• Intercept form of a quadratic equation and how this applies to rockets

School Values: Critical Thinking - Identification of Changes: In our paper rocket experiment, the intercept form y = a(t - p)(t - q) helps us analyze the timing of the flight. The intercepts p and q represent the time of launch and the time of impact when the rocket's height is 0. By looking at my tracker data, I can use these time intercepts to find the exact moment the rocket reached its peak height, which is always the midpoint between the launch and landing times.

• Learning and using the software to track parabolas (process)

Growth: Collaboration/ Feedback: In last Monday's class, Mr. Kemper came in and taught us in using the tracking software to track the ball. For homework, we are assigned to record a video of throwing a ball ourselves each and upload them onto the software to track them. This was very difficult for me because the teacher's computer was in a different setting than mine and I was not able to upload anything at first. I struggled in turning in the homework since I am really bad in using computers and the instructions of the assignment was a little confusing to me. This was a cool experience to track a ball by using this software and a meaningful project to apply math to real things, but if I could choose, I might prefer regular class works.

• Paper rockets (process, launch, and recording)

School Values: Critical Thinking - Connection to Other Classwork: In last Friday's class, everyone in class teamed up and made paper rockets. I was in the same team as Emerald and we made three rockets with different fin designs. One rocket's was with four big fins, one with smaller fins, and one without any fins. Later, we recorded when we tested out our rockets and tracked it with the software after uploading the videos. After a class of tracking many balls, I believe that I am a little more used to the software. This project is really challenging to me since I am bad in computer and finding the equation of a parabola is a new thing to me that I have to spend more time in practicing and catching on the class. However, this class connects to my computer science class in PBL last semester, and I believe that this is a good chance for me to improve in this category.

• Finding the equation mathematically in root form from one point on your rocket parabola

Growth: Vertical Growth: My understanding of math improved because I learned how to turn a real rocket launch into an equation. I used the root form, y = a(t - p)(t - q), where p and q are the times when the rocket is on the ground. To find the full equation, I picked one point from my tracker data, like (0.067, 0.0754), and used it to solve for a. This shows that I understand the points on my graph and the formula are actually the same thing. 

• Class-specific 1: Conceptual Understanding of Mathematics: In this Angry Bird project, my teammate and I were trying to reach our goal to let every single bird hit the structure or pigs. To succeed that, I had to find a vertex for each parabola first, and then I get to know which points on the structure will go through the equation. Next, I find the symmetrical point of the starting point based on their vertex to make sure that they all hit something. After that, we find the vertex form of the parabola by plugging in the vertexes into h and k and then we find a with a program that calculates for us since the numbers might be very complicated to calculate. Next, we expand the square binomial and then multiply the a into the bracket to get the standard form.

• Growth: Work/ Study Habits: The Angry bird project is something harder than I thought since I had to make sure they all hit the pig or the structure. I was in charge of what the parabola should look like. This was a little more difficult than regular work we have done in the class before since I always only remember the formula to solve math questions and mostly don't understand the meaning behind it. This is something I noticed and should surely change in my future math study habit. Instead of memorizing all the formulas and not knowing what to plug in, I shall understand all meaning of them and understand the definition to solve problems with more flexibility. This is a working habit I really want to change before I enter another semester with more difficult math. I believe the change would allow me to solve problems when I also understand what each equation and formulas represent. 

• Growth: Connection to Future Plans: In this project, I worked with one of my classmates. We were struggling in the process of the project because we didn't divide our work properly and led to some times when she didn't do something I expected her to do. This was a serious problem and I am not blaming her for anything. I believe that it was responsibility to both of us since we wanted a peaceful teamwork time without misunderstanding each other all the time. At the very end, we managed to message each other to make sure that we completed every part nicely and that we both approved each others' work and also made sure that there were less mistakes. There were one major big problem when my teammate wanted to work on the big piece of paper completing all the forms of the parabola instead of the worksheet since it was a lot of work for one person. To solve this, I went to complete 80 percent of the worksheet and then when she comes, she could polish my work and complete the very last part. This made the project done well and peacefully. I believe that this is a lesson I have learned through team work. I hope in my future, in college, or even in my future job, I could always remind myself that team work requires not just communication, but also checking on each other to make sure they don't misunderstand you. Dividing work may be difficult sometimes, but always remember to do them before actually working to prevent thinking that your teammates didn't meet your expectations or only one of them working hard while others waiting for results.

• School Values: Global Citizenship - Identification of Global Issue: In this math test, I can tell that there is a strong connection between the triangle problems I solved on the paper and real-world global issues. Specifically, Word Problem C talks about a fire station that helps three different towns. Calculating the exact distances and driving times for fire trucks is not just a school exercise; it represents a major real-life challenge. Many countries around the world struggle to build good emergency services. That's why I believe that using math rules like the Law of Sines helps people plan faster routes to save lives during natural disasters or fires. To improve my reflection in this category, I want to think more about how math can help solve these global problems. While I successfully found the travel time for the fire truck (around 40minutes), I should think deeper about why some countries have better emergency systems than others. In my future projects, I will try to explain how global organizations can use math and geometry to build safer neighborhoods and help people in danger around the world. 

• School Values: Global Citizenship - Identification of Local/ Regional Issue: I can also connect these math problems to specific local issues in Taiwan and Taipei. Taipei is a very crowded city with many mountains, which means urban planning and building safety are very important local topics. For instance, the math I used to find the height of the Peace Tower in Word Problem A is very similar to how engineers measure tall landmarks like Taipei 101. They must use these exact formulas to make sure buildings are strong enough to survive local earthquakes. To get a higher score here, I need to make a clearer link between my math answers and a real local plan. For instance, I could connect triangle area formulas to Taipei's new building projects or to how we protect the land in mountain areas. In the future, I will make sure to talk about specific challenges in Taiwan to show how precise math can help our local government design safer public spaces and facilities. 

• School Values: Global Citizenship - Appreciation of Difference: This math test allowed me to see how different cultures and history have shaped the way we measure the world. The problems use names and places from different countries such as Ottawa. Working on these questions reminds me that math is a universal language. It was created by many different groups of people over time, from scholars from ancient countries who helped create the sine rules. It shows that even though our cultural backgrounds are different, we all use the same logic to solve problems. To show an even better understanding of different perspectives next time, I want to think about how different cultures view land and space. For example, some groups might care more about protecting nature than building straight roads, which changes how they use geometry in the real world. In the future, I will try to learn about these different cultural views to show that I respect and understand the different ways of thinking.