How does the Monte Carlo method work?

Abstract: The paper describes the practical work for students visually clarifying the mechanism of the Monte Carlo method applying to approximating the value of Pi. Considering a traditional quadrant (circular sector) inscribed in a square, here we demonstrate the original algorithm for generating random points on the paper: you should arbitrarily tear up a paper blank to small pieces (the first experiment). By the similar way the second experiment (with a preliminary staining procedure by bright colors) can be used to prove the quadratic dependence of the area of a circle on its radius. Manipulations with tearing up a paper as a random sampling algorithm can be applied for solving other teaching problems in physics.