![Picture](/uploads/2/4/3/7/24372539/screenshot-2016-09-12-at-9-09-46-am_orig.png)
1: The purpose of this week of investigations was to learn to make mistakes and struggle. You want struggle and make mistakes because your brain grows more than it would if you got the answer right. The investigations also lead you out of the beginning of school into doing some challenging math problems that get you to really think. The purpose of the videos were to teach you key concepts that will help you in the math class such as, your brain grows when you make a mistake, have a growth mindset, speed does not matter, believe you can do it, and use you fingers to help yourself visualize.
2: On the first day we watched a video from Stanford University that showed us how our brains grow when we make a mistake. We then started an activity. We were quickly shown a pattern of dots (left) and we identifies how the pattern was growing. We began another activity where we drew an 11 by 13 rectangle and tried to fill the rectangle only with squares, and using the fewest amount of squares. The next day we watched a video on on how mistakes are very good and you learn more when you make mistakes then when you get the answer right. We also watched another video about having a growth mindset and how when you think you can do it your brain will grow more. Were were then tasked with a new problem. We were given figures of stairs and were asked to draw what figure 55 looked like, and if you could make a figure with 190 cubes. On the third day we worked on a problem that mathematicians have been unable to solve, called hailstone sequences. With these sequences, you start with any number, and if the number is even you divide the number by 2. If the number is odd you multiply the number 3 and add one. I found with these set of rules you always get down to 1, and then it gets stuck in an endless loop, ( 1-4-2-1-4-2....) Mathematicians have been unable prove that every number will eventually get down to 1. On the last day we learned how important it is to learn about math visually and that its OK to use your fingers, in the last of the Youcubed films made my Stanford University. The last problem we worked on was a problem called painted cube. The problem challenged to think about a 3 by 3 by 3 cube dipped in paint, and to think of how many individual 1 by 1 by 1 cubes would have 0 sides painted? 1 side? 2 sides? 3 sides? 4 sides? We then expanded our thinking to a 4 by 4 by 4 and so on.
3: The video where we learned that our brain grows whenever make a mistake is very personally significant to me. I have always been avoiding mistakes, but knowing that I will learn and grow from making mistakes more, than if I avoided them, makes me want to make more mistakes. Another video we watched that has personal significance to me is to have a growth mindset. By believing that you can accomplish the task your brain will grow more and the task will be easier to accomplish. That helps me in a lot more than just math.
4: The problem that I have chose to extend is the 11 by 13 rectangle problem. In this problem we were given a 11 by 13 rectangle that we drew on graph paper, inside the rectangle we had to see how many squares we could fit inside the rectangle. We tried to get the fewest number of squares. I chose to do this problem because over the week I found this one to be the most interesting to me. I am genuinely interested to see if I can get any less that 6 squares (witch is the least I have gotten so far) and to change the size of the rectangle and see how many squares I can get when the rectangle is a different size. I first approached this problem by drawing the biggest square I could fit and then filling in the rest of the squares, I got 10 squares. I then kept shrinking the largest square in the rectangle, from 11 by 11 - 10 by 10... I eventually realized that you want large squares but you want room for other large squares so you don' want your first square to be too big or too small. I found that you could fill the whole area with squares if you started with a 7 by 7 square. I then realized that the problem said nothing about using half a square, so I decided to make my first square numbers like 6.5 by 6.5 and 7.5 by 7.5. I found that, that made no difference and that the number of squares was always 6 or more. A challenge I had was trying to get a low number of squares. I had not yet realized that you want big squares but you want to save room for other big squares, so I was trying huge numbers for my first square like 10 or 11. I overcame it by getting down to 6 squares by first using a 7 by 7 square. I am going to extend the problem by trying a different sized rectangle, I am going to try 14 by 11 rectangle. I found that The most I could get with a 14 by 11 rectangle was 7 squares. My work for getting 7 squares in below.
5: This week was very good for me. Knowing that your brain grows when you make a mistake, really helps me because I don't want to avoid mistakes anymore. I also really enjoyed the math problems. I like the kinds of math problems that seem simple but are fairly complicated.
2: On the first day we watched a video from Stanford University that showed us how our brains grow when we make a mistake. We then started an activity. We were quickly shown a pattern of dots (left) and we identifies how the pattern was growing. We began another activity where we drew an 11 by 13 rectangle and tried to fill the rectangle only with squares, and using the fewest amount of squares. The next day we watched a video on on how mistakes are very good and you learn more when you make mistakes then when you get the answer right. We also watched another video about having a growth mindset and how when you think you can do it your brain will grow more. Were were then tasked with a new problem. We were given figures of stairs and were asked to draw what figure 55 looked like, and if you could make a figure with 190 cubes. On the third day we worked on a problem that mathematicians have been unable to solve, called hailstone sequences. With these sequences, you start with any number, and if the number is even you divide the number by 2. If the number is odd you multiply the number 3 and add one. I found with these set of rules you always get down to 1, and then it gets stuck in an endless loop, ( 1-4-2-1-4-2....) Mathematicians have been unable prove that every number will eventually get down to 1. On the last day we learned how important it is to learn about math visually and that its OK to use your fingers, in the last of the Youcubed films made my Stanford University. The last problem we worked on was a problem called painted cube. The problem challenged to think about a 3 by 3 by 3 cube dipped in paint, and to think of how many individual 1 by 1 by 1 cubes would have 0 sides painted? 1 side? 2 sides? 3 sides? 4 sides? We then expanded our thinking to a 4 by 4 by 4 and so on.
3: The video where we learned that our brain grows whenever make a mistake is very personally significant to me. I have always been avoiding mistakes, but knowing that I will learn and grow from making mistakes more, than if I avoided them, makes me want to make more mistakes. Another video we watched that has personal significance to me is to have a growth mindset. By believing that you can accomplish the task your brain will grow more and the task will be easier to accomplish. That helps me in a lot more than just math.
4: The problem that I have chose to extend is the 11 by 13 rectangle problem. In this problem we were given a 11 by 13 rectangle that we drew on graph paper, inside the rectangle we had to see how many squares we could fit inside the rectangle. We tried to get the fewest number of squares. I chose to do this problem because over the week I found this one to be the most interesting to me. I am genuinely interested to see if I can get any less that 6 squares (witch is the least I have gotten so far) and to change the size of the rectangle and see how many squares I can get when the rectangle is a different size. I first approached this problem by drawing the biggest square I could fit and then filling in the rest of the squares, I got 10 squares. I then kept shrinking the largest square in the rectangle, from 11 by 11 - 10 by 10... I eventually realized that you want large squares but you want room for other large squares so you don' want your first square to be too big or too small. I found that you could fill the whole area with squares if you started with a 7 by 7 square. I then realized that the problem said nothing about using half a square, so I decided to make my first square numbers like 6.5 by 6.5 and 7.5 by 7.5. I found that, that made no difference and that the number of squares was always 6 or more. A challenge I had was trying to get a low number of squares. I had not yet realized that you want big squares but you want to save room for other big squares, so I was trying huge numbers for my first square like 10 or 11. I overcame it by getting down to 6 squares by first using a 7 by 7 square. I am going to extend the problem by trying a different sized rectangle, I am going to try 14 by 11 rectangle. I found that The most I could get with a 14 by 11 rectangle was 7 squares. My work for getting 7 squares in below.
5: This week was very good for me. Knowing that your brain grows when you make a mistake, really helps me because I don't want to avoid mistakes anymore. I also really enjoyed the math problems. I like the kinds of math problems that seem simple but are fairly complicated.