Tuesday, July 23, 2013

Lesson Learned

Today's Puzzler was one of the hardest. I don't necessarily agree it is the hardest one we have done., but it is definitely up there. Dawson told us that no class has ever solved it without him pushing us in the correct direction. It was another hat puzzle: There is a prison colony in the South Pacific with 12 prisoners and a twisted warden. He tells the prisoners he has a game they can play the next day. Each participant will have a hat placed on his head, and they will all be lined up just like before, so that each person can see the people in front of them. There are yellow hats and white hats. If the prisoner is able to guess what color their hat is, then he is released. If not, he is thrown to the sharks. The prisoners can only say yellow or white, nothing else. The prisoners get to think about participating overnight, and one of them comes up with a plan that guarantees that at least 11 out of 12 of them will be set free. They draw straws for who will be the 12 person. What is the plan, and why do they have to draw straws? As always, STOP reading if you want to solve the puzzle yourself. 

Eventually Dawson dropped the hint that it depends on what type of number of hats is left. We then figured out that the person in the back could be giving a code. If he sees an odd number of yellow hats, he would say yellow. If he sees an even number of yellow hats, he says white. Then the person in front knows his hat color. If the back man said yellow, and the person in front of him sees an odd number of hats, he knows his is white. If he sees an even number of yellow hats, he knows his hat is yellow. Everyone is guaranteed safety (if they pay attention) except for the back person. The back person has a 50-50 chance of surviving.  Therefore, 11 are guaranteed safety, and the 12 has a 50-50 chance. 

After the Puzzler, we had our first of four student lessons for the day. The first lesson was on the Angles of a Polygon. The first Missions Holder's task was to talk as much as possible. The Second Mission Holder (Me) had to pack up five minutes early, and not do any work after that point. The Academic Mission Holder mixed up interior and exterior angles. Overall, I thought his lesson went pretty well. The teacher's explanations were good, and when students misbehaved, he made them come to the board and do work. (Sometimes, he made them write the notes on the board, other times they had to solve problems.) When I packed up early, I made sure it was really obvious, and even put my backpack on. He sent me up the to the board to solve the difficult problem he just wrote on the board. He gave me 30 seconds. I knew what to do, and almost finished, but when the time ended, he sent me back to my seat, telling me to get out my notebook again. Then he proceeded to erase all my correct work, and redo the problem himself for the class. I thought he should have just left it up, but he was the teacher, not me. 

The next lesson was on the Pythagorean Theorem. The First Mission Holder (Me again) had to lose interest, and read a book. (Dawson gave me The Catcher in the Rye.) I got caught after about 15 minutes, and the teacher took the book away, so I started reading my math textbook. She told me to close the book 4 times throughout the rest of the lesson, but she never took it. The Second Mission Holder already knew all the material, and wanted harder problems. The teacher did not handle this very well. The problems she gave were not much harder than the regular ones. The Academic Mission Holder always added the squares of the two given sides, even if the hypothenuse was given. The teacher really tried to make the lesson interesting, and I actually had a hard time staying focused on my reading. She started the lesson with a song about the Pythagorean Theorem, and at the end showed a Who Wants to be a Millionaire clip where a contestant lost $15,000 because he did not know the Pythagorean Theorem. 

After this lesson, Dawson started us on the "Unknown Area Project." We were divided into 4 groups. I was with Alex and Brenden. Each team was given a poster board with a obscure combination of shapes, made into one megashape. Our first task was to find the area of the shape.  In the 30 minutes we had before lunch, my group was able to divide up, and calculate the area of the shape. We actually did all this, and had 5 minutes left, but Dawson told us to wait to cut it until after lunch.

After lunch we had two more lessons. The first was on Right Triangle Trigonometry. The first Mission Holder was another know it all, who always had an answer almost immediately. After a while, the teacher got pissed off, and gave him a hard problem to do. I thought this was a great solution. It kept him busy while the teacher taught the rest of the lesson. The Academic Mission Holder got the Opposite, Adjacent, and Hypotenuse mixed up. In my opinion, this lesson did not go that well. To start off with, the teacher showed us Sin, Cos and Tan. That worked fine, but when he showed us the inverses, it fell apart. He found an angle with one method, but did not get the same answer using a different method. It turned out that the side lengths did not make a right triangle. Once I pointed that out to him, he fixed it, and did not make the mistake again. (Dawson told us afterwards that his lesson plan was full of false right triangles, so the rest of the problems were changed on the fly.) Also, he did not give a hard problem for the know it all until class was almost over.

The last lesson of the day was my favorite, because we were laughing almost the whole time. The lesson was on Inscribed Angles. The first Mission Holder had to try to engage the teacher in conversation to get her off task. The teacher handled this very well, saying her work life is separate from her personal life, so she does not talk about it with her students. After a while, she sent the student to the corner of the room, as far away from her as possible. The second Mission Holder had to have issues with a difficult problem. The student took it to the extreme, and water to make it look like he was crying over the problem. We all knew it was fake, so we could not stop laughing for over 2 minutes. The teacher handled this well, and let him go outside to "calm down." The Academic Mission Holder would forget to divide by two when converting an arc measure to an inscribed angle measure. The lesson was hilarious, because all the students saw Mission Holder #2 preparing his tears. The teacher did not notice what was going on, but we could not stop laughing. The answer to one of the problems was mAC =12 degrees. The second Mission Holder made a comment that that was awful cool to be running the AC. (Haha...) Just in general, the second Mission Holder made the class funny. This was by far my favorite lesson. It was lots of fun, but also somewhat challenging.

Our Megashape!
During Study Hall, we finished the Unknown Area Project. Our group was done after 15 minutes. We then cut out the object, and weighed the scraps. Dawson had already cut an weighed a whole poster board, so we found the weight of our object. We then calculated what percent of the area of the poster board was covered, and what percentage of the mass was used in the object. We were off by 1.7%. Dawson told us that in his Honors Geometry class (which he gives this project), he multiplies the error percent by 5, and subtracts it from 100% to get your grade. After we finished, we talked until Study Hall ended at 4 PM.

Our pile of scraps to weigh.
From 4 to 6, we had to spend time with our proctor groups. All three of the third floor proctor groups got together and played games on the Wyatt lawn. We started with Capture the Flag, but there was also a smaller group playing football. We ended up playing four games of Capture the Flag. This time my team won them all. I actually enjoyed this round of Capture the Flag more. (Not just because we won.) With fewer people, the game gets more strategy based. Losing one person is a much bigger deal in a small game. After four games of Capture the Flag, people started to lose interest. We were going to play another round with a bigger field (the area from Hank to the Wyatt lawn), but we did not have enough time. We ended up playing a quick game of soccer instead. After this fun-filled time with my floor mates, we headed to dinner.

Tomorrow is going to be a great day. We have the final two student lessons and a lecture on Game Theory in the morning. In the afternoon, we have the Poker Tournament, and afterwards a class trip to Ben and Jerry's. Tomorrow evening, we have the VSA Talent Show. Once again, the only bad part is that means there are 2 days left of VSA.

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