The StairCase Problem SLC
I feel that the “Staircase Problem” POW was the one problem of the week where I grew the most in terms of examining what a problem is asking, figuring out multiple equations and narrowing my work down into one formula. An example would be that my formula N(N+1)/2 was totally different than a fellow class mates formulas. The solutions that I figured out were: 5,050 Legos are needed to create 100 levels, 140 floors being the closest you can get before going over the 10,000 Legos, at 140 floors 9,870 Legos would be used and 130 would be left over. This can reflect into my math performance this semester because with each assignment given I tried my best and usually succeeded in creating accurate and quick formulas/equations. I feel that in comparison to my current math class and 10th grades math class, I have accomplished so much more in my current class such as grasping greater understandings for complex problems and questions. I am most proud that I figured out an equation for the Staircase Problem on my own before a lot of people even understood what the problem was asking us to do. What I have learned from both this POW and semester of math class is that what can sound like an easy problem to solve, in the end can be very tedious, time consuming and hard work. Two Habits of a Mathematician I used were being patient and persistent through the trial and error process. I had to also visualize what the staircase would look like at x amount of blocks in order to see if my final answer would look correct. This problem has changed my perspective of math by allowing me to realize that what could look like an easy problem to figure out could be the exact opposite and require a lot of thought and effort. I feel that I connected to the math this semester and during this POW because some of it has been a challenge and an enjoyable experience for me. I don’t mean challenging as in hard or unsolvable but, you did have to think for a while on the worksheets assigned in class and homework. Although I do feel like I am a fairly good mathematician, I feel that one major aspect I could improve on is expanding my thoughts on fabricating equations and formulas. Usually when given a problem such as this POW, I will sometimes just think of formulas that were used in the past and try to see if they could work with the question given. The problem with this is that it will usually take more time to relate formulas than just thinking on the question given alone and making one yourself. In the future I plan on fabricating more of my own formulas by thinking more in depth and asking more questions during class to clarify my thoughts.
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File Type: | rtf |