To me, the purpose of this weeks investigation was to realize that other people can get the same answer as you in another way. When we get a problem placed right in front of us we start to look at it in different ways and try to solve for solutions. Everyone has their own way to getting to the correct answer. The purpose of watching those videos was to give us confidence for this year's math course. It was also a way we learned about how our brain works and when we do things that could trouble the way it functions.
During this week we have been working on four activities, they are the Tiling a 11x13 rectangle, Squares to Stairs, Hailstone Sequences, Painted Cube. The tiling 11x13 rectangle was an activity to try to persuade my classmates that the amount of squares I was able to create in the rectangle were the lowest you could possibly get. For example, the lowest amount of squares I was able to create in the 11x13 rectangle were six squares. The Squares to Stairs activity was an activity which was introduced to us by getting a glimpse of the image of squares in a stair form. By getting that glimpse we had to guess how many squares were used to make the image. We then had the task of figuring out the pattern of which the squares landed in. Everyone saw it in their own way but the way I saw it was it being like the game Tetris, where the squares land in their designated spot as in a puzzle piece does. Another way I saw it was the squares falling diagonal. The second to last activity we worked on was my favorite, the hailstone sequence. The hailstone sequence was putting down a number at random and dividing it by two, if it couldn't be divided by two without it having a decimal point you would need to multiply that number by itself and add one. For example, if you have 50 and divide it by two you get 25, but 25 divided by 2 is 12.5 meaning that we need to multiply 25 by 25 and adding one, which is 626. We got to experience with different ways of approaching this problem. The final but activity of this week was the painted cube activity which what we did was use sugar cubes to create some type of rubix cube. We wanted to see how many sides were to be affected if we were to dip it into paint. While watching the videos this week I learned that everyone is a math person it just depends on who wants to really let in the information that is being taught to them. There was one video that really stood out to me which was the one about being timed. I learned that when we have a timed test or we have a limited amount of time to finish something we tend to forget most of the important information
A message that really stood out to me was that no one does really well when we are given a limited amount of time to complete a task. I am actually quite happy to have learned this because growing up and still to this day I have been given tests that have been timed and I haven't been able to finish them on time or at all. I always used to think something was wrong with me and wanting to take my time. Since everyone always finished before me i had decided to start rushing through my tests but that wasn't very good. I made a lot of mistakes while rushing, but there is no reason to be ashamed of making mistakes because I have also learned that once I make a mistake and catch it my brain actually grows. Everyone makes mistakes and that is okay because in the process we gain knowledge.
The problem I chose to extend was the hailstone sequence, the problem was interesting because in order to accomplish it I needed to choose a random number to begin with. Since we did it in class I just chose three numbers that popped in my head that happened to be 6, 10, 14. These numbers are all even as you can tell, I didn't try anything too crazy until now. I decided to explore further on using negative numbers, both odd and even. The numbers I ended up using were -20, -50, -7, -5, I used two sets of odd numbers as well as two sets of even numbers. What I did was I started with -20 and I divided it by 2, I then got -10 which I then kept the process of dividing by two which I then ended up with -5. Since I couldn't divide -5 by 2 without getting a decimal I multiplied it by itself and added one. I then got 26 and I kept going with my process. A challenge I faced during this experiment was that as I thought I was getting near the end I ended up having a mix and got to a higher number than the one I was at already. I ended up getting as far as I could but as I saw the number get bigger I decided to leave it and move on to the next set. The habit of the mathematician I used was stay organized. I tried to stay organized as I put my numbers down. As I wrote them I started noticing that I couldn't keep using a comma because the I would get confused on where the number ended so to stay organized I used a Colin to separate my numbers.
During this year I will now be able to tell myself that I am a math person and that in order to understand I have to let information in to work well. I am excited to be learning new information and tricks, this time if I make a mistake I will be reminded that my brain has grown from it. I wont fear making a mistake as much as I did before. I am also excited to be working with different people so I can understand their way of working with the same problem as I am. I feel confident starting off this year, starting out strong with great knowledge that will help me get through the days of telling myself that I wont be able to understand this problem because I am not a math person.