We prove many statements in middle and high school mathematics, so it is necessary to have some method for understanding the modes of proof. But it is hard to discuss about the modes of proof without knowing logics. Venn-diagrams can be used in a great variety of situations, and it is useful to the students unfamiliar with logical procedure. Since knowing a mode of proof that could be used may still not guarantee success of proof, it is also necessary to illustrate many cases of proof strategies. To achieve the above requirements, (1) Even though intuition, the modes of proof used in middle school mathematics should be understood by using venn-diagrams and the students can use the right proof in the right statement. (2) We must illustrate many kinds of proof so that the students can get the proof stratigies from these illustrations. (3) If possible, logic should be treated in middle school mathematics for students to understand the system of proof correctly.