Week of Inspirational Math Questions
1. What was the purpose of this week of investigations and video-watching?
The purpose of this week's investigations and video watching was to convey a strong message towards us. This message was to strengthen our self confidence and make us realize you can solve any math problem in any matter of time, or make a mistake on a math problem. We watched a series of videos that told us how our mind works when we are problem solving or thinking and they explained how to resolve or move forward from a math problem. Next we tackled four activities that made us problem solve and to spark collaborate with our group members. We needed to learn how to collaborate and to be inquisitive with our partners. One video that I took the most away from was a learning video that taught me that the amount of time it takes you to solve a problem does not determine your skill set. I will definitely take this lesson and use it to approach future problems.
2. Give an overview of all the activities and videos.
The intro mindset video was very beneficial for me because there are times where I was in the bad situation of the video where they teach you what not to do. Now I know how to overcome a situation while working with my classmates because of the videos we watched in class and the activities we worked together on. For example with the Mistakes video, I can personally relate to and utilize the message because of how many times I have felt defeated from several problems and I felt as if my own skill level was stopping me from accomplishing this task. Another video we watched in class was the “Speed is not important video” and this video I could also relate to because of how many times I felt like the odd one out, from the amount of time it took another to finish a problem correctly. From the last video we watched in class I now know if I ever feel that a problem is not accomplishable, then I will draw, or find another way visually to better understand a problem and accomplish it in sections. I took a lot away from these videos and have learned that new ways to accomplish and better understand a math problem. Plus, I am going to focus on asking more questions because it's not a bad thing to be inquisitive, in fact I learned that it benefits you more than anything. The stacked marshmallow experiment was not hard because I have had experience working with my table group before, so when we all work together, we were proud of our collaborative effort. But of course group communication is something I feel a lot of people need to work on including myself. I really enjoyed the squares to stairs activity and the hailstone sequence because I love trying to find a pattern in a sequence or a series of objects. I found the pattern of the squares of stairs pattern and I was proud that I tried to find other ways to determine the pattern. The painted cube activity was a challenge for me because I kept dwelling on this problem even though the answer was so clear for everyone else, but that proved to me that the time of you accomplishing a problem does not matter.
3. Choose two messages from any of the five videos we watched.
Explain the personal significance of those two messages.
The intro mindset video was very beneficial for me because there are times where I was in the bad situation of the video where they teach you what not to do. Now I know how to overcome a situation while working with my classmates because of the videos we watched in class and the activities we worked together on. For example with the Mistakes video, I can personally relate to and utilize the message because of how many times I have felt defeated from several problems and I felt as if my own skill level was stopping me from accomplishing this task. Another video we watched in class was the “Speed is not important video” and this video I could also relate to because of how many times I felt like the odd one out, from the amount of time it took another to finish a problem correctly. These are important messages that I have been keeping in mind during any work time because now I know these messages are encouraged and understandable.
4. Provide a write-up of the problem you chose to extend.
The hailstone sequence is a sequence of numbers that go up and down in range. If a number is even, divide it by 2 and if a number is odd, multiply it by 3 and add 1. The activity we did in class was to choose our first number and continue our sequence with the rules. I chose this problem because It was interesting to see the sequence repeat again once you have reached 1. My conjecture was, once you end your pattern with the odd 1, you are finished, but you could continue your pattern if you’d like to repeat. I also like I originally tried to find the pattern of the sequence before I was introduced into the rules. To solve this problem I had to find a conjecture on my sequence that I made, and I was able to find a conjecture in mine. For my rework I decided to make a hypothesis based on the little data I had gathered with negative numbers, so to take this a step further I decided to see the difference in numbers once starting your sequence with a negative number. I started my new extended sequence with -10 and the first thing I noticed was my sequences numbers were instantly increasing. My new conjecture is the numbers are going to get larger and will never reach one because of the large negative number I used. A challenge that I faced while extending this problem was determining whether or not to continue my sequence once I thought it was becoming too much of a pattern. I had to look ahead and decipher whether or not my conjecture was infinite. A Habit of a Mathematician that I used when working on this problem was to make a conjecture and test, and also seeking for patterns. I mentioned that we were told to make a conjecture and test it out on our hailstone sequence, and that is something i’ve always done with work time. For example, during any tests or warm ups I always take a problem and trying any conjectures, so I can better understand what the problem is asking.
5. A reflection of your work and effort during the Week of Inspirational Math: how will this week inform your effort and participation in math for the rest of the year.
During this week of inspirational math, I have learned so many new messages and rules towards my group work and thought process. I have tried to ask more questions, seek out new patterns or important sections of a math problem, and I have tried to become a better communicator and group partner. I will inform any of my group members that are so focused on time or speed on solving a problem, and tell them about taking our time to get the best final outcome. I am so motivated to incorporate my new mind set into my work time because I will approach every problem in a different way. I am proud of how I worked in the week of inspirational math because I broke every problem into pieces and was able to work with my new teammates on finding patterns.
