What was the purpose of this week of investigations and video-watching? In other words, why did we spend 5 days of class time on this? The purpose of doing this was to practice our Habits of Mathematician. By practicing the different activities we had to use some of the Habits of Mathematicians to solve or work on the problems. I think we did the video watching to help us be confident in math and be able to work comfortably. Also some of the messages were very inspiring and personally helped me to be fine with myself if I make a mistake or overthink a problem. Overview: We did four activities in which we all used different habits of mathematician. 1.) In the first activity we got a rope and we were given shapes to make.There were extremely hard ones and some easy ones. Even if we had created the shape we had to explain our answer and justify why its that shape. I feel like we had to use the start small habit of mathematician. Going from easiest to hardest was the best way to start. 2.) The second activity was Number visual Pennies. In this activity we had 5 groups and those five groups had to add up to 100 pennies. The thing was that in each group the stacks had to be the same. The question that we got was if there was more than one solution and we found out that there is tons of solutions for this problem. I think that in this activity we had to conjecture and test. 3.) The third activity was One-cut Geometry. In this activity we got a piece of wax paper and we had to draw a scalene triangle in the middle of the paper. No side of the triangle was able to be a line and it had to be in the middle. After you fold it you had to cut the triangle with one cut. An extension to this problem was to do the same with other shapes. I think in this activity we used a lot of conjecture and test. 4.) The fourth activity was Square mania. In this activity we got an image of a shape with squares on them. The question asked different things like if we agreed if there was - line segments and - squares to create the squares. We had to agree or disagree but we had to explain our reasoning. In this activity we had to describe and articulate. You-cubed Videos 1.)Strategies for learning Mathematics: I feel like I could relate to a lot of the people in the video. I think I work better when I am sharing my ideas with my peers and we are all sharing answers. Also when I start a math problem I like to have someone explain to me to make sure that I have the same concept as my peer. 2.)Speed is not important: Speed is not important is a big one for me because I have always thought that if you finish first you are the smartest. I feel like my 3rd grade teacher affected me a lot because she use to hand out papers with multiplication tables and whoever finished first she would give prizes and awards to them. She planted a seed in my brain that if you finished first you are the smartest but that is not true at all some famous mathematicians are slow too and that is alright. 3.)Brains grow and Change: This video was about the difference about having a fixed mindset and having a open mindset. I feel like this was a problem for me in middle school because I was very bad at math and my peers seem to do math really easy. I thought I wasn't a math person until I found out that having that mindset is bad and that we should have a open mindset. 4.)Believe in yourself: I find it really interesting and cool that if you believe in yourself when doing math you do better. I find this interesting because not that I have found this out I believe in myself every time I do math and I find math to be simpler and am able to enjoy myself while doing math. 5.)Mistakes are powerful: Out of all the videos I learned the most from this one and it motivated me to be alright with my self if I make a mistake. I have absolutely always thought that mistakes are horrible. That is completely wrong and making mistakes actually helps you become a better mathematician. Activity:Number visual Pennies Description:In the activity Number Visual Pennies the are pennies stacked in the patterns of the number visuals for 3,5,6,7 and 9. With the 100 pennies you have split them so they sum up to a $1.00. The thing is that all the stacks have to be equal i each group. The question was What would be the size of each stack of pennies for each number visual if the sum of the pennies is $1.00? Is there more than one solution? Why did you choose this problem? I chose this problem because it was one of the activities that I understood very well and was able to explain it to the class very clearly. Also I really enjoyed working on this problem with my peers and finding all sorts of solutions. Approaches that I took while solving this problem? When I first looked at this problem right way I already knew what I was going to do. I first approached the problem with a lot of confidence thinking that I already had a solution and I was right. I thought of going for the easiest possible solution and it worked I had a solution before the teacher could hand out the paper. I later approached the problem with more complex patterns and was able to figure out different solutions. Challenges: A challenge that I faced while solving this problem was find different solutions with more complex patterns. IO was having lot of trouble with finding different solutions and it was difficult for me to continue working on this problem. I decided that I would ask my peers for help and together we figured out a lot of solutions and overcame the obstacle. Habit of Mathematician: In this activity I used starting small . I tried to look at the problem the simplest way instead of starting with complex patterns that would require all 100 pennies. This helped me out a lot and I was able to figure out different solutions later on. I also used conjecture and test when trying different ways to add up to $1.00. Reflection: I think that learning all about the videos and being able to enjoy math is going to affect me a lot for the rest of the year. I would put tons of effort in the problems we get and will apply all of this skills to future problems.