Two highways intersect in a county. The highway patrol wants to place a station so that it is equal distances from both. At what point(s) can they place the station?
To start with this problem, I drew a visual of the two lines intersecting. I then plotted all of the points that would satisfy the constraints. I then did this for the other two problems in which there were additional lines.
The solution varies based one the number of lines, but in general, the point will be dead center of the polygon. This is true for all cases except for when you have two lines. In that case, you will have multiple solutions. If I hadn’t had grid paper to complete this assignment, it would have been more difficult, but because I did, I found it very easy.
Final Project Reflection
I really love independent projects because it gives you more room to dive into a topic of your interest. It also gives you a lot more freedom to present your project however you want. It doesn’t force the science kids to do an art project or the artsy kids to write a paper. The one downfall however, is that sometime there is a too little guidance. That’s how I felt with this project actually. It was hard for me to not know if there was a word count requirement and how much math content it actually needed to have. I think that the project was so broad that it was hard to give people requirements for their project beyond not having spelling and grammar errors. This would be something that I would change if I were teaching this project. I would narrow down the options for project options and make very clear guidelines so it was easy to know what was expected.
This being said however, I learned a lot through this project. I did a biography on Alan Turing, so I learned a lot about his contributions to the math and science community as well as his struggles in his personal life. Additionally, I got to dig deeper into his conviction for being a homosexual, his suicide and his eventual pardon from his crime.
Junior Year Math Relflection
I don’t really feel like I met my math goals this year. I really hoped to get a lot more out of this year than I did. I think that this was due to a combination of things. I didn’t feel like I was learning a lot in the class so it quickly became my least favorite class. The SAT Prep we did was way way less helpful than all of the prep I did on my own and I just didn’t feel like it really helped progress my knowledge. My confidence in math definitely decreased because the math we did do, I didn’t understand even after asking for help from my teacher, my friends, parents and the internet. This class became to bottom of my focus list because I wasn’t interested in what we were learning and it wasn’t making sense to me. It was hard to find the motivation to complete the work and this shows in my grade. I don’t really feel that prepared for senior math. I feel like I’m going to have to spend a lot of time this summer on Khan Academy trying to catch up on math.
POW's (Problem of the Week)
With only 29% of Earth being land, it doesn’t leave much room for us to spread out and populate while also having enough room to have agriculture and other open areas. At the current rate of population growth, we will be experiencing shortages of resources sooner than we care to admit. There are already places in the world where they are running out of space. Not to mention the fact that some places aren’t even hospitable. It would take more resources to build in some places than it is worth.
Our natural resources will eventually run out since with haven’t figured out ways to make synthetic resources. The United States is one of the largest consumers of natural resources in the world and we are also some of the biggest deniers of resource depletion. It is estimated that there are only 850 billion tons of coal left in the world. There is an estimated 2,355 trillion cubic feet (tcf) of natural gas left in the United States, which is only enough to last about 92 years worth at our current consumption rate of 24 tcf per year. Since it is hard to know the exact count, it is estimated that we cut down between 3.5 and 7 billion trees per year. These trees are used for building homes, making paper and other lumber needs or are cleared to make room for buildings and the expansion of civilization.
All of the aforementioned things also increase climate change (it’s real, sorry Mr.President.) Deforestation adds about 1.5 billion tons of carbon dioxide to our atmosphere every year. One of the largest causes of deforestation worldwide is large scale agriculture. This is an issue in and of itself. We struggle with deforestation caused by agriculture but there is such a high demand for the things being produced by the agriculture.
Not only does agriculture cause deforestation, it also is one of the largest consumers of fresh water. Did you know that it takes 13.8 gallons of water to grow one orange? It takes 1,799 gallons of water to raise one pound of beef and 576 gallons to raise one pound of pork. The amount of fresh water that agriculture consumes is insane. The majority of our beautiful planet is covered in water, but only a small portion of that water is drinkable fresh water. But instead of saving this, we waste it watering plants.
You can do your part by educating yourself about your carbon footprint and being a conscious consumer of goods. Eat less meat and know where your goods come from. Take shorter showers and plant a xeriscape instead of that lush green lawn.
Growth of The Rat Population(POW 4)
Problem Statement: Two rats end up on board a ship. When the ship lands on a deserted island, the rats disembark. On January 1, the day they land, the female gives birth to a litter of six. She will give birth to another litter every 40 days. Each litter will start having their own litters 120 days after they are born then they will also have litters every 40 days. The problem is, how many rats will be on the island by January 1 the next year if all the rats survive and they have no natural enemies on the island?
Process: To start this problem, you can start by dividing 365 days in the year by 40 to find how many litters will be born in one year. You end up getting nine plus the first litter that was born on day one, which gives you 10. Right there you already have 62 rats on the island. Then you can calculate how many litters each original litter will have based on how many days are left in the year after they start having litters. At first, I missed a couple litters and ended up with only 108 rats by the beginning of the next year. I then went back and redid my calculations and got a higher number.