The purpose of this week's investigations and video watching was to convey a strong message towards us. This message was to strengthen our self confidence and make us realize you can solve any math problem in any matter of time, or make a mistake on a math problem. We watched a series of videos that told us how our mind works when we are problem solving or thinking and they explained how to resolve or move forward from a math problem. Next we tackled four activities that made us problem solve and to spark collaborate with our group members. We needed to learn how to collaborate and to be inquisitive with our partners. One video that I took the most away from was a learning video that taught me that the amount of time it takes you to solve a problem does not determine your skill set. I will definitely take this lesson and use it to approach future problems.
2. Give an overview of all the activities and videos.
The intro mindset video was very beneficial for me because there are times where I was in the bad situation of the video where they teach you what not to do. Now I know how to overcome a situation while working with my classmates because of the videos we watched in class and the activities we worked together on. For example with the Mistakes video, I can personally relate to and utilize the message because of how many times I have felt defeated from several problems and I felt as if my own skill level was stopping me from accomplishing this task. Another video we watched in class was the “Speed is not important video” and this video I could also relate to because of how many times I felt like the odd one out, from the amount of time it took another to finish a problem correctly. From the last video we watched in class I now know if I ever feel that a problem is not accomplishable, then I will draw, or find another way visually to better understand a problem and accomplish it in sections. I took a lot away from these videos and have learned that new ways to accomplish and better understand a math problem. Plus, I am going to focus on asking more questions because it's not a bad thing to be inquisitive, in fact I learned that it benefits you more than anything. The stacked marshmallow experiment was not hard because I have had experience working with my table group before, so when we all work together, we were proud of our collaborative effort. But of course group communication is something I feel a lot of people need to work on including myself. I really enjoyed the squares to stairs activity and the hailstone sequence because I love trying to find a pattern in a sequence or a series of objects. I found the pattern of the squares of stairs pattern and I was proud that I tried to find other ways to determine the pattern. The painted cube activity was a challenge for me because I kept dwelling on this problem even though the answer was so clear for everyone else, but that proved to me that the time of you accomplishing a problem does not matter.
3. Choose two messages from any of the five videos we watched.
Explain the personal significance of those two messages.
The intro mindset video was very beneficial for me because there are times where I was in the bad situation of the video where they teach you what not to do. Now I know how to overcome a situation while working with my classmates because of the videos we watched in class and the activities we worked together on. For example with the Mistakes video, I can personally relate to and utilize the message because of how many times I have felt defeated from several problems and I felt as if my own skill level was stopping me from accomplishing this task. Another video we watched in class was the “Speed is not important video” and this video I could also relate to because of how many times I felt like the odd one out, from the amount of time it took another to finish a problem correctly. These are important messages that I have been keeping in mind during any work time because now I know these messages are encouraged and understandable.
4. Provide a write-up of the problem you chose to extend.
The hailstone sequence is a sequence of numbers that go up and down in range. If a number is even, divide it by 2 and if a number is odd, multiply it by 3 and add 1. The activity we did in class was to choose our first number and continue our sequence with the rules. I chose this problem because It was interesting to see the sequence repeat again once you have reached 1. My conjecture was, once you end your pattern with the odd 1, you are finished, but you could continue your pattern if you’d like to repeat. I also like I originally tried to find the pattern of the sequence before I was introduced into the rules. To solve this problem I had to find a conjecture on my sequence that I made, and I was able to find a conjecture in mine. For my rework I decided to make a hypothesis based on the little data I had gathered with negative numbers, so to take this a step further I decided to see the difference in numbers once starting your sequence with a negative number. I started my new extended sequence with -10 and the first thing I noticed was my sequences numbers were instantly increasing. My new conjecture is the numbers are going to get larger and will never reach one because of the large negative number I used. A challenge that I faced while extending this problem was determining whether or not to continue my sequence once I thought it was becoming too much of a pattern. I had to look ahead and decipher whether or not my conjecture was infinite. A Habit of a Mathematician that I used when working on this problem was to make a conjecture and test, and also seeking for patterns. I mentioned that we were told to make a conjecture and test it out on our hailstone sequence, and that is something i’ve always done with work time. For example, during any tests or warm ups I always take a problem and trying any conjectures, so I can better understand what the problem is asking.
5. A reflection of your work and effort during the Week of Inspirational Math: how will this week inform your effort and participation in math for the rest of the year.
During this week of inspirational math, I have learned so many new messages and rules towards my group work and thought process. I have tried to ask more questions, seek out new patterns or important sections of a math problem, and I have tried to become a better communicator and group partner. I will inform any of my group members that are so focused on time or speed on solving a problem, and tell them about taking our time to get the best final outcome. I am so motivated to incorporate my new mind set into my work time because I will approach every problem in a different way. I am proud of how I worked in the week of inspirational math because I broke every problem into pieces and was able to work with my new teammates on finding patterns.