Desmos Project Reflection
Unfortunately I do not have the final dismiss calculator link, as it was lost and I forgot to save it, but here is a link to a draft! Thanks. https://www.desmos.com/calculator/msoqp5t5va
Unit 3 Reflection
For me the most interesting content for myself was surface area and volume because it was very visual, and I happen to be a visual learner. It was very easy for me to visual a 3d object and derive a equation from what I already know.
This content has helped me grow mathematically by learning how to take large, complicated equation and break it down into a more workable equation that I can understand. Learning about surface area has also taught me how to derive equations.
This content has helped me grow mathematically by learning how to take large, complicated equation and break it down into a more workable equation that I can understand. Learning about surface area has also taught me how to derive equations.
Unit 2 Reflection
In this unit I am most proud of my final quiz. I haven't received the test yet, but I felt very confident who doing it. I felt like I was doing well in my process and explanation, which I don't experience a lot during my math class, yet. I understood the concept of trigonometry and how it works using sine, cosine and tangent. (Update 3/10/15) On my final quiz on only received a C+. I did turn in some quiz corrections and I hope that will bring my grade up and further my understanding of the subject. I think my fault was not in taking time to study the content or getting help from my resources. Starting this week I am going to get help from my step mother who happens to be a local math professor at a college in my hometown.
In my geometry class I am learning the skills of using a graphing calculator, and the basics of trigonometry, which I enjoy. With my graphing calculator I have learned how to insert equations, and graphing the equations I come up with. In trigonometry I have used that calculator to understand the rules of trig.
Trigonometry is the study of right triangles and their corresponding side lengths and angles. In trigonometry problems either a angle or side length is missing from the triangle, so you must find either that angle or side to have all needed measures. This can be applied to finding the height of a very tall objects, finding distances from on point to another or determining the angle of a tall object from yourself.
In my geometry class I am learning the skills of using a graphing calculator, and the basics of trigonometry, which I enjoy. With my graphing calculator I have learned how to insert equations, and graphing the equations I come up with. In trigonometry I have used that calculator to understand the rules of trig.
Trigonometry is the study of right triangles and their corresponding side lengths and angles. In trigonometry problems either a angle or side length is missing from the triangle, so you must find either that angle or side to have all needed measures. This can be applied to finding the height of a very tall objects, finding distances from on point to another or determining the angle of a tall object from yourself.
POWs (Problem of the Week)
POWS are made in order for us students to further our math knowledge, refine our thinking skills and breaking down problems. I have a love/hate relationship with POWs because I don't have the proper problem solving skills, but do really enjoy when I can get the answers right and showing my thinking through diagrams and writing. They have helped me understand how to organize my thoughts into a logical order that can make sense to other people and how I could attack a complex and difficult problem.
POW #2 (Triangle Congruence 1st semester)
POW #2 Write Up Vivien Doucette p.6
This POW was about triangle congruence. We were given a problem where a triangle had five congruent features (angles and sides) with another, but the two triangles were not congruent. We had to find a rule were that would follow, basically make five features of the triangle congruent, but the triangles could not.
The process of finding my answer, I will admit, was painstaking. I first began just to draw out some equilateral triangles and used marks to show where the features could be congruent. I tried this four times until I realized I should take it with a more practical approach. I then asked my step dad for a little of help, as I was sure this problem was impossible (which it was not). He had a little trouble with the problem too, but we talked about the SAS and AAS idea and came up with the idea of all three angles can be the same, but the lengths can not. This made sense to me so I began to experiment with these ideas, while my step dad researched on the internet, so he could help me. He used a website to help him understand the idea. The website was fg.math.ca. I tried using the same method of drawing out the congruence marks, but yet again, had no luck. But then my step dad asked me why all my triangles were equilateral. This then clicked in my mind that there could be no way it was possible if the triangle was equilateral. I also decided that using a ruler would help with measurements, as I am a visual learner. I began to draw out the triangle when my step dad then told me, that the sides can be congruent, but may not need to be in the same order. It instantly made complete sense to me. It was sort of a question where you had to really play with the rules for it to make sense. From there I could easily understand the problem and solve it.
I’ve included large diagram, step by step as I did it to show my work. It shows the beginning of my process and how I progressed, with small notes on how I was thinking and (sometimes) felt. I used a red pen to show my mistakes and tried to keep it nice so other people could understand it. My solution was that it is possible, but only if your triangle is not equilateral, and if you change the order of the side lengths, then it becomes much easier to understand.
An extension that could be possibly on this project, is limiting what types of triangles could be used. You could make it so you can only use isosceles triangles or scalene. This may or may not change the question that if it is possible, but I would be highly interested on how different triangles affect this question.
This POW was about triangle congruence. We were given a problem where a triangle had five congruent features (angles and sides) with another, but the two triangles were not congruent. We had to find a rule were that would follow, basically make five features of the triangle congruent, but the triangles could not.
