.The purpose I feel like was given during the entire week during working on the puzzles and watching the videos was to go over sort of like an introduction to the class before we start working on the puzzles and problems we're given. I feel that the week spent in introducing us to what kinds of things and ways the teacher taught us were very beneficial. That's the case because when you know how your teacher does things, you're better prepared for the future lessons and socially as well.
The two quotes I chose from watching the videos were ones that I found to be motivational to me in a way. I'll simply be paraphrasing mainly because at the time I'm writing this I can't watch anything. The first one was something along the lines of "No one is born being able to do math," and I found that to be uplifting because whenever I think about the times before now, it gets fairly bothersome. When I was younger, the stereotype that Asians were good at math was still there. I used to be, for a time. Then when I got to middle school, my grades dropped so fast they broke through the ground. That's when I first learned that yes, grades can drop despite stereotype. Ever since then, I've had a hard time lifting them back to what they used to be in elementary school. Surprise! I used to be a straight A student! But basically skipping past all my past experiences, being able to acknowledge that although I may not feel as well versed in math as I do in my other subjects, I still can work to make sure that I end up with a good grade and actually end up properly soak in the methods to solving these problems.
O.Q
The problem I chose out of the options was Tiling a 11 x 13 Rectangle, the first problem of the week we started on. What the objective was is we had to cut up the rectangle into segments. The challenge was to do it in the least amount of squares possible, and be able to be confident in our answer. The main reason why I chose this problem is I feel like I was the most productive on this problem in particular, and that It'd be the least complicated to explain due to it not exactly being my forte. Tiling a 11 x 13 rectangle was an interesting experience because finding the smallest amount of squares able to be found in the rectangle had me question if we were supposed to draw out a specific pattern in the first place. I questioned to myself whether we had to set all the squares in a spiral shape or if we were supposed to set it a certain way. Regardless, we were able to recreate it in different manners so long as we didn't overlap the squares. As you can see in the image below, I did what looks like three, but is actually several compiled into what you see now. This is due to the face that I would constantly experiment on the rectangle used at the time. I would have had more set as examples, but I didn't have much space to begin with. Thankfully however, I still remember all the experiments I did on them so I'll be able to transcribe them here.
For the first rectangle, I originally wanted to start my largest as 8 x 8, but I quickly found out that if I wanted to reduce the amount of 1 x 1 squares made I'd have to try something else. I did my best to avoid 1 x 1 squares because they were the quickest way to hike up the amount of individual squares made in a 11 x 13 space. So as a result, I simply reduced 8 x 8 into 7 x 7 which seemed to work significantly better. From the 7 x 7, I used the remaining space it gave me to slowly cut off section by section until the point where I reached simply making a singular 1 x 1 square. My total amount of squares cut in that one was only 6. The 8 x 8 square process I was talking about earlier is actually the third one! So if you're ever wondering what that ended up looking like, it's right there. The amount of 1 x 1 squares is what I meant when it came to reducing the amount found. In total, thirteen squares were found for that one. The last one is the rectangle in the center. I figured that if you want a smaller amount, first try to cover as much ground with the first one as possible, which is what happened. The largest possible square in those conditions would be size 11 x 11. If it got any bigger, then it would surpass the 11 x 13 criteria and thus be null. From that point, I'd only be able to make 2 x 2 or 1 x 1 squares. I thought it would result in a smaller number, when in fact it increased it by a mere two squares.
Just a little note, I thought of what would happen if the square I had in the middle be a few units sparse than the 11 x 11 square such as a 10 x 10, and quickly determined that it would be a smart idea only if I was trying to find a large quantity of 1 x 1 squares and following along with it, a higher square quantity.
A challenge I faced while working on it has got to be planning out the squares so that I wouldn't end up pulling any unnecessary steps or necessary otherwise on or off the rectangle. It was moderately difficult to keep track of which squares were occupied before sketching it out mainly due to the worry that it wouldn't be the most efficient route. Another issue I came across was the minor worry that my answers wouldn't be the same as my peers and I'd be ridiculed if it turned out my rectangles had a lot more squares than theirs did. I was able to come over it, for the first one holding the places where the squares were and maintaining the spots in my head. As for the second problem, my solution's a lot more personal so I won't be saying anything about that.
The habit of a mathematician that I used would have to be experimentation & play, because this involved a lot of experimentation and messing around in order to get the results I wanted. This kind of problem is a lot different from the standard equation only in the way that it's displayed as an interactive visual piece where it's more hands-on rather than a line of mathematical terms that you have to dance around in order to find a solution to. Both of them can be experimented on, but because the problem is a visual you have no trouble moving it around without worrying that you lose track of it.
Overall, I feel that this project was a very interesting start to a grade. I was sort of confused to begin with when the week started so I'll be honest and say that I didn't really put as much effort into the work as I normally would with something else. That doesn't mean I didn't put any effort into it, however. Of course I worked on it, otherwise I wouldn't be here, typing my night away. Small complications aside, I don't really think that this first week will predict my effort and participation in math for the future parts of the year simply because this is just the beginning. It's like pushing a cart down a hill from the top. Once you give it that little boost, it'll begin rolling down the hill. It won't go at top speed just yet, but gradually as it goes down it'll get faster and faster, and essentially that's my metaphor for the fact that we've only just begun after an entire summer devoted to rest. So therefore, I believe that I'll be able to work a lot more efficiently throughout the year as I regain my grasp on math.
