In this unit, I learned a lot about graphs, tables, sigmas, and how to program a calculator. These are just some of the subjects in this unit. We learned these through the pows, classwork, online programs, and the homework. The pows really help me learn how to figure out real life problems. The pows also get me thinking about alternate ways to solve everyday problems. The graphing we learned was easy to understand with all of the different families. These families are the quadratic family, absolute value family, cubic family, and the square root family. These acted like guidelines for your formulas so you know that you have the formula but you just punch in the information. The earlier subjects like the garden borders problems were problems that you had to use different thinking because you couldn't just count the outside tiles. When you had to find the amount of tiles outside of the garden you had to find more than just one way to find how the tiles could be counted. For an example you could say there's ten tiles so the side tiles would be nine if it was a perfect square. This problem was like nothing I have ever done usually in my old math classes you would just have to find an equation and never know how it related to real life. Pows are the Problem of the week. In these we have one week to finish a problem and this problem usually has multiple steps. Our last pow we have to find a formula for a problem. The problem was about gumballs the first table that we made was that there was two kids and they both wanted the same colored gumball so you had to find how much money the mom would have to spend.
The central problem this unit is to find a “fair” insurance plan for everyone. The mathematical ideas that we used were based off of people's income and how much their insurance should reasonably charge them. Another factor that weighed into our decision was their pre existing conditions. Some of the plans did not allow you to get insurance. The ideas were developed through equality and singling people out for the better of the plan. For example when everyone pays the same it sounds like it could be a even plan but it can really be unfair for the people that have a lower chance of getting the disease or cancer. This will cause a lot of people to drop out of the insurance plan and if they do get injured then the cost of the other peoples insurance will go up. Another thing that we focused on in this project is probability. The way that we went about doing this is by rolling dice and having a bag of money and pulling from it and seeing what we get. A method we used is called area models. The way they work is by making a graph and taking the numbers that you have and placing them on the outside of the graph. For example if you have 1 ten, 2 fives and 3 ones. So the graph would have to be a 6 by 6. The thing that I learned from the “fair” insurance plans was that every one of the plans had a least one or two cons to them. The plans that we went over included Mandatory insurance, everyone pays the same and pre-existing conditions. The Con for mandatory insurance is that everyone has to have insurance even if you don't have a high chance or never get into an accident. The con for everyone pays the same is that people will just start dropping out. The last con is for pre existing conditions, this con in this plan is that if someone has a condition that they can't control they are still denied. All of these plans have their own pros and cons but in my opinion the mandatory coverage is the best and most “fair.”
The way I have grown in this unit is my POWs are improving. The way I think I have improved in this area is because I have been making my process the main part of my POW. What I mean by this is that my earlier POW’s my process was maybe 1-2 paragraphs that didn't go very in depth. I have been making them dive into what I did good and what I struggled with. I have also grown in my time management with POWs and other homework. I have always had a problem with this and I feel I have improved. I have not had a late assignment in this unit.
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