The programs dealing with the application of mathematical modelling to the solving activities in real-life problems have been conducted mainly in the United States, Australia, and several European countries such as Holland, Germany and so on. The students who have participated in these programs vary in age, academic ability, and other things. This present program deals with a solving activity in scientific problems for junior high school students. It was carried out as the trial step of the mathematical modelling challenge program we have been carrying forward in Japan. In this thesis, we report the content of this program, the feedback from the students and what we gathered from it. “The movement of a cart rolling along the slope” is taken up as a teaching material and some third-year students at junior high school (ninth graders) tackled it. As a result, it turned out that these scientific problems were effective as the mathematical modelling challenge. But, on the other hand, it was confirmed that Japanese students lack modelling skills in thinking flexibly considering the various conditions and uncertain numerical values arising from complicated real-life problems. At the same time, it is suggested that the activity like this can foster the students’ attitude to try to find answers from a broader point of view instead of just staying within the area of functional formulas which they have already learned.