One topic that I think I have mastered this semester is using the Pythagorean theorem, I have mastered it (truth be told I still can’t spell it). I think I have mastered this topic because of all the time in class that we have dedicated to working on this topic and all of the assignments that had been testing us on this topic. An activity that has helped me learn this skill was my Pythagorean theorem test that I did when we were first learning this concept. This was a test that asked me to answer Pythagorean theorem questions that pertained to the real world. I also believe that I have mastered this topic because it is one that I use a lot in everyday life and due to it’s very present use in my life I am given many opportunities to memorize it. One assignment that has given asked me to use the Pythagorean theorem is my POW 2. This POW asked us to find the perimeter of a rectangle and in the process use the Pythagorean theorem to find the sides that were missing in the rectangle, using this correctly led me to the answer that was correct. Another activity that I have used the pythagorean theorem in that I believe is proof that I have mastered this subject is an activity that I didn’t do in school but still required me to use the theorem for measurements and that was when I was designing a flat down flat ski rail that I was going to make out of wood and pvc. I needed to find the correct measurements so I knew how much of each supply I needed and I used the pythagorean theorem to calculate the size of the triangle made by the down section and the supports, I had side C (the pvc section) side A (the horizontal section) and I needed side B (the vertical section), so I used the equation C squared minus A squared equals B squared to find the missing side.
Pythagorean Theorem test
Understanding the Problem:
This problem is asking me to take the two triangle in this quadrangle and use the Pythagorean theorem to get all the lengths in these two triangles by using the known sides. Once I do this the problem is asking me to get the sum of the rectangle that you got from the triangle sides. This would lead me to get the perimeter of the quadrangle with the sides AB, BC, CD, and DA by adding them together.
The process that I used to find my solution to this problem was to break the quadrangle into two triangles, I did this because it would let me use the pythagorean theorem to get the sides that I need to find the perimeter. Once I divided it into two triangles I found the right angles in those triangles because I was Planning on using the pythagorean theorem to find the missing sides. One of the right angles was at angle B, I decided to start here because I already know 2 out of the 3 sides, I took the pythagorean theorem A2+B2=C2 and plugged in the values which gave me this equation 324+441=765. Now that I had the missing side squared I needed to find the square root of this which is 27.6 which I rounded to 28. Now I had 2 out of the three sides of the other triangle so I plugged it’s values in 196+784=980. I then found the square root of 980 which is 31.3 which I rounded to 31. At this point I had all four side lengths to the quadrangle so I needed to add them up to get the perimeter of the quadrangle. To get this I added 31+28+18+21=98.
The solution is the perimeter is 98.
My justification is that if a triangle has a right angle you can use 2 of the sides to get the length of the third side. I got the length of the third side which gave me the second side of the third triangle. I know that my answer is correct because the sum of all the sides that I calculated is equal to the perimeter.
Explorations have changed my experience as a math student this year because they have given me an opportunity to apply the concepts that I had learned during that week and it lets me internalise them and not just forget them like I think I would if these worksheets didn’t exist. These explorations really test that you understand what we have been learning and I think that this is something that is needed for us to not forget these concepts. When we finish explorations we divide into groups of four and discuss the questions and the answers that we got on them. This gives us an opportunity to further understand the problems because it gives us one on one support from our peers that we would not get other wise. Say you got the answer to question five wrong and your homie to the left got it right he could show you how he got the answer and coach you through what you did wrong which leads to a further understanding. The explorations have made math more challenging because they have pushed me to retain this knowledge and look back upon it and remember it which can be difficult because I have to relapse to what we were learning and how it applies to different subjects. Although explorations have made class more difficult it has also made it easier because it lets me retain this knowledge and when we have an assignment such as a test or a quiz I don’t have to study because I already possess the knowledge. And when I don’t possess the knowledge the group where we discuss these concepts helps me to.
One example of when I have had a breakthrough in math is when we were working on conditionals. A conditional is a statement where they have a subject and a predicate and the predicate is dependent of the subject to either make sense and be logical or to be not correct. In this I was confused because I didn’t see how the different forms of conditionals could work and still stay fluid. This led to me being really confused and not knowing what to do with different forms of these conditionals and just having a lot of trouble trying to figure them out, and a lot of the time I wouldn’t be correct in them. But when my friend Nat saw that I was having trouble he looked at my work and explained which ones I got right and why and which ones I got wrong and why. This led to my breakthrough in conditional statements and gave me an understanding that I still possess. This gave me more power to move forward because it showed me that just some help from a friend can change everything you thought about a topic and really make it click for you. what I learned from this experience is to not be afraid to take help from someone that understands something better than you do, it can really make you understand.
