- One topic that I feel I have mastered this semester is the pythagorean theorem and how to tell if a triangle is a right triangle. We did one activity called “More Triangles Practice” that showed us that a triangle is a right triangle if the sum of the two shortest legs is greater than the length of the longest leg. Problem 13 on this worksheet showed a right triangle. The two legs measured 4 and the hypotenuse measured 5. The sum of the two legs is 8 which is greater than the measurement of the hypotenuse, proving that the triangle is a right triangle. This method works if it is not immediately obvious that a triangle is a right triangle. This skill helped me figure out problems that I was previously confused by. We learned a lot about triangles in 8th grade so it came easily for me this year. Although this is a subject that I feel very proficient in, it is not the subject that I feel I have grown the most in this semester. I feel that I have grown a lot in my understanding of logic. When we did logic problems in the beginning of the year, I was very confused and had no idea what was true and what was false. But by the end of the semester I understood how logic related to math. I figured out how to tell which statement was true and which was false because I realized that everything was in terms of negative and positive. So I understood which combination of negatives and positives made something true or false. I have not necessarily mastered this skill, but I think I have grown the most in understanding it.
- The explorations that we did this year helped me learn in a different way than I’m used to. We got a bit of base information on the subject of the exploration, then we set out to figure out the different word problems and puzzles. If we really didn't understand something we could ask our peers. This was a good experience for me because it gave me a chance to figure out how to do things on my own. It taught me how to learn something by myself and with using my peers and resources. It made my brain work through things step by step and turned math into one big puzzle. Explorations were very challenging for me because it was a different way of learning but it did help me understand a lot. The discussion were great because if I hadn't figured out a problem yet, then it would be explained and I could see what I did wrong. It was also useful to see how other people solved a problem so I could get a different perspective on the problems.
- One problem that was very difficult for me was POW #6. I never solved this pow. The reason I was confused by this problem was because I didn’t know how to make the graph to scale without making it really tiny. When I tried that, I still couldn’t see how to find out the area or even the side length of the square below the line. Since it seemed that the two right vertices of the square were in between 1 and 2 on the graph but closer to two, I just estimated that the length of the square was 1.75. But after I estimated that, I didn't have to do much work to figure out the rest. Because of that, I felt like I did something wrong. There must have been more work to the problem than that. In the end, I was still very confused about the POW and I had a feeling that I didn't quite go about solving it the right way.