Modeling
Linus Pauling, scientific modeler, said “The models themselves permit you to throw out a large number of structures that might otherwise be thought possible.” In my understanding, modeling is an efficient way to experiment with possible designs and notice various advantages and disadvantages that do not obviously appear before the models are constructed.
For this modeling assignment, within my general topic of science and sports, I chose the relationship between racing and ramps. I then began thinking of a lesson I could do with students in which they would race marbles across the classroom by modeling the construction of ramps. I would tell groups of students that their goal is to build a ramp to get their marble all the way across the classroom as quickly as possible. Before they begin making their models, I would show them videos of ski jumping and skateboarding to show them, without explicitly discussing, some of the factors that influence the construction of a ramp, including height, slope, width of the ramp, type of surface, and whether the surface of the ramp is flat or curved. These are all examples of the dimensions related to ramps their could affect their modeling of ramps.
I would then instruct students that, in order to make their ramps, they could use any of their own classroom items and any of mine if they asked first. To show how the different dimensions listed above might influence the effectiveness of students’ models, I have created drawings to represent what may be common “good” and “bad” models. The first “bad” model is designed to show the disadvantages of steps as compared to a smooth ramp. In the first “good” model, this problem is solved by placing a ramp across two steps. The second “bad” model is designed to show how a very thin or unstable ramp will decrease chances of success because the marble might fall off. In contrast, the second “good” example shows how students might solve that problem by using a ruler with a groove in the middle that the marble could travel down. The third “bad” model is based on the ski jump video, with the “jump” created by using a bendable ruler, but students would learn that this might not be effective for this particular ramp problem if the marble ends up going up in the air and then bouncing instead of rolling. The third “good” model would take advantage of a higher height for the ramp, but would avoid the bouncing issue if students are able to set it up properly for the marble to land the jump. The rest of the “bad” models show other dimensional choices that students might make that would not lead to good results. In the fourth “bad” model, the ramp is too steep and the marble might bounce instead of roll, just as if it were dropped from straight above. In the fifth “bad” model, the ramp is pointed in the wrong direction and the marble will lose because it is not headed straight for the finish line.
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Through this activity, students will learn about the different dimensions that affect the construction of ramps through modeling. I chose each of the examples I drew above to show the effects of changing these dimensions.