Question 1
During this week of inspirational math the purpose was to work together with the table mates as a group to solve very weird but very mathematical problems. We would receive the problem and most of the time get stuck. But then we would watch a video about thinking and why we are stuck on the problem. We then would retry the problem with more success. For the problems there was not a normal way of solving the problem so everyone at the table had to come up with their own idea of solving it. Most of the time we would do a very long process and repeat it to solve the problem and then someone would find a much faster solution. The faster solution would give us the same answer as the long and hard way so we knew it worked.
Question 2
There were four problems this week that we had to do. The first one is where we were given a 11x13 grid and we had to fill the whole box with the lowest number of boxes posable. This was hard because we could not just split it into 4 sides because 11 and 13 does not split evenly. so there were many complex ways of trying to get the lowest number but even then they were very high. Squares to stairs was another problem where we were given one square and for every step had to add a square to every side on the top row. Doing this would start making a stair case that would get bigger every time. We were told to make a stair case that contained 190 squares in it to see if it would fit with the equation that was forming. The third was a equation where you take any number and if it was even divide it by 2, but if it was odd multiply it by 3 and add 1 to get the next number. Even starting at a very low number would make this long path all the way down to 2.The final was we took a 3x3 cube and if it were dunked into a jar of paint how many sides would be pained. how many sides would be painted 0, 1, 2, and 3 sides on each cube.
Question 3
I like the first video "Ways We See Math" and the fourth video "Visualizing". Both of them had similar themes where if you think your doing bad stuff in math most of the time you are not. The first video explains a lot that being stuck at a math problem is good because your brain works very hard and learns math better. The fourth video says that there is no shame in doing very old and simple tricks when working on problems. Even just counting with your fingers is very good.
Question 4
The problem I chose was the 3x3 cube problem. If you took a 3x3x3 cube or any cube and put it in a bucket of paint how many 0, 1, 2, and 3 painted sides would there be. This would include every cube in the whole cube. From the side cubes to the outside cubes. I chose this problem because it was the only problem with a 3D object involved. The first approach we took at solving the problem was to take sugar cubes and build them into a 3x3x3 cube and every side we could see on the outside we put a mark on it. We then split up all the cubes in to different categories. How many had 0 sides 1 sides 2 sides and 3 sides. We then rested the same process with bigger ones like 4x4x4.
Question 4 continued
There was one challenge we faced. We would not have enough sugar cubes to make the really bit cubes, like 10x10x10. So what we did was we learned that no matter how big the cube is it will have only 8 three sided cubes on it. So we did not need to solve that again. For 2s we found out that with one bigger cube would just add 12 more of the 2s. 1 was hard at first because finding a equation for it was imposable. So what we did was build a 10x10x10 square and count all squares that were not exposed to the outside. Take that number and multiply by 6. For zeroes we took the total number if cubes of the cube and subtracted it by all the outside ones that we already figured out. and that would give us the answer we needed.
One habit of a mathematician that i did over this problem was to visually see things. we built a real 3D 3x3x3 cube to find out answers. This is just counting with your fingers or splitting up actual objects for dividing.
One habit of a mathematician that i did over this problem was to visually see things. we built a real 3D 3x3x3 cube to find out answers. This is just counting with your fingers or splitting up actual objects for dividing.
Question 5
A reflection on this past week was show that simple questions could be very hard to solve. a lot of thinking and group thinking was involved to calibrate ideas on how to solve the problem. this will help me later on this math year because it showed me that sharing ideas with other in a group is very important. working all year by my self would be very hard to do. I need other people to give me ideas on how to solve it so i can get it any math problem done faster and better.