During this unit we learned all about health insurance and how to use it to maintain a healthy population. We studied how to find the average yearly price, how to make the costs even for each citizen, and how to determine expected value. In this unit I learned a lot about how to find information with other things I knew about the problems. This was very helpful for me because before this unit I could only really do math and understand it if all had all of the information in front of me. I think that every piece of evidence that I chose showed the important parts of the unit, some of them were topics that I was having trouble with and I now understand.

In this unit we learned about the fairness of health insurance and how you can change the prices to differ in many ways. When the citizens have a higher probability of getting sick they then have to pay more for treatment, meaning that it can be unfair for them to pay such a high price. One of the questions I still have about health insurance is how are the companies able to pay for so much of the costs. I have learned to be able to use mathematics to make things fair by getting the expected probability then you can use that and divide it by the amount of citizens to make it fair or do whatever you need to do with those numbers. One of the unfair situations is when when you have to pay a lot more than others for treatment. While working with groups in this unit I learned that it can be very helpful in order to get useful information, but other times it is difficult to work in groups because it is just harder. I would like to get better at problem solving in the next unit because I feel like that it my biggest problem but I would like to be able to do that. This unit I learned a lot about how probabilities work and now its a lot easier to understand them. Because everyone uses probabilities it's really helpful to know more about them. I can use them more realistically now that the unit has helped me with them.

During this unit we learned all about patterns and how to find them. We studied things like what sigmas are and how to use them, how to find complicated patterns in, in and out tables, curve fitting, how to use simple information to make tables and graphs and then find the formula to them. We also learned how to write out and explain out process instead of just doing the math. This was a really helpful skill that we used a lot while doing things like the write out for the problems of the week. This was a very challenging portion of the unit, especially because each problem had so many aspects, we also had to write out our process which was difficult to explain, plus i've never had to do in math alot.

The problem of the week that I chose as my example was the 1234 puzzle. In this we could only use the numbers 1,2,3,4 and different equations to come up with the numbers 1-25. Even though this was simple for some problems I still wasn't able to find every number.This was a difficult one because there were so many different equations but most of the ones I tried equaled a number I had already found an equation to, though I did try to find an equation to every number I wasn't able to. Another challenging portion was finding complicated patterns in the in and out tables. I had done this before but this math class made me look at it in a whole new way. With some I would have to look at the table confused for a long time until finally it just came to me, sometimes I would feel frustrated until I found it then I felt really proud.

One activity that helped me understand the more simple in and out tables was Homework 5, in this we found the formulas and patterns. This was interesting to do especially because instead of using numbers, the tables also used letters and words. This helped me start to get a grasp on finding more unusual patterns and that was a large portion of this unit. I selected most of my example work because I felt that it showed some of my growth throughout the unit. Also some of it was work I was struggling with but finally grasped, there is also some of I found most interesting about the patterns unit.

Through the patterns unit I feel like I have grown a lot and learned really useful skills. I think my ability to work with others has improved a lot and I have learned how to work with a group in math because this isn't something that I have really done in previous math classes. I feel like my skills in presenting have definitely improved but not as much as I had hoped. I think that in general my ability to present has improved, this is something that I want to improve on more because this is something that I want to be good at. I am now able to write out and describe my princess. I think this is a very important skill to have especially now that we write so much to describe our process in out problems of the week. I really like being able to show my work in a clear process instead of it just being a confusing mess, so now that I am able to to describe my work more clearly I feel like it it is more presentable and therefore I am more proud of my work. My thought process has progressed a lot throughout the the unit, at the beginning when we started our first problem of the week, I felt really discouraged and intimidated by it. Now when I get any work that looks challenging I feel so much more confident about it.