1. This week in class, we watched a series of videos and completed a number of problems. They all fell under the same purpose; Brain growth. Now, I know that this is a broad category. So I am going to specifically talk about how our brains grew, at least in my case. We did problems and experiments and found solutions. These solutions came with trial and error. Every time you make an error, a new synapse in your brain fires. During this same time, we would watch videos about how our brain grows and how everybody is a maths person, and that you just have to practice. Besides the growth of our brains, the other purpose of these problems and videos was to open our minds up and warm us up to maths this year.
2. The activities we did in class consisted of;
1. Tiling a 11x13 rectangle, where we had to find the the smallest number of squares that could fit inside a certain rectangle.
2. Squares to stairs, where we had to find our own theorem of how we could find the number of squares that would be inside a certain staircase.
3. Hailstone sequence, where we had to start with a number of our choice, and continue with the rule of when we had an even number, we would divide it by 2, and when we had an odd number, we would multiply it by 3 and add 1.
4. painted cube, where we had to make a 3x3 cube out of sugar cubes, draw a dot on each exposed side of each sugar cube, and then figure out how many cubes had 3 sides painted, 2 sides painted, 1 side painted, and 0 sides painted.
We watched videos about how our brain works, and about how it grows when we make a mistake. We also learned that everyone is a math person, and that we just have to try.
3. There were 2 very important messages that I took away from the videos that we watched. The first being that everybody is a maths person. I have always been fond of maths, and I remember always being pretty good at it. I remember when I was in elementary school, there would always be kids who would struggle with their maths. I would always help them, and I would think to myself, "Wow, I guess i'm a maths person and they aren't.". After watching the video that we watched, I see now that those kids maybe just had to try a little bit harder to be good at maths. The other important message that I took away is that our brain grows every time we make a mistake. Now, I know that sounds cliche, but I really think that it is amazing that our brain grows with every mistake we make, and we don't even realize it.
4. Out of the 4 problems that we did in class, we got to choose 1 and expand on it. I chose the "Painted Cube" problem. This is where we had to take a make a 3x3x3 cube out of sugar cubes, then put a dot on each of the exposed sides on each of the sugar cubes. We then had to calculate how many cubes had 3 dots, 2 dots, 1 dot, and 0 dots. I chose this problem because I felt like I didn't really get too deep with it in class. I wanted to understand it more. The approach that I took to this problem was pretty simple. I calculated to amount of exposed sides with a 3x3x3 cube, all the way up to a 7x7x7. I started out with calculating everything by just looking and counting, then I came up with an system to help me. To show my work, I made a diagram;
2. The activities we did in class consisted of;
1. Tiling a 11x13 rectangle, where we had to find the the smallest number of squares that could fit inside a certain rectangle.
2. Squares to stairs, where we had to find our own theorem of how we could find the number of squares that would be inside a certain staircase.
3. Hailstone sequence, where we had to start with a number of our choice, and continue with the rule of when we had an even number, we would divide it by 2, and when we had an odd number, we would multiply it by 3 and add 1.
4. painted cube, where we had to make a 3x3 cube out of sugar cubes, draw a dot on each exposed side of each sugar cube, and then figure out how many cubes had 3 sides painted, 2 sides painted, 1 side painted, and 0 sides painted.
We watched videos about how our brain works, and about how it grows when we make a mistake. We also learned that everyone is a math person, and that we just have to try.
3. There were 2 very important messages that I took away from the videos that we watched. The first being that everybody is a maths person. I have always been fond of maths, and I remember always being pretty good at it. I remember when I was in elementary school, there would always be kids who would struggle with their maths. I would always help them, and I would think to myself, "Wow, I guess i'm a maths person and they aren't.". After watching the video that we watched, I see now that those kids maybe just had to try a little bit harder to be good at maths. The other important message that I took away is that our brain grows every time we make a mistake. Now, I know that sounds cliche, but I really think that it is amazing that our brain grows with every mistake we make, and we don't even realize it.
4. Out of the 4 problems that we did in class, we got to choose 1 and expand on it. I chose the "Painted Cube" problem. This is where we had to take a make a 3x3x3 cube out of sugar cubes, then put a dot on each of the exposed sides on each of the sugar cubes. We then had to calculate how many cubes had 3 dots, 2 dots, 1 dot, and 0 dots. I chose this problem because I felt like I didn't really get too deep with it in class. I wanted to understand it more. The approach that I took to this problem was pretty simple. I calculated to amount of exposed sides with a 3x3x3 cube, all the way up to a 7x7x7. I started out with calculating everything by just looking and counting, then I came up with an system to help me. To show my work, I made a diagram;
One cool thing that I noticed was that the number of 3 dots exposed stayed the same. This is because a cube only has 8 corners. A challenge that I faced during this was actually counting out the cubes. I used a virtual image of these cubes. Because of that, it was hard for me to see how many of the actual little cubes there were. So, I found out how many times in which spots that the cubes with the number of sides exposed I was looking for occurred. And I would just multiply that number by the amount of cubes there were in the one spot that I was looking at. A habit of a mathematician that I used is generalize. In order to get the work done faster, and more correct, you had to find an equation, so I just started assuming things were multiples and seeing if they would work, and sure enough, one way worked.
5. I feel like I put in a decent amount of effort this week. I feel like I could've gone a little bit deeper on some of the problems in class, but overall, I feel like it was alright. This will help me with the rest of the year in maths by showing me to take more time with smaller problems and really go deep with them rather that just going through problems really fast just to get them done.
5. I feel like I put in a decent amount of effort this week. I feel like I could've gone a little bit deeper on some of the problems in class, but overall, I feel like it was alright. This will help me with the rest of the year in maths by showing me to take more time with smaller problems and really go deep with them rather that just going through problems really fast just to get them done.