I current tutor for Year 4, 5, 6 and Year 12 maths (Mathematics, Mathematics Extension 1 and Mathematics Extension 2). My tutoring approaches vary depending on the students but this is the set routine that I slightly vary to accommodate various needs.
Junior Kids: I have 2 textbooks where one of them is for beginner + normal level students and the other one that is quite advanced. The ones that I am tutoring are preparing for Selective School tests so what I do is I first go through each topic and do questions there. I select the questions before I do my tutoring so I won't waste time (good tutors should definitely do this in order to maximise productivity). Then I slowly understand where they are weak yet. While they do some of the questions I set, I write up my own questions quickly which target the questions they got wrong so that they can come back and try these questions again.
As homework, I usually set them past Selective School test papers (3-4 pages) and make them do it. I would then come again and check how they did and analyse their strengths and weaknesses and target them through our textbooks questions.
Mathematics: I believe that key to success in HSC Mathematics and beyond is trying as many past papers as one can. However, it's important to understand the concept beforehand. So I use Fitzpatrick and Cambridge as my main textbooks and selectively choose the questions prior to tutoring for the tutees to try. I make sure the questions that I ask are effectively testing the concepts and relevant questions for HSC syllabus (which I still have ><).
Then if I have time, we go through some past paper questions. Then when we finish, I give them a sorted past paper which has questions from just the topic that we have covered. When we meet again, I would go through the ones that they don't know and yeah, that's how I do my tutoring.
Mathematics Extension 1: Pretty much same as Mathematics. However, the content is obviously more difficult so I also take extra time beyond tutoring to answer their questions online e.g. e-mail. BTW, I use Cambridge and Fitzpatrick as textbooks.
Mathematics Extension 2: Same as above. However, I have found that many of the contents are not properly covered by many students. For example, ,any of tutees I had were not completely sure of how vectors work so I had to take some time to explain that from the beginning. So my main concern here is to cover everything that could be tested in HSC and focus on the main points and reinforce these points. I encourage my students to be broad-minded and think of ways to solve questions in many ways. BTW, I mainly use Terry Lee and Cambridge for this subject.
All in all, you should really tailor your tutoring to your tutees. From first lesson, get to know more about him/her then try to think of ways to maximise productivity. I find that: concept explanation -> practice questions -> past paper is the best way to go. Nevertheless, tutoring's first priority is to get tutees interested in the subject or enthusiastic about studying more. So show your passion for the subject or push them to their maximum potential.