Geometry DP Update
40 points: Describe one topic you feel you have mastered this semester. Describe the activities that helped you learn this activity (show 1-2 pieces of evidence). How do you know you have mastered this skill (show 1-2 pieces of evidence)? You should reference 3-4 pieces of evidence for this answer. Your evidence should be annotated and described, not just pasted on your DP.
One topic that I feel I have mastered this semester is fractals. Fractals are a repeating pattern that will never distort no matter how they are viewed. At first this unit seemed daunting and I feared I would be lost and unable to recognize fractals and their mathematical importance. However, once we began to cover the material I realized the multiple ways to work through any difficulty fractals pose and moved on to master them. One activity that helped me learn fractals was the NOVA Worksheet that we completed at the beginning of this unit.
This worksheet looked at fractals from the viewpoints of many different people such as, film makers, fashion designers, artists, and traditional mathematicians. Being able to see fractals from these multiple perspectives helped me further understand the subject material and go on to master it. In addition the design element of our pumpkin project has lead to me becoming better at fractals. This is because one of the project requirements was incorporating a fractal, which we did.
After a month of working on fractals I know that I have mastered the skill due to my work on the fifth Problem Of The Week.
As exemplified through my marked annotations I thoroughly described fractals and their components completely. My understanding of fractals earned a 10/10 on the assignment and assured me that one topic I have mastered this year is fractals.
10 points: How have the Explorations (and group discussions of Explorations) changed your experience as a math student this year? In what ways have they made math class more challenging, and in what ways have the Explorations and discussions helped you learn?
This year, the process of doing Explorations both in groups and alone has taken the place of rigorous note taking and forced memorization and has helped me better visualize and understand most topics. Explorations have changed my experience as a math student by offering something non-linear that could help me see a problem or equation from multiple angles. An example of this can be found in my 12/8 exploration in which there were 10 questions that utilized conditional statements in different ways and lead to me better understanding the topic. Singular explorations have shaped me into a more well rounded math student this year, but group explorations have given me the tools and information to take my work above and beyond. This is apparent in the 11/19 exploration which was full of time consuming and challenging problems. By working in a group not only did I learn the problems at hand due to the brain power of many people, but I learned the underlying concepts and equations that I could then apply to any other problem. All in all, explorations both in groups and alone have changed me from an average math student to a student given the skills, practice, and subject exploration to go above the expectations.
What is the hardest math problem you have encountered this semester? Explain how you solved it, or if you didn’t, why you weren’t able to.
The hardest math problem I have encountered this semester is POW six. This problem showed the graph of 3x + 4y = 12. It also showed the shaded figure of a square, three of whose vertices are on the coordinate axes. The fourth vertex is on the line. This POW had students find:
a) the x and y intercepts of the line
b) the coordinates of the vertex that falls on the line
c) the length of a side of the square
d) the area of the square.
Not only did this problem deal with x and y coordinates which I was already struggling with, but it then required that the area of the square be discovered. At the time I had no idea where to start so I utilized what I had learned through explorations and went back through the problem, dissecting it in an attempt to reveal any hidden clue. After this proved little use I went on to study the diagram which lead me to see the two triangles on opposite sides of the square. This gave me the chance to use the Pythagorean Theorem to discover the answer to this POW, which is: the area of the square is 2.9. In conclusion, this is by far the hardest math problem I have encountered this semester, but through perseverance and determination I was able to solve it and learn many important skills along the way.
30 points: Which Habit of a Mathematician do you feel you have the most mastery over? Explain what this skill is and what it means To you. Explain how you have demonstrated this skill, the activities that helped you develop this skill, and how you have grown in that problem-solving skill this semester. You should reference 2-3 pieces of evidence for this answer. Your evidence should be annotated and described, not just pasted on your DP.
