Problem Statement:
The around kings Arthur table task was to find out a general rule or pattern to show which chair a knight should try to sit on in order to become the winner of the game. The way the game worked was by having King Arthur going around the table in a order of saying you are in and the next one you are out, and so on, he would skip a space if he already said you are out and the space was empty. The knights that are out are removed from the round table, and the rest stay in until King Arthur says, “You’re out.” and there's only one knight left than the mean the only one left is the winner. The last knight remaining at the round table is the winner of the evening. There is a different winning “seat” depending on the number of knights there are, and in order to figure out which chair a knight should sit in to become the winner, one must find a pattern or formula. The task was to find a formula and a solution with our group and test if or theory worked.
Process:
For the processes the first thing that my group and I attended was by making a sort of list and table in order to find a pattern and from there make a theory. We first started by listing the first 16 chairs from 1 knight to 16 knights around the table, and basically just just used our own thinking and doing and we went around the table in a order of you are in and you are out and from there we kinda found a pattern that was difficult to define with a formula. But we decide that if we maybe added more chairs we could find something else so we continued the list to 31 knights around the round table. We noticed that the winning seat is always an odd number, and that there is a pattern at the start of each power of 2 number of knights, for example 21 =2 knights 22 =4 knights 23 =8 knights, 24 = 16 knights. And that was one of the most steps we had taken as a group during this problem we also talked about how when the number of knights is a power of 2, the pattern starts from 1 again the pattern begins at 2, 4, 8, 16, and will again at 32.
Something else that we found and it was something really helpful was that at the start of the pattern we had founded, the difference would always be always 1 less than the number of knights. For example, if we had 8 knights around the table, the winning seat would be 7 less than the number of knights 8 - 7 = 1. The next winning seat has a difference of 2 less than the number of knights.
Solution:
Towards working for the solution of this problem it was still kinda hard for my group and I to find a actual formula that worked, because there could be multiple ones and once my group and i found one that we thought it would work we showed our teacher and said that's a good one but there could be some other ones or is that the most effective one.? but finally what my group and i came up with was a way to being able to tell which one was the winning chair to sit on, even if the knights sitting number was eight or one hundred. What we did was subtracted from our peer which are the number of knights the largest power of two less than it, and then we times that answer by two, and then we added one. The actual rule people can follow to see if the seat a knight should try to sit in is by trying to look for the biggest power of two that is less than the number of knights than front that they subtract that number from the number of knights in the circle and than times that number by two. And finally add one to the answer This is the final and most effective rule that can easily be use and put to work if you are able to get number count or see how many knight are or might sit in the cahr in this case around king arthur's table.
Evaluation/Reflection:
Something that definitely pushed my thinking during this mini problem was seen how my whole group was so intrigued into learning more about it and actually finding a solution and engaging everyone to take part and share our very own ideas and thoughts. Some of the ways I was challenged were many ways, such as being the one that doesn't really share and stayed the quietest was very challenging to me when it came to asking questions and sharing ideas. Also keeping track and not forgetting about what he just went over was a challenge because I would forget the next day.
Mathematically I was a bit challenged when we drew our graphs to show the chairs and the knights because sometimes they would come out a bit messy. For sure I would be able to recognize when I am not doing something correctly and when I need help on something because I don't that I would just stay stuck and stayed in the same spot without moving forward because I wouldn't know what to do. Sometimes I am a bit shy when it comes to asking for help but most of the time I don't get something I ask or try to have a conversation with someone to maybe feel more confident when I ask the actual question or when I ask for help. Some of the thing that I feel I do better it's helping other in fact sometimes I don't know why but I think it's just in my natural habit to always put other and help others before helping myself. I would say that sometimes it's not as good to help other that much before helping yourself because then who is gonna help you, but definitely,
I would 100 percent help other people around me with anything they need help on. Honestly at first I thought that the group that we were assigned to wasn't gonna work out pretty well and the reason for that was because of the people in it, for example, I thought well me I am just gonna be the silent waiting for others to come up with the answer so I could copy it down but actually I don't do that I was trying my best to share thoughts and ideas and also ask question and the reason for that was because the group was pushing everyone to contribute and if some one sint gt something we would take time and go back and don't move from there till everyone got it. Then, we had nick I thought he wasn't gonna do anything because he was shy to ask or share ideas but no he always shared and asked if he needed, then we had beto I thought he was just gonna do everything and not share the air and not let other share butch did the opposite, he would step back and bring everyone into the conversation and re explain if something doesn't make sense, and then we had nayeli I felt like sometimes she was a bit unfocused because she was the only girls in the group and she felt weird but at the end I really liked how she was sharing ideas and explaining stuff to me and nick if we didn't get them and also stepping a lot into the conversation. So the thing the group we got worked effectively because other than work we had a great tie and it was a really fun cool experience doing it in this group and at the same time we learned and got a lot from the activity.
I feel like the group quiz did not affect me at all but in fact, helped me ad my group interact better with each other and having everyone instead of one person sharing and talking. If I was to grade myself I would give me a plus because we did everything we had to do and the group worked really well with each other and we had lots of fun, it felt like a really good working place/ environment.
