme.
Throughout sessions I want to encourage a rather informal, pleasant environment. I enjoy mentor, and also I really hope students have a good time in my training sessions, and an unwinded mind is much better at studying.