For my second semester of Algebra II, I have honed my skills as a mathematician through explorations, POWs, and my own project, and grown in many areas. I’ve grown in the area of generating ideas through most of my explorations when I identified and used the right math tools such as graphing, equations, and formulas. For example, in one exploration I was asked to solve an equation and I ended up not being able to find the answer multiple times. I then realized that I could use a graph to find the value I was looking for. I identified what tool I needed to use after realizing my mistake through using logic. As far as communicating my ideas clearly, I think I excelled in doing so in seminars. In seminars where we worked together and shared our answers, I contributed through not only saying what I got but explaining my thought process and going through each step I took on the whiteboard. Aside from that I asked clarifying questions to my peers to understand what they had done so that I could better understand the problem. Many times during a seminar, I would find that I had a mistake on an exploration. Instead of just correcting my answer, I would make a separate note in highlighter saying what the correct answer was and what I did wrong to get to an error. This way I had resolved my error and made note that I had made a mistake so that I could grow from it instead of just fixing it. I reflected on my work and synthesized it by connecting it to real world situations. For example, one of my favorite explorations talked about parabolas that exist in real life, such as a parabola in the arch of a bridge. We graphed the arch and found height limitations for trucks, sidewalk lengths, and height limitations for people walking on the sidewalk. This was algebra that was completely applied to the real world and was relevant, which I reflected on and was then able to do the same with other problems and math concepts.
This semester in Algebra II, I’ve learned and mastered the content skill of converting units. I learned how to convert from one unit to another using the method of setting up fractions. I also learned that you can convert any type of unit, not just things like the metric system and the imperial system. Some activities that have helped me learn this are practices and explorations. For example, on exploration 2, question 1, the problem asks for me to find how many miles per hour Tony is going when he travels home if he is 1.4 km away and it takes him 11 minutes. In order to find this, I had to convert 1.4 km to 0.875 miles by dividing 1.4 by 1.6, the amount of km in a mile. Then, I converted 11 minutes to 0.18 hours by dividing 11 by 60, the amount of minutes in an hour. I divided the miles by the hours to get the miles per hour, which was 4.7. I am fairly confident that I’ve mastered this skill because on practice 2, question 1, I converted between monetary units. The question asks how many euros Kai will receive if he exchanges 500 pounds. I converted 500 pounds to 615 euros by multiplying 500 by 1.23, which is how many euros are in a pound.
Problem-Solving Skills
One problem solving skill that I mastered this year has been identifying and applying the appropriate tools. To me, this means that when I see a problem, I can see without being told what type of formulas, methods, or tools that I can use to solve it and I use them correctly. I’ve demonstrated this skill through my explorations and POWs. For example, in POW 5, part of the question asks how much time has passed when 4.2 lbs of Carbon-14 (which has a half-life of 5,370 years) remains and it started out at 10 lbs. I solved this problem by first representing it using the f(x)=Pbkt function. The function was then turned into the equation 4.2 = 10(½)t/5,370. At first, I couldn’t understand how to solve for t, the amount of time. But then I realized that I can graph the function f(x) = 10(½)t/5,370 and look at its line to find that when the y-coordinate is 4.2, the x-coordinate is 6,720 years. I solved the problem by using a graphing calculator and a graph as tools. Another time when I identified and used tools was when I did my spreadsheet workshop, which you can find above. In my second sheet, “Part 2: Making Calculations”, three of the calculators that I made all used specific formulas. In the first calculator, the Speed Calculator, I used the formula s = d/t. In the second calculator, the time calculator, I used the formula t = ds. I identified and used specific formulas, the speed, distance, and time formulas, to make my calculators.