Geometry POL Prep - Semester 1 Reflection
Geometry Skills
In Geometry this semester, the one topic I feel I have really mastered would definitely be the Pythagorean Theorem. At the beginning of the year, I already had a fairly firm grasp on how and when to use it, but Aliza has effectively taught me where to use it. It’s surprising how many different ways one equation can be used. The activities that most taught me where to apply the Pythagorean Theorem were the POW’s, which stands for Problem Of the Week. Every week, Aliza assigns us with a new POW, and each one teaches us how to use the Pythagorean Theorem, or another equation, in a new way. Another activity that was useful for learning the Pythagorean Theorem was the Explorations. These were the lists of math problems that we used to learn how to use the equations we added to our repertoire. Every time the exploration was due, then we would discuss it as a group, making sure that everybody understood each problem. I know I’ve mastered the Pythagorean Theorem because I can use it to problem solve. For example, if I can’t figure out a math problem, I can look and see if the Pythagorean Theorem will be useful. It’s a new way of thinking in my tool box. I definitely feel like the Pythagorean Theorem is my strong spot this semester.
We had something called Explorations this semester. They were a set of about ten problems that we had to finish and then discuss with the class in groups. Their most useful assistance for me was helping me learn how to problem solve with the Pythagorean Theorem. Every week, the Exploration was the next new challenge to overcome. My least favorite part about them was that they made everything seem jam-packed, like it was just too much. But they also gave me new problems to experiment and play with, especially when I didn’t have anything better to do. Overall, Explorations were like a breath of fresh air every week.
My favorite breakthrough moment was when I finally understood logic. It was like the clouds cleared and I was just like, “Oh! I get it!” I was actually redoing some work that I’d lost, and I just ‘got it.’ I was helped by the redoing, and now I’ve learned that, as Thomas Palmer once said, “If you don’t succeed, then try try again.” It kind of made me feel like I could do anything. And now I have logic in my repertoire.
We had something called Explorations this semester. They were a set of about ten problems that we had to finish and then discuss with the class in groups. Their most useful assistance for me was helping me learn how to problem solve with the Pythagorean Theorem. Every week, the Exploration was the next new challenge to overcome. My least favorite part about them was that they made everything seem jam-packed, like it was just too much. But they also gave me new problems to experiment and play with, especially when I didn’t have anything better to do. Overall, Explorations were like a breath of fresh air every week.
My favorite breakthrough moment was when I finally understood logic. It was like the clouds cleared and I was just like, “Oh! I get it!” I was actually redoing some work that I’d lost, and I just ‘got it.’ I was helped by the redoing, and now I’ve learned that, as Thomas Palmer once said, “If you don’t succeed, then try try again.” It kind of made me feel like I could do anything. And now I have logic in my repertoire.
Content Skills
I think my best habit, as a mathematician, is to generate ideas. I like making plans, but sometimes I don’t follow them. For example, I used the Pythagorean Theorem when last year I would have been unable to think of using that equation on that problem. Also, on the extra credit POW, only a few days ago, everyone I spoke with couldn’t figure the problem out. I just decided to draw it as precisely as I could, and leave it as that.
I feel like I have a lot of room to grow in recognizing problems. I think that’s why I’ve gotten some of the problems I’ve gotten wrong wrong. My eyes just glaze over and I just assume it’ll be okay. The reason I never notice these problems, however, is fixable. If I quit surrounding myself with distractions, such as music, I might not be so inattentive toward mistakes. An example of my distantness from the world is that I didn’t notice for about two months, one of my friends and I are a terrible team. We just don’t work well together, and we both always end up distracted. This is a very major problem, but it is fixable.
I feel like I have a lot of room to grow in recognizing problems. I think that’s why I’ve gotten some of the problems I’ve gotten wrong wrong. My eyes just glaze over and I just assume it’ll be okay. The reason I never notice these problems, however, is fixable. If I quit surrounding myself with distractions, such as music, I might not be so inattentive toward mistakes. An example of my distantness from the world is that I didn’t notice for about two months, one of my friends and I are a terrible team. We just don’t work well together, and we both always end up distracted. This is a very major problem, but it is fixable.
POW's
In POW's, or problem's of the week, we were testing the skills that we had recently learned.
Problem of the Week 8
Due Friday, December 11
Four mathletes, Brianna, Andy, Courtney and Brandon, competed in the finals of the Animas High School Math Bowl. Prizes were awarded for the top three competitors as follows: first place received an anniversary Math Faculty Pink Tie, second place received a book of Brain Teasers, and third place received an “I Love Math” T-shirt.
Three staff members of AHS predicted how the prizes would be awarded.
It turns out that each staff member predicted exactly one prize winner correctly.
Determine precisely how the prizes were awarded.
In this POW, we were trying to figure out who got what.
I had absolutely no idea what it was going to be. Because Lauren and Hannah both guessed that Courtney was going to get the T-shirt, that means that they were both wrong. That means that Brandon has to get the T-shirt, because he was the only other option. We now know that anything else Aliza said was untrue, because each teacher was only correct once. We also know that Brandon could only get one prize, so he and Courtney are both out of the equation altogether. Therefore, the only other options are for Andy to get the book and Brianna to get the tie.
Brandon got the t shirt, which Aliza predicted.
Andy got the book, which Lauren predicted.
Brianna got the tie, which Hannah predicted.
This is the only answer that is logical. There is no other way to reason that I could find.
Due Friday, December 11
Four mathletes, Brianna, Andy, Courtney and Brandon, competed in the finals of the Animas High School Math Bowl. Prizes were awarded for the top three competitors as follows: first place received an anniversary Math Faculty Pink Tie, second place received a book of Brain Teasers, and third place received an “I Love Math” T-shirt.
Three staff members of AHS predicted how the prizes would be awarded.
- Lauren predicted that Brandon would win the pink tie, Andy would win the book and Courtney would win the T-shirt.
- Hannah predicted that Brianna would win the pink tie, Brandon would win the book and Courtney would win the T-shirt.
- Aliza predicted that Andy would win the pink tie, Brianna would win the book and Brandon would win the T-shirt.
It turns out that each staff member predicted exactly one prize winner correctly.
Determine precisely how the prizes were awarded.
In this POW, we were trying to figure out who got what.
I had absolutely no idea what it was going to be. Because Lauren and Hannah both guessed that Courtney was going to get the T-shirt, that means that they were both wrong. That means that Brandon has to get the T-shirt, because he was the only other option. We now know that anything else Aliza said was untrue, because each teacher was only correct once. We also know that Brandon could only get one prize, so he and Courtney are both out of the equation altogether. Therefore, the only other options are for Andy to get the book and Brianna to get the tie.
Brandon got the t shirt, which Aliza predicted.
Andy got the book, which Lauren predicted.
Brianna got the tie, which Hannah predicted.
This is the only answer that is logical. There is no other way to reason that I could find.