While I originally came to teaching via helping my siblings with their homework, I tend to use a pretty standard format, adapted from my work in the charity sector helping disadvantaged students.

I start out with a quick recap of the content of the last lesson, to ensure it has stuck in the mind, before giving the child a selection of numerical brainteasers as a warmup. Once we move on to the main content of the lesson, I start by going through worked examples of the use of whichever mathematical concept I am trying to teach, inviting the child to follow along, before moving onto example questions with help (that is, the child may ask me for help with parts of the question while they are doing it), and finally moving the child onto questions done without help--that is, I mark their answers at the end. If there is any remaining time in the session, we may then move onto working through their wrong answers to find where they made their mistakes. If not, I would move onto self-assessment, asking the child what they felt they did and didn't understand about the topic, taking notes to ensure that later revision sessions will be productive.

The aim with each session is to foster a level of back-and-forth dialogue between myself and the student, where they feel comfortable asking me questions and are engaged in what they are learning. The ideal is a high level of interactivity, which will help them learn.