Students in eighth-grade accelerated math continued their study of linear relationships by building (well, folding really) bridges last week, and using the results of a weight test to chart their results.
The bridges you use every day are built with frames of steel beams, which are very strong but may bend or break with too much weight. That’s a thought that’ll stick with you as you drive across one! The good news is that engineers carefully design, test, and redesign to make sure bridges are safe. They often use scale models to test the strength of their bridge designs, and that’s exactly what our talented mathematicians did.
First, students made a paper bridge by folding up one inch on each long side of a paper strip. They suspended their „bridge“ between two books of the same height, and placed a cup in the center. Then, they gently placed pennies in the cup, one at a time, until their bridge crumpled. They recorded the weight—the number of pennies—as the „breaking weight“ of their bridge. For their second experiment, they used two stripes of paper to create a bridge of double-thickness before adding weight again. They repeated this process with three, four, and five strips of paper.
After carefully collecting the data, students then created a table and noted the dependent and independent variables. Using paper, pencil, Excel, and their Ti-Nspire calculators, they graphed their data as a scatter plot, using a reasonable scale for each axis. „The data is not linear but rather produces a scatter plot of data where students can determine lines of best fit,“ explained Middle School Math Teacher Dr. Jody Marberry.
Mathemeticians drew lines of best fit for their scatter plots, remembering that a line will fit the pattern if it goes through as many points as possible while also having the same number of points above and below the line. Using their data, they answered these questions:
- Describe the pattern you see in the data.
- Make a prediction of the breaking weight of a bridge made of six strips and a bridge made of seven strips.
- If your data does not have a pattern, explain why not.
- Suppose you could use half-layers of paper to build bridges. What breaking weights would you predict for a bridge 2.5 layers thick and a bridge 3.5 layers thick? Explain how you chose those quantities.
- How would you expect your results to change if you used a thicker material, such as poster board? Explain your rationale.
Students could also practice more plotting with Excel by using factions about 15 buildings ranging from 23 stories (National City Center) to 110 stories (Sears Tower) and their corresponding height in feet (301 for the first, 1,454 for the second). They graphed the data for the buildings using a scatter plot in Excel and drew a line of best fit that they felt best models the trend in the data, and then pondered what value for height occurs if they extend their line to cross the vertical axis? Does this make sense as the height of zero stories? Why or why not?
What a fun way to bring data to life!