I chose to use this portfolio writeup because I struggled a little bit in this unit. I usually do not struggle at all in math and I had to put in a little extra effort into it to understand the concepts. I also chose it because this unit has a lot of real-world applications to many very different types of data. I incorporated my real-world interests into my extension question and it is probably my favorite one that I've written.

 

PART A: MASTERY

In the unit The Pit and the Pendulum, our task was to figure out if the character in Poe’s story would escape. Above him was a 30-foot pendulum that would complete 12 periods (swings back and forth) before it got to him. We had to figure out how long this would take in order to decide if he would escape bu rats chewing the ropes restraining him. At the end of the unit, we figured out that he did have time to get out because the rats could chew the rope in one minute, and the 12 periods to 70.682 seconds. To come to this solution, we began by looking at the variables that could possibly affect the length of the period. We experimented with changing the length, weight, and drop angle of small pendulums. Through these trials, we decided that only the length of the string affected the length of the period. The other two variables all fit into a normal data set. We came to this conclusion by making a normal curve of the data. We found the mean of each variable’s trials and then found the standard deviation. The weight and drop angle’s data all lied within 2 standard deviations while the length's was outside. After we found this, we found the time of 4 periods with pendulums of various different lengths. We collected the data for pendulums that were 2, 4, 6, 8, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, and 84 inches. We tried each of these lengths at least 4 times in order to create a wider data set. We then found the average time for each length and put it into our calculators to be graphed. After the points were graphed, we worked to find an equation for the curve of the data set. The equation that I came up with was P(x)=1.24√x. I then used my equation to find out how long it would take a 30 ft (360 in) pendulum to complete 4 periods which is 23.5273 seconds. I used this data to figure out the unit question by multiplying it by 3 which would make 12 periods. I applied my knowledge of creating normal curves for our Lies, Damn Lies, and Statistics assignment. I took the data from a chart I found online and was able to come up with the mean and standard deviation of the data. I also put it into a curve and was able to determine that all the information portrayed on it was normal. I didn’t understand curve fitting very well until we were working on finding equations for answering the unit question. I struggled with them in the assignment where we found the data for the fuel efficiency of the Volkswagon. I did not know how to create an equation and I just relied on my table members to give me the answers. I gave myself a 27/30 for my mastery grade because I put effort into understanding the concepts to produce quality work
 

PART B: EFFORT/GROWTH

I think that I put a lot of effort into this unit. I made sure that I knew the concepts before I applied them to my work. One example of this was the effort that I put into using the calculators to find the standard deviation, mean, median and range of any given data set. When we collected the data for the amount of sleep people got, I was the only one in my group that put in the effort to use the calculators to find the statistics on the data set. Once I found them, I used the numbers to make a normal curve and answer the rest of the questions. After I knew how to use the calculators, I used them to find the statistics on an intro question about donuts. With the effort I put into this unit, I demonstrated a lot of growth. When I did the Volkwagon fuel efficiency assignment, I was incredibly confused and I did not know how to find an equation for the data set. After asking for help, I was able to find an equation on the calculator to answer the unit question. I then used my knowledge to find equations for the lines on our first curve fitting assignment that I missed.

 

PART C: CURIOSITY

Climate change is an incredibly real and urgent problem that the nations of our earth are facing, yet there is still a large percentage of people that still don’t believe in it. If we took a poll of every state in the United States to see what percentage of people don’t believe in it, what would be the mean and standard deviation of the numbers. If we put these numbers on a bell curve, would it be normal for a state to have 50% of people not believing in it?