Solution: My solution was a lot lower than everyone else I checked with but I’m not sure how their numbers ended up so high. My final population for the rats on the island was only 230. Other people that I talked with got 500 or higher.
Evaluation: Overall I liked this POW. It had some cool aspects to it that made you really think about it and you had to make sure to consider all of the variables in the problem. I learned that it’s okay sometimes to not always have the right answer, especially when you put in the time and effort to try to find the solution but don’t get it. I don’t think that I would change anything about this POW.
Self Assessment: I don’t know what letter grade I would give myself on this POW but I would give myself a pretty good store. I think I deserve a good grade because after I had already completed the problem, I went back and redid my math so that I could refine my answer to at least be closer to being correct. This shows my striving for beautiful work and trying to create beautiful work.
Assessment of POW's
I am proud of these POW's because I feel that they show my best work and they are beautiful work. I also enjoyed working on them. The first one focused less on math which was a nice way to ease into POW's at the beginning of the year. And the last POW, I just thought was fun because there were a lot of little elements to it that you had to consider and think about.
Silverton Write Up
Task Statement: The juniors were asked to solve a series of mathematical problems with the three streams in Silverton to find the streamflow, turbidity, and other factors in the Animas River, the river in which the streams all flow towards.
Introduction: The water issue in Silverton has been a problem for some years now. On the 12th of October, we took a trip there to find the streamflow, turbidity, pH, conductivity, and temperature of the three streams that flow towards the Animas River. These streams are as follows: Mineral Creek, Cement Creek, and the Upper Animas. This data was collected by using taking the standard deviation, weighted average, mean, median, range, maximum, and minimum of the data from each group at each stream. After we collected the required information, we were then told to find the same information for the Animas River by using the data we had collected from the streams.
Solutions/Predictions: The data the AHS students collected was incomplete and a small samples but we worked with what we had to make our predictions. The graphs below show the data for each water quality variable we tested, except dissolved oxygen. We don’t have dissolved oxygen because it was only taken at one of the three creeks so building an accurate prediction for what it is in the animas river. To make our predictions for what the Animas River we used weighted average. A weighted average is a type average that is used when the things you are averaging aren’t equal. The stream flow from the creeks aren’t the same this works best. To find the temperature we took the the streamflow of the first creek and divided it by the total streamflow, then multiplied it by the average temperature for the first creek. Repeat this for all the creeks and add together. Our formal looked like this:26.48/119.37(9.48)+72.284/119.37(6.883)+20.6/119.37(4.72)= 7.0868. Our predations for the river below the confluence are; streamflow is 119.37, temperature is 7.08681069,turbidity is 24.55957106, conductivity is 531.4971615. These predictions are extremely close to the USGS historical readings of the animas river. Due to the fact the fact that the reading stations were covered in ice on the 12th when we took our readings, I decided to use the data from the 18th.
Methods: We had to run multiple tests during our time in Silverton. These included, turbidity, pH, dissolved oxygen, and temperature. To conduct these tests we used turbidity and dissolved oxygen sensors.To find or predictions of what these numbers would look like below the confluence, we simply calculated the averages then found the weighted averages of the figures. The only thing that didn’t work using this process was pH. We tried multiple things to try and calculate pH without the numbers canceling each other out. What we were unaware of was the way you calculate and add pH is different than how you do it for anything else.Despite this fact, we still managed to get close to the actual pH of the river below the confluence. We also had some issues running a couple of the tests. We got a negative turbidity due to the fact we only did a one point calibration rather than a two point. We also couldn’t get a reading on the dissolved oxygen because of technology errors.
Evaluation: I (Malcolm) did not find this overall useful, fun or educational. This is because I had done things like this is in the past. However it was a good way to teach weighted averages. I kinda felt like it was a section of time that we could have spent doing something else.
The Importance: It is important to know the health of the rivers and streams. The calculations that we did help tell us the current stream health and the healthiness the past. It is important to know this so we can correct anything that is wrong and correct it to keep a healthy ecosystem. To protect our water we can keep trash out of it and protect against the epa (after all the mine wouldn’t have broken without them).
Self-Assessment: Assign your group a grade for their work on this I believe that my group should A or B, I feel that we met all the requirements our calculations were correct.
I feel like I didn't meet any of my goals this semester, in any of my classes, not just math. I know what I'm capable of and this semester hasn't been a good example of this. I want to do better second semester and have the opportunity to show the work that I am able to produce. Throughout this semester I feel that I have come to realize that things being hard outside of school has a major impact on how well you do in school. This being said, I have also come to the realization that this is not an excuse to slack off. This was part of the reason I didn't achieve my goals this semester. I am hoping that during second semester I will learn a lot of new math skills so that I can get a high score on my SAT.