2.1+Testing+Bridge+0910

SM 30/8/09 Block F


 * Lesson 2.1 Testing Bridge Lengths**

Big Idea: Many real world situations can be modeled and predicted using mathematics.

Essential Question: How can I model a non-linear relationship?


 * Notes:** A non-linear model is not a straight line unlike the linear model which is


 * A. Do the experiment with bridge length and pennies and create a table for your data. Do you think the relationship between bridge length and and breaking weight is linear?**


 * Length (inches) || Breaking weight (no. of pennies) ||
 * 4 || 94 ||
 * 5 || 42 ||
 * 6 || 14 ||
 * 7 || 17 ||
 * 8 || 10 ||
 * 9 || 11 ||
 * 10 || 8 ||
 * 11 || 8 ||

I don't think the relationship between bridge length and breaking weight is linear because even though the length is decreasing by the same number each time, the breaking weights are not. Instead it is going up and down. There is no specific patter but overall, the breaking weights do seem to be decreasing.

The data does not seem to be linear because the results keep going up and down and the breaking weights do not seem to be decreasing by the same number each time.
 * B. Make a graph of the data from your experiment, and describe the pattern you see. Does the data seem to be linear?**

I think my graph models the data well because overall the breaking weights are decreasing.
 * C. Draw a straight line or a curve that seems to model the trend in the data. Do you think your graph fits the data satisfactorily? Explain**

My prediction for a bride that is 4.5 inches long is 60 pennies, 35 pennies for a bridge that is 5.5 inches long and 25 pennies for a bridge that is 6.5 inches long.
 * D. Use you graph model to predict breaking weights for bridges of lengths 4.5, 5.5 and 6.5 inches.**

The difference between the bridge-length and breaking weights and the linear models studies in the last investigation is that there is a curve that is graphing this data instead of a straight line that graphed the data from the last investigation. The slope is also negative in this investigation unlike the slope in the first investigation which was positive. As the bridge length increases, the breaking weight decreases. In the first investigation, as the bridge layers increase, the breaking weights would increase. There really aren't any similarities.
 * E. How is the relationship between bridge length and breaking weights in this problem similar to or different from the linear relationships you studied in the last investigation?**


 * F.U**

If I were using strips of paper 12,13, 14 and 15 inches long for the bridge-length experiment, I'd expect the breaking weights to decrease each time because the bridges will get weaker and hold less pennies as the length increases.
 * 1. If you were to do the bridge-length experiment using strips of paper 12, 13, 14 and 15 inches long, what pattern would you expect to see in the results? Explain your reasoning,**

I would expect the breaking weight to be 140 pennies for a bridge that is 3 inches long. This is because the shorter the bridge, the stronger it will be and the more pennies it will be able to hold.
 * 2.What breaking weight would you expect for a bridge 3 inches long? Explain your reasoning.**