Let's start off the year with a bang!
The two quotes I chose from watching the videos were ones that I found to be motivational to me in a way. I'll simply be paraphrasing mainly because at the time I'm writing this I can't watch anything. The first one was something along the lines of "No one is born being able to do math," and I found that to be uplifting because whenever I think about the times before now, it gets fairly bothersome. When I was younger, the stereotype that Asians were good at math was still there. I used to be, for a time. Then when I got to middle school, my grades dropped so fast they broke through the ground. That's when I first learned that yes, grades can drop despite stereotype. Ever since then, I've had a hard time lifting them back to what they used to be in elementary school. Surprise! I used to be a straight A student! But basically skipping past all my past experiences, being able to acknowledge that although I may not feel as well versed in math as I do in my other subjects, I still can work to make sure that I end up with a good grade and actually end up properly soak in the methods to solving these problems.
O.Q
The problem I chose out of the options was Tiling a 11 x 13 Rectangle, the first problem of the week we started on. What the objective was is we had to cut up the rectangle into segments. The challenge was to do it in the least amount of squares possible, and be able to be confident in our answer. The main reason why I chose this problem is I feel like I was the most productive on this problem in particular, and that It'd be the least complicated to explain due to it not exactly being my forte. Tiling a 11 x 13 rectangle was an interesting experience because finding the smallest amount of squares able to be found in the rectangle had me question if we were supposed to draw out a specific pattern in the first place. I questioned to myself whether we had to set all the squares in a spiral shape or if we were supposed to set it a certain way. Regardless, we were able to recreate it in different manners so long as we didn't overlap the squares. As you can see in the image below, I did what looks like three, but is actually several compiled into what you see now. This is due to the face that I would constantly experiment on the rectangle used at the time. I would have had more set as examples, but I didn't have much space to begin with. Thankfully however, I still remember all the experiments I did on them so I'll be able to transcribe them here.
For the first rectangle, I originally wanted to start my largest as 8 x 8, but I quickly found out that if I wanted to reduce the amount of 1 x 1 squares made I'd have to try something else. I did my best to avoid 1 x 1 squares because they were the quickest way to hike up the amount of individual squares made in a 11 x 13 space. So as a result, I simply reduced 8 x 8 into 7 x 7 which seemed to work significantly better. From the 7 x 7, I used the remaining space it gave me to slowly cut off section by section until the point where I reached simply making a singular 1 x 1 square. My total amount of squares cut in that one was only 6. The 8 x 8 square process I was talking about earlier is actually the third one! So if you're ever wondering what that ended up looking like, it's right there. The amount of 1 x 1 squares is what I meant when it came to reducing the amount found. In total, thirteen squares were found for that one. The last one is the rectangle in the center. I figured that if you want a smaller amount, first try to cover as much ground with the first one as possible, which is what happened. The largest possible square in those conditions would be size 11 x 11. If it got any bigger, then it would surpass the 11 x 13 criteria and thus be null. From that point, I'd only be able to make 2 x 2 or 1 x 1 squares. I thought it would result in a smaller number, when in fact it increased it by a mere two squares.
Just a little note, I thought of what would happen if the square I had in the middle be a few units sparse than the 11 x 11 square such as a 10 x 10, and quickly determined that it would be a smart idea only if I was trying to find a large quantity of 1 x 1 squares and following along with it, a higher square quantity.
A challenge I faced while working on it has got to be planning out the squares so that I wouldn't end up pulling any unnecessary steps or necessary otherwise on or off the rectangle. It was moderately difficult to keep track of which squares were occupied before sketching it out mainly due to the worry that it wouldn't be the most efficient route. Another issue I came across was the minor worry that my answers wouldn't be the same as my peers and I'd be ridiculed if it turned out my rectangles had a lot more squares than theirs did. I was able to come over it, for the first one holding the places where the squares were and maintaining the spots in my head. As for the second problem, my solution's a lot more personal so I won't be saying anything about that.
The habit of a mathematician that I used would have to be experimentation & play, because this involved a lot of experimentation and messing around in order to get the results I wanted. This kind of problem is a lot different from the standard equation only in the way that it's displayed as an interactive visual piece where it's more hands-on rather than a line of mathematical terms that you have to dance around in order to find a solution to. Both of them can be experimented on, but because the problem is a visual you have no trouble moving it around without worrying that you lose track of it.
Overall, I feel that this project was a very interesting start to a grade. I was sort of confused to begin with when the week started so I'll be honest and say that I didn't really put as much effort into the work as I normally would with something else. That doesn't mean I didn't put any effort into it, however. Of course I worked on it, otherwise I wouldn't be here, typing my night away. Small complications aside, I don't really think that this first week will predict my effort and participation in math for the future parts of the year simply because this is just the beginning. It's like pushing a cart down a hill from the top. Once you give it that little boost, it'll begin rolling down the hill. It won't go at top speed just yet, but gradually as it goes down it'll get faster and faster, and essentially that's my metaphor for the fact that we've only just begun after an entire summer devoted to rest. So therefore, I believe that I'll be able to work a lot more efficiently throughout the year as I regain my grasp on math.
Let's start off the year with a bang!