One topic I feel that I've mastered this semester is the Pythagorean Theorem, A squared plus B squared equals C squared. We were first introduced this in October and even though I had learned this in middle school, I didn't remember how to do it. At first, I wasn't really good at it, then I did POW four. This problem was where I really tried to figure out the Pythagorean Theorem and use it right. Doing POW 4, I felt very stuck and unsure how to do the problem which was, Jason and Maya travel 130 miles at different speeds and different paths at a certain time. Our job was to find out what time it would be when both of them are 130 miles apart and how far they travelled. But because we were learning about the Pythagorean Theorem and we were told that the POW included it, I used that equation to figure out the time they would be 130 miles apart and how far they travelled.
One way I feel that I've mastered the Pythagorean Theorem is because it is the one thing that I feel we've used the most this year. I learn best when I keep repeating the equation and continue to use it over and over. Then it gets drilled into my head and whenever a problem comes up that includes the Pythagorean Theorem, I can easily figure it out. One way this is shown is in our 9/2915 Exploration where we had problems that involved using the Pythagorean Theorem to calculate the missing sides of triangles.
Another topic I feel like I've mastered this semester is fractals. Fractals are shapes and patterns that keep repeating but get smaller or larger in scale. We made many small Sierpinski Triangles that eventually all made up a big one. Then to show our knowledge of quadrilaterals and fractals, we had to carve pumpkins using quadrilaterals and fractals. I collaborated with Hannah Bissell to create a pumpkin that ended up winning 3rd place in our competition and had a great use of fractals and quadrilaterals. In POW 5, we were told to show the steps to creating a Sierpinski Triangle and our justification for why the triangles we made were authentic Sierpinski Triangles.
To me, the discussions we had for the explorations were very beneficial. If I don't understand a problem I usually put it off or ask someone for help who doesn't understand the problem either and give up. But during these discussions, other people can describe what they did to solve certain problems and they can help you have a better understanding of the problems. I would say these discussions have helped me learn that it's ok to ask other people for help, whether you're friends or not. If you don't understand something that another person does, it is okay to ask for their help.
The hardest math problem I had to encounter would have to be POW 8. This POW was more logic based, which I'm not really good at. So I worked with Hannah Bissell on parts of the problem. I drew out a table and used the process of elimination to determine my final answer.
One problem solving skill I feel that I've mastered is communicating thinking in a clear and accessible way. When doing the write up for POW 7 I wanted to make it very simple and easy for people to understand, even if they were never taught the problem. Because this POW involved cards and had many confusing steps, it was a challenge to explain how I solved the problem. I had asked peers for help and clarification on the problem and also had peers ask me for help. Having someone explain their solution to me was very helpful because if I could understand what they were trying to communicate to me, then I could also use their methods to help explain my own solution. Having to explain my solution to other peers was very beneficial because if I could verbally explain what I was thinking, then I could explain it on paper much more easily. In each POW we have to explain our solution to the problem, whether we solved it or not, and our justification for our answer if we had one. Usually my explanations on POWs last year were very confusing and didn't always tell how I solved the problem. This year I feel like I've improved on explaining my answer to the best of my abilities and asking clarifying questions to make the problem easier for me and my peers.
Even in POW 3, where I didn't solve the whole problem, I still wrote out my solution for the parts I did complete and solve. I also wrote out my justification for why I didn't solve the whole problem but did get a few of the answers.
One problem solving skill I feel like I could improve on second semester would be recognizing and resolving error. Usually when I get stuck on a problem I copy off of other people, come up with a fake answer to get it out of the way, or avoid it all together. I think one way I was held back from improving o this skill this semester was the fact that I would put things off and not worry about it until the last minute. If a couple answers were wrong or I didn't get the best grade, I didn't worry about it. This led to a string of bad grades and I had to get my grade up in a small amount of time because I waited until the last couple of weeks of the semester to really buckle down and do my work. This next semester I want to work on this by turning all my assignments on time, asking questions if I don't understand something, come afterschool or during study hall to get the help I need, and working with peers to solve problems.