Then, Mr. Tsubota let the students experience the marble-throwing-game by themselves on their desks. After a while, he asked several students to present their results on the blackboard. By looking at presentations by their peers, the students began to realize that there are a variety of scattered ways. Mr. Tsubota then asked the students how to decide which marbles are scattered more and how to convince others that is a reasonable decision. Several students raised their hands and made proposals. Many of them capitalized on their knowledge as sixth-graders and put their focuses on lengths and areas. Discussion was gradually shifted to the differences among proposed ways of making decision.