The around kings Arthur table task was to find out a general rule or pattern to show which chair a knight should try to sit on in order to become the winner of the game. The way the game worked was by having King Arthur going around the table in a order of saying you are in and the next one you are out, and so on, he would skip a space if he already said you are out and the space was empty. The knights that are out are removed from the round table, and the rest stay in until King Arthur says, “You’re out.” and there's only one knight left than the mean the only one left is the winner. The last knight remaining at the round table is the winner of the evening. There is a different winning “seat” depending on the number of knights there are, and in order to figure out which chair a knight should sit in to become the winner, one must find a pattern or formula. The task was to find a formula and a solution with our group and test if or theory worked.
Process:
For the processes the first thing that my group and I attended was by making a sort of list and table in order to find a pattern and from there make a theory. We first started by listing the first 16 chairs from 1 knight to 16 knights around the table, and basically just just used our own thinking and doing and we went around the table in a order of you are in and you are out and from there we kinda found a pattern that was difficult to define with a formula. But we decide that if we maybe added more chairs we could find something else so we continued the list to 31 knights around the round table. We noticed that the winning seat is always an odd number, and that there is a pattern at the start of each power of 2 number of knights, for example 21 =2 knights 22 =4 knights 23 =8 knights, 24 = 16 knights. And that was one of the most steps we had taken as a group during this problem we also talked about how when the number of knights is a power of 2, the pattern starts from 1 again the pattern begins at 2, 4, 8, 16, and will again at 32.
Something else that we found and it was something really helpful was that at the start of the pattern we had founded, the difference would always be always 1 less than the number of knights. For example, if we had 8 knights around the table, the winning seat would be 7 less than the number of knights 8 - 7 = 1. The next winning seat has a difference of 2 less than the number of knights.
Solution:
Towards working for the solution of this problem it was still kinda hard for my group and I to find a actual formula that worked, because there could be multiple ones and once my group and i found one that we thought it would work we showed our teacher and said that's a good one but there could be some other ones or is that the most effective one.? but finally what my group and i came up with was a way to being able to tell which one was the winning chair to sit on, even if the knights sitting number was eight or one hundred. What we did was subtracted from our peer which are the number of knights the largest power of two less than it, and then we times that answer by two, and then we added one. The actual rule people can follow to see if the seat a knight should try to sit in is by trying to look for the biggest power of two that is less than the number of knights than front that they subtract that number from the number of knights in the circle and than times that number by two. And finally add one to the answer This is the final and most effective rule that can easily be use and put to work if you are able to get number count or see how many knight are or might sit in the cahr in this case around king arthur's table.
Evaluation/Reflection:
Something that definitely pushed my thinking during this mini problem was seen how my whole group was so intrigued into learning more about it and actually finding a solution and engaging everyone to take part and share our very own ideas and thoughts. Some of the ways I was challenged were many ways, such as being the one that doesn't really share and stayed the quietest was very challenging to me when it came to asking questions and sharing ideas. Also keeping track and not forgetting about what he just went over was a challenge because I would forget the next day.
Mathematically I was a bit challenged when we drew our graphs to show the chairs and the knights because sometimes they would come out a bit messy. For sure I would be able to recognize when I am not doing something correctly and when I need help on something because I don't that I would just stay stuck and stayed in the same spot without moving forward because I wouldn't know what to do. Sometimes I am a bit shy when it comes to asking for help but most of the time I don't get something I ask or try to have a conversation with someone to maybe feel more confident when I ask the actual question or when I ask for help. Some of the thing that I feel I do better it's helping other in fact sometimes I don't know why but I think it's just in my natural habit to always put other and help others before helping myself. I would say that sometimes it's not as good to help other that much before helping yourself because then who is gonna help you, but definitely,
I would 100 percent help other people around me with anything they need help on. Honestly at first I thought that the group that we were assigned to wasn't gonna work out pretty well and the reason for that was because of the people in it, for example, I thought well me I am just gonna be the silent waiting for others to come up with the answer so I could copy it down but actually I don't do that I was trying my best to share thoughts and ideas and also ask question and the reason for that was because the group was pushing everyone to contribute and if some one sint gt something we would take time and go back and don't move from there till everyone got it. Then, we had nick I thought he wasn't gonna do anything because he was shy to ask or share ideas but no he always shared and asked if he needed, then we had beto I thought he was just gonna do everything and not share the air and not let other share butch did the opposite, he would step back and bring everyone into the conversation and re explain if something doesn't make sense, and then we had nayeli I felt like sometimes she was a bit unfocused because she was the only girls in the group and she felt weird but at the end I really liked how she was sharing ideas and explaining stuff to me and nick if we didn't get them and also stepping a lot into the conversation. So the thing the group we got worked effectively because other than work we had a great tie and it was a really fun cool experience doing it in this group and at the same time we learned and got a lot from the activity.
I feel like the group quiz did not affect me at all but in fact, helped me ad my group interact better with each other and having everyone instead of one person sharing and talking. If I was to grade myself I would give me a plus because we did everything we had to do and the group worked really well with each other and we had lots of fun, it felt like a really good working place/ environment.