The habit of heart and mind that I feel that I have had the most mastery over is Reflecting and synthesizing. To me this habit of heart and mind means to have a reflection over problems that you may have not done very well on so that you can try to do better work in the future, or to reflect on problems that you outdid yourself on so that you can reflect that into other problems of the same nature. I have demonstrated this skill in my classwork when I have done say an exploration and not liked the grade that I got on it, I will reflect what I did wrong, not in the work but in the process that I took to make sure the work was correct. Once I reflect on my process I see what I did wrong and how I can fix this in my future explorations. The activities that I have done to develop this skill are my POWs, my explorations, and my pythagorean theorem test. I used these to develop this skill because they are all examples of when I didn’t do something to my full potential and came up short, but then later through reflection got them up to my full potential and had a good final outcome. An example of when I did my pythagorean theorem test, the first time I did it I got 16/23 and I was not satisfied with this grade, due to this I looked at the amount that I studied for this test and saw that it would have been better if I had put in more work into studying before I took the test. After I applied this new found knowledge I got a 21/23 which I was proud of. Another example of this is in my POW 1 my first attempt at my POW 1 was not up to par and was not answering the question in the correct form which led to me getting a 5/10 which I was not satisfied with, due to this I looked at my process of writing this POW and found the best way to fix this which led to me having a much better final product on my rewritten POW 1. I have grown in that skill this semester in the way that I reflect a lot of the work that I think needs improvement in my process as opposed to in previous years when I lacked this skill.
Understanding the problem:
This problem is asking me to get the sizes of different places in a flower bed. There are 5 different places for flowers to go and there are five different types of flowers in five different prices. This problem is asking me to find the cheapest combination of flowers that she could use in her flower bed, one type of flower has to fill the entire bed that it is in and you can't repeat flowers in different beds. Once I find the sizes of the beds I need to organize them from smallest to biggest and have the cheap flowers to go in the big beds and have the expensive a ones go into the small beds.
The process I used to multiply the lengths of each square space to find the areas of each bed. Once I found the areas I ordered them from smallest to largest, once they were in order from smallest to largest I ordered the flowers from cheapest to most expensive. Then I paired the cheapest flowers with the biggest beds, and the most expensive flowers with the smallest beds. The cheapest flower (the daisy) went with the biggest square, the 7 by 3 sized square (21 square feet), the second cheapest flower (the begonias) went with the sencount biggest square the 5 by four sized square (20 square feet), the third cheapest flower (the cannas) went with the third biggest square a three by five sized square (15 square feet), the the fourth cheapest flower (the roses) went with the fourth biggest square a 1 by 6 sized square (6 square feet), and the most expensive flower (the cattleya orchid) went to the smallest space a 2 by 2 sized square (4 square feet). My solution. Then I multiplied the area by the cost of the flowers (dassie is 21 feet at $1 21*1=$21) (the begonias are 20 feet at $1.50 20*1.50=$30) (the cannas is 15 feet at $2.00 15*2=30) (the roses are 6 feet at $2.50 6*$2.50=$9) (the cattleya orchids are 4 feet at $3.00 4*$3.00=$12). And after that I added all those values up ($21 + $30 + $30 + $9 + $12) and I got $102 for all of the beds
My solution was $102 for all the beds is the cheapest price that she can get.
My justification was that to have the cheapest price you have to have the large spaces paired with the cheapest flowers, say you put the roses in place of the dassies, then you would add $1.50 to the price per square foot to the price, as opposed to just having the dollar per square foot.
I think that one skill that I need to work on the most and that I did the worst on this semester is rrecognizingand resolving issues. I think that I need to work on this the most because I don’t think it is something that I have put my best foot forward in this semester. I think this because when I am doing my work I don’t look over my answers as much as I should and this leads me to having there be an error in the answer that I could have corrected if I had put in the time to look over and analise the problem. I think the thing that has held me back from improving this skill this semester is just the unwillingness to look over the problem and the eagerness to finish that denies me from checking my answers twice to make sure that they are done right.