WSMC 1998 Regional Contest
Team Problem
In a nearby recreational trail area, a bridge needs to be constructed across a small creek. Your math teacher sees this as a great opportunity to put your math class to work gathering and analyzing data. Your class is able to gather materials in your classroom to test the strength of the bridge decking The boards are of the same material in thicknesses of 1, 2, 3, 4, and 5 cm, and widths of 10, 20, 30, 40, and 50 cm. The boards are all of the same length. Your class uses distances between supports (symmetrical to the center of the board) of 1, 2, 3, 4, and 5 m. For each combination of width, thickness, and support distance that was set up, the weight that would be safely supported was recorded. The results of the data gathering is contained in the table below:
| Dist btwn supports | width of plank | thickness of plank | weight safely supported |
2 1 2 2 1 4 2 1 2 1 2 3 1 4 2 1 2 5 4 3 1 4 3 5 1 5 4 5 |
40 20 50 40 20 40 20 50 30 20 20 50 30 40 10 20 30 10 50 30 10 30 10 30 20 50 40 10 |
5 5 4 4 4 5 5 5 4 3 4 3 2 3 4 2 2 5 2 2 2 2 3 2 1 1 1 1 |
250 250 200 160 160 125 125 125 120 90 80 75 60 45 40 40 30 25 25 20 20 15 15 12 10 5 5 1 |
Your task is to analyze the data and determine a model, ie. an equation, that the architects could use in determining the strength of the bridge deck based on the support and dimension of the planks used. Using the model you have developed, discuss the relationship of bridge strength to each of the variables in the data table. Although you have no data on cost or efficiency, try to make some reasonable conjectures or recommendations as to what the optimum construction of the bridge might be and why.
Use the two sides (max) of the page provided to build tables, draw graphs, and/or write text to fully investigate and document your proposed solution. Be sure your work is complete, clearly written, and provides logical structure leading to your conclusions.
The back side of this sheet contains the rubric that will be used to
score your solution to the problem.