The process of finding my answer, I will admit, was painstaking. I first began just to draw out some equilateral triangles and used marks to show where the features could be congruent. I tried this four times until I realized I should take it with a more practical approach. I then asked my step dad for a little of help, as I was sure this problem was impossible (which it was not). He had a little trouble with the problem too, but we talked about the SAS and AAS idea and came up with the idea of all three angles can be the same, but the lengths can not. This made sense to me so I began to experiment with these ideas, while my step dad researched on the internet, so he could help me. He used a website to help him understand the idea. The website was fg.math.ca. I tried using the same method of drawing out the congruence marks, but yet again, had no luck. But then my step dad asked me why all my triangles were equilateral. This then clicked in my mind that there could be no way it was possible if the triangle was equilateral. I also decided that using a ruler would help with measurements, as I am a visual learner. I began to draw out the triangle when my step dad then told me, that the sides can be congruent, but may not need to be in the same order. It instantly made complete sense to me. It was sort of a question where you had to really play with the rules for it to make sense. From there I could easily understand the problem and solve it.
I’ve included large diagram, step by step as I did it to show my work. It shows the beginning of my process and how I progressed, with small notes on how I was thinking and (sometimes) felt. I used a red pen to show my mistakes and tried to keep it nice so other people could understand it. My solution was that it is possible, but only if your triangle is not equilateral, and if you change the order of the side lengths, then it becomes much easier to understand.
An extension that could be possibly on this project, is limiting what types of triangles could be used. You could make it so you can only use isosceles triangles or scalene. This may or may not change the question that if it is possible, but I would be highly interested on how different triangles affect this question.
POW #1 (The Knights, semester 1)
This problem is asking us to move black and white nights around so they switch original positions. The black knights need to be replaced by the white nights and vise versa, but you can only move in a L shape, moving either 2 spaces up or down and 1 space left to right. This all must be done in the least amount of moves possible. To solve this problem I had to try twice. My first time, I almost solved the problem, but I had ten moves and I knew that there could be less than that. I drew out boxes and arrows to show my movements. After I saw that I had too many steps I then redid the question. I asked a friend if she had any tips and she said that you can rotate the knights to make a diamond shape. I did this and instantly saw how it could be done. My solution to the question it can be done in eight steps. I am certain that this correct because there is four pieces to move and they should move twice and therefore four times two is eight. To add extension to the question you could use different chess pieces. A queen would change the number of questions that are possible. If I would grade myself in this project I would give myself a 20/30. I could of put much more quality time for this and made my work easier to understand from a outsiders standpoint. I feel that I could of not needed to ask for help from a friend and got slightly lazy, but now I know how POWs work, how much work I should do to be successful on this project.
Snail Trail GeoGebra Lab
To make the snail trail lab I used the computer program GeoGebra. I first made a large circle with six sections. I then used a point and applied the reflection tool. I made each reflected dot a different color so I could tell which one was which. I noticed that the snails and their trails mirrored each other, but in different locations. I also noticed that I could change the design and the trail would still be reflected. If I ignore the color I see that the snail trail is rotational symmetry.
Tessellation Project
The theme of my tessellation is tribal triangle. I based it of the design of the popular tribal print that I see on a lot of cool things. It's more geometric design and very simple. It is simple because of two reasons. First because I enjoy simplicity in life and don't like things to be over complicated and my first tessellation was over complicated to make.
My original design was made of rectangles, but now I used a more simple design that I could make easily, but still have it as beautiful work.
The debate whether a tessellation is art or math is based on your natural inclination. If you are an individual who likes math and finds it easier, you will believe it is a math problem, but if you are more inclined to art, you will see it as art. There is no definite answer to the question because of the way that you see it.
My original design was made of rectangles, but now I used a more simple design that I could make easily, but still have it as beautiful work.
The debate whether a tessellation is art or math is based on your natural inclination. If you are an individual who likes math and finds it easier, you will believe it is a math problem, but if you are more inclined to art, you will see it as art. There is no definite answer to the question because of the way that you see it.
How the Tile Was Made
To make a tessellation tile you must be able to fit the entire tessellation around each other. To do this you must do to what you did to each side. If I cut out a triangle from one side I must attach that cutout to the other side. In my tessellation I did a triangle which one of the most simple shapes to tessellate because when they are fit upside down they successfully tessellate.
The Burning Tent Problem
Question 1: When you get a minimal path the incoming and outgoing angles become even in numbers.
Question 2: The path between the Camp and the Tent Fire is the smallest because you do not need to take a detour towards the river.
Question 3: The river point should be in the center of the river and between the Camper and Tent, to minimize the distance.
Question 2: The path between the Camp and the Tent Fire is the smallest because you do not need to take a detour towards the river.
Question 3: The river point should be in the center of the river and between the Camper and Tent, to minimize the distance.