Analyzing Graphs in Algebra I
Math
I have always loved doing math, and this year in the 8th grade, it got me really excited for what we will do next year. Math has interested me, so I did a couple of math clubs. I did MATHCOUNTS for about 3 years and went to district all three years. But, I wasn’t really the best at math all the time. I got B’s and C’s in 4th grade, but my 5th grade teacher was really helpful and the syllabus we used was really helpful. This said reflection is going to let you know a little bit about my growth in math this year, which I thought was tremendous. We have done many endeavors and learned many topics. This year was a bit different for the school because we didn’t use the CMP3 books. Instead, we used online resources /worksheets and Aleks. Aleks is an online program that helps you get better at math, by teaching you different topics. This year we did Algebra I, so we looked at lots of graphs like parabolas, linear, etcetera. I think that I grew in interpreting graphs. This meant that after I look at a graph, I know what type of data it is trying to represent (quadratic, linear, cubed, and exponential). After weeks and weeks of just doing activities about graphs, I can say that I got a lot better and got used to seeing them.
The first artifact that shows growth at this school is the Average 8th Grader project. This project was just to get us familiar with summarizing data. First, we took a survey of all the 8th graders, asking them various numerical and categorical data. These two words are something new that I learned this year. Numerical data means that you get a set of numbers as data. Categorical data is where you have different responses, and how many people gave that response. In the project, we were assigned two sets of data, one numerical and the other was categorical. For the numerical data, we got 102 responses answering the question ‘How many hours of electronics do you watch in a day?’ Now that we had the data, we could interpret the data and find the standard deviation. The standard deviation is how much the data varies from the mean of the data. We made algorithm on Excel earlier, so we could just punch in all the numbers to get the mean and the standard deviation. It turns out that the first time I did it I was wrong. I got the mean wrong which then directly got the deviation wrong. My partner corrected me and then I got it right. Once we got the standard deviation, we made what is called a bell-curve graph. This graph shows what a normal set of data should look like. The graph itself looks like a wave, and the intervals are the standard deviation that we found. I could now tell that whenever look at a bell it is talking about standard deviation. A normal bell curve is one where there is a lot of average people, and a lot less of below and above average. This is because there is probably more average people in this world. At the start of the year, I really didn’t like the standard deviation unit because it was something that I didn’t see myself using in the future, but when I looked at how easy and simple it was, I was really interested about looking at data and statistics. I think that I will definitely use it in the future if my job is analytical.
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The second artifact that I am going to talk about is the Road Trip Problem. The road Trip Problem was an activity where we had to design a cool road trip for a chance to be on the show “Illest Road-Trip of all Time.” We had to manage the money and time we had; 8-31 days and $9500 - $10,000. The trip had to be on road, so you couldn’t cross over waterways (like to Europe). We started off with brainstorming all the people that we wanted to go with us on the trip. Then, we were given a choice of dining, lodging, and baggage. We chose different prices depending on how many people we had or how luxurious of a place you want to go to. Then, we had another choice for the car we would take there, and the choice was based on how many people there are, and how much money you have left for the gas. Yes, we even had to account for how much gas we used based on the distance to the destination. Like I said before, there were a lot of choices, so there were many outcomes that you could get. When we made the choices, we had to write an equation. For example, we could look at the car choices, where I picked the Honda Prius. The Honda Prius cost $34 a day, so that would mean that in the equation where y=total cost and x=#of days, y=34x. Then, since the Honda Prius has a 50 MPG efficiency, we could find out how many gallons of fuel we would need for the entire trip. Then we simply added the cost of fuel to the car rental to get how much renting a car really costs. When we made an equation, we could make the graph of the equation. This time, the graph was linear. Linear is a line on a graph that goes in a straight line. Our graph was linear because we spent a fixed amount of money each day. The amount that we spent was the same every day. We used these graphs to see at what time our money will run out and manage our money properly.
The third artifact that I am going to present is the Parabola Worksheet. This was a worksheet that we did in Algebra I that was all about graphing parabolas. Parabolas are the graph of a quadratic function, usually making a U shape. A quadratic function is any function which has a variable with the power of two in it. So y=x2 is a simple quadratic function. That is all the stuff that I already knew. Something new that I learned about parabolas this year was the Step Method. The Step Method was a simple algorithm that we could use to graph a parabola quickly without having to make a table. To use it, your equation had to be in the form y=a(h-k)2+b. From that, we could figure out the vertex which is just (k,b). Since a parabola is not linear, the numbers don’t relate to each other in the same way, rather exponentially. Instead of the parabola’s y values going up 1,2,3,4…, they go 1,3,5,7…So from all of this, we concluded that when we move over one on the x-axis, we would go up 1*a on the y-axis. Then from there we would go 1 on the x-axis and 3*a on the y-axis and so on. This was a really helpful tool that was taught which I had never learned before. I think that being able to graph this parabola may make it easier for me to interpret parabolas because I can derive the equation for the line.
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Like I said before, I have grown a lot this year in Algebra I. I look at graphs differently now. I can tell a linear apart from a quadratic and tell what graph it is going to be just by looking at the equation. I know for sure that these skills will help me out next year, and maybe even for my career. If I ever want to be a data analyst, these skills would come very handy then. As for next year, we will be learning even more graphs like hyperbolas, so I am very excited for that. I hope you learned a little about math and how I grew in in this year at DRSS
