The first two lessons are mostly algebraic. Actually, problems on decimal representation are perhaps the most common number-theoretical problems in maths olympiads for students of age 11-13 (because other number-theory requires much more knowledge). So it is worth talking about it.
Then we will talk about graph theory, a subject that is unfairly neglected by educational institutions in many countries. The set up is easy and moreover graph theory is one of the branches of mathematics that has tons of real-life applications, especially in IT. In this one lesson we will start from the very beginning, but as always there will be a number of interesting problems in the extra sheet.
Next: invariants and monovariants. Both are simple ideas that are useful for olympiad-style problems and in serious mathematics later. It is likely that most of the people already know the idea, but it is not likely that many students can solve all of the problems we will give on this one idea :)
Finally, we will talk about a cool simple formula for evaluating the area of figures on a grid, known as Pick's formula. Moreover, we will prove this formula and give some problems on it.