Intercept form of a quadratic equation and how this applies to rockets
During the flight of a rocket, the intercept form of quadratic equations can help us identify key moment of the rocket. When the quadratic equation it is written in intercept form : y=a(x-p)(x-q) . The values p and q allow us to identify when the rocket leaves and returns to the ground. The difference between these two values is the duration the rocket was in the air for. In addition, the maximum height of the rocket occurs in the middle of the parabola, which can be calculated through the midpoint formula.
Learning and using the software to track parabolas (process)
When we first learned about this software, my graphs were all inverted and the complete opposite of my classmates', I was really confused and I thought the software was glitching. But it turns out that it was inverted since I accidently flipped the axis in the begining. This mistake taught me to be more careful in when doing math since one small mistake could lead to the whole thing being wrong and to always double check my answers.
Paper rockets (process, launch, and recording)
The assembling process of the paper rockets was pretty easy, but our rockets didn't fly as I expected them to. When we built the rockets, we were very careful and made everything as tight and neat as possible. Which resulted in our paper wrap being so tight that it was nearly impossible to shoot out. We had a hard time fixing this since we already stuck on the fins and we didn't know how to loosen the rocket. But eventually, we managed to loosen the rocket thanks to the suggestion from a classmate that we unroll it a bit and re-roll the rocket.
Finding the equation in root form either mathematically or using desmos
I first found the two roots, which in y=a(x-p)(x-q) are p and q. Then I plugged the two roots in along with another point on the parabola (x, y) to find a. And finally I wrote the final equation using a, p, and q.
Angry Birds Quadratic Equation Project
School Values: Critical Thinking - Identification of Changes
Here are some changes I would make to improve this project. Firstly, I would change the flight paths of some birds to make them not hit anything, that way I would have the opportunity to investigate how and why they missed, therefore making the project more complete. Then I would make more drastic changes to either the vertex, a, or landing point of all the parabolas so that the difference between them could be visible, making it easier to figure out which factors contribute to changes in the parabola. The last change I would make is the place the launcher at (0,0), while calculating the equations of the parabolas, I noticed that it was quite difficult to figure out the root form and the zeros since the parabola didn't start on the x axis. So moving the starting point to (0,0) would make the entire calculation process much easier.
Growth: Vertical Growth
This angry birds project is connected to the super mario quadratics activity we did at the end of the first semester because they both require us to manipulate some factors in the quadratic equations in order to make the characters hit a certain point. For instance we wrote down equations to make mario cross rivers, jump over objects and eventually defeat bowser. We did the same thing this time but just the other way around, we made the birds hit the pigs first before calculating the equation. Therefore I believe that these two actvities are connected to eachother and doing the super mario quadratic project last semester made this project easier to understand.
Class-specific 2: Application & Problem Solving
I talked about how I would make changes to some factors of the parabola, the following would be what each change contributes to the parabola. If the vertex was higher, the bird would land closer the the starting point, making it miss the structure and the pig entirely. If the vertex was lower, the bird could go farther, making it hit the middle of the structure. If the vertex was moved to the left a bit, the bird would land closer to the starting point, making it miss the structure and pig. If the vertex was moved to the right, the bird would hit some of the pigs on the right. The bigger the a the more vertically stretched it is. But in this project, the a is a negative, which means that the smaller the a (the bigger the numbers without the negative) the more vertically stretched the parabola is. So the movement of the vertex would affect the landing point, which can determine if the bird hits a structure or pig. And the size of the a determines the shape of the parabola.
Trig Comic
School Values: Critical Thinking - Connection to Other Classwork
Similar to the Atlas project I did in geography, these two projects both require us to first understand a problem, solve it, and prove our undertstanding by visualizing it on paper. This project is also quite similar to the shatterbelt matrix project we did in geography because in both of these classes, we had to first learn a concept and then apply that concept to real world concepts. I learned about Geopolitics in geography and I applied my learning to the cyprus issue, crafting a boardgame in the end. And similarly I learned trigonometry in Math and I applied it by solving questions and drawing a comic based on those questions and my undterstanding of them. Finally, this project is connected to my PBL project because they both require accessability thinking. In my PBL project, we made keychains with non offensive symbols and tactile features to stop casual ableism. While in this comic project I focused on using bright colors, clear black lining and clear visualization to make it more readable.
School Values: Global Citizenship - Identification of Global Issue
The first comic that I drew was a plane, the main character flew on a plane to Hawaii to go on vacation. But aviation actually worsens the environment globally due to its extreme environmental impact. Aviation contributes to climate change (due to CO2 emissions), noise pollution (aircraft noise), water pollution(due to their extensive use and handling of jet fuel, lubricants and other chemicals), and air pollution (due to the burning of fuels). This global issue could be mitigated by reducing air travel, optimizing flight routes, and restricting short-distance flights.
School Values: Global Citizenship - Identification of Local/ Regional Issue
There was a scene where I drew a boy looking at a coral while snorkeling, I wasn't quite familiar with how to draw corals so I searched it up, but what I saw shocked me. I learned that coral reefs in Taiwan are dying and "bleaching" because changes in conditions such as temperature, light, or nutrients make coral reefs expel the symbiotic algae living in their tissues, causing them to turn completely white. And Taiwan is especially prone to this issue since the country is on level 2 alertness. The solution to this issue is quite promising, by drastically reducing global carbon emissions to mitigate climate change, coupled with local interventions such as coral gardening, assisted evolution, and improved water quality management, we can successfully fix this regional issue.
School Values: Global Citizenship - Appreciation of Difference
When I was drawing this comic, I kept thinking how wonderful this Hawaiin vacation is and what I would do to have one, from my point of view this trip was a perfect getaway. But I also understand that maybe some people view vacation as a waste and environmental harm. While researching aviation environmental impacts I realized just how much greenhouse gas planes release per flight and how it contributes to climate change, which would then negatively affect the coral reefs. So I think it's important to think of the environmental impacts before vacations.
Unit 8 Assessment
Growth: Connection to Future Plans
I have started studying the stock market and how to invest, and I hope that I am able to invest wisely and make a living off of it in the future. Therefore math is extremely important in order to fufill that plan. This assessment helped me see how well I understood the topic and what I need to improve on, giving me a quick understanding of my progress so far and what I can improve on. Making it a crucial milestone.
Class-specific 2: Application & Problem Solving
After looking over my test, I found that my main issue is my fractions, sometimes my subutraction is incorrect, sometimes I forget to round my numbers. These mistakes are more on the mathematical side instead of the comprehension side so therefore they are easier to understand and fix. Therefore, in future assessments and projects I need to spend more time checking if my calculations are correct and if I missed anything in the questions (like rounding the number).