I feel that I have the most mastery over Communicating thinking in a clear and accessible way. To me this means that I can concisely convey and explain my ideas to any fellow student or teacher. I have demonstrated this skill in the pumpkin project. I did this through creating a rough draft for the write up and then explaining each piece to my group members in order to reach an understanding of the topic. This practise of this habit is also evident in my latest exploration in which I had to explain my thoughts to a tablemate. I have grown in this problem solving skill by coming from a mindset of poor explanation only to master it through this work.
Pumpkin Project
12/8 exploration
10 points: For which Habit(s) do you feel you have the most room to stretch? What do you think held you back from improving in this skill this semester?
Out of the habits of a mathematician, I feel I have the most room to stretch in the Generating ideas category. I feel this way because I have trouble formulating a plan, identifying the appropriate mathematical tools. and even generating multiple means of approach. The main thing that held me back from improving this skill this semester is my attitude. I say this because I do not have the mentality of someone who can take charge and lead a group. This means that I usually do not formulate my own plan, but instead use one that someone else created. This can be seen in my pumpkin project in which I did not formulate my own design, but went with Lyrics instead.Additionally, my struggles with certain areas of math such as coordinate planes and conditional statements often obscure me from generating more than one kind of approach or strategy. Finally, I usually take one or more tries to identify the appropriate mathematical tools due to my unwillingness to look deeper into the problem beforehand. An example of this is the extra credit POW which I mistook for a coordinate plane project before realizing it had nothing to do with coordinates. In conclusion, I know that I have the most room to stretch in the Generating ideas category and my attitude towards math is to blame. Through the completion of this paragraph I have realized that I can master the Generating ideas category if I opt to take a leadership role in more situations, make more attempts to generate multiple means of approaching a problem even if they are incorrect, and hone my familiarity with certain math skills so I can identify and apply appropriate mathematical tools to any problem.
Pumpkin Project
Explanation: Our pumpkin is composed of trapezoids, triangles, rhombus, quadrilaterals, pentagons, nonagons, octagons and hexagons. The eyes mainly represent nonagons and octagons. The nose is shaped as two triangles, and the majority of teeth are trapezoids and triangles . The nose is demonstrative of reflective symmetry and the eyes and some teeth show elements of fractals. Specifically the self similarity of the left eye and the repetitive pattern in outreaching teeth.
Dialogue:
HERBERT THE PUMPKIN:
Our pumpkin is Herbert, he really likes sherbert. that’s his favorite dessert
he’s psyched for halloween and going trick or treating with his friend eugene, he’s decorated his house from the roof to the latrine, it's now that magical night and he dresses as a fiend he calls eugene and gulps some caffeine. He went out into the night and trick or treated with might! It’s the next morning now, the night finished in a flash he woke up and saw his brains were mash and now he wonders with eugene what a smell so foul his face had been contorted into a permanent scowl the teeth are crooked with eyes bent and curved his beautiful face now left children unnerved. “Nevermind“ ,he said through his jagged teeth “ I never minded polygons anyways, what matters is beneath.” with a raise of his fractalized eye he and eugene were off walking down the way and eating his sherbert there’s no mistake it’s herbert THE HALLOWEEN PUMPKIN.
Dialogue:
HERBERT THE PUMPKIN:
Our pumpkin is Herbert, he really likes sherbert. that’s his favorite dessert
he’s psyched for halloween and going trick or treating with his friend eugene, he’s decorated his house from the roof to the latrine, it's now that magical night and he dresses as a fiend he calls eugene and gulps some caffeine. He went out into the night and trick or treated with might! It’s the next morning now, the night finished in a flash he woke up and saw his brains were mash and now he wonders with eugene what a smell so foul his face had been contorted into a permanent scowl the teeth are crooked with eyes bent and curved his beautiful face now left children unnerved. “Nevermind“ ,he said through his jagged teeth “ I never minded polygons anyways, what matters is beneath.” with a raise of his fractalized eye he and eugene were off walking down the way and eating his sherbert there’s no mistake it’s herbert THE HALLOWEEN PUMPKIN.