GSP 1

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

Project Description.

In the class we have reviewed about how to find quadric equation, plug things in and find different variable.And now we are using Tracker this app, we need to find the quadric equation and intercept form from the graph and data that Tracker give us base on the rocket path.From the process, first we have learned how to find quadratic equation and intercept form.

Class-specific 2: Application & Problem Solving

I calculate the point that we need with both familiar and unfamiliar contexts. For example, I use factored form to solve for our equation back. Factored form is the thing that I do not get very good at, because when I solve the problem, I don't use factored form. For the familiar part, I use the intercept form that I have already learned before; I use the intercept form most often. When I finished calculating the math, I always confirmed with my teammate, and we both always got the same answer.

Learning and using the software to track parabolas

Project Description.

In class, we have learned about how to track the parabola of the ball in the tracker.Tracker are mostly a application that we can use to track for each pin, and it will automatically give us the parabola of this thing and also the equation of it.

Class-specific 3: Mathematical Communication

In this project, I have used precise math language, using the correct formula, for example, using the quadratic equation and intercept form to help to find the highest point and point we need for tracking the path of the rocket, also using the coordinate to pull the equation out. How I got these equations: The steps are clear and organized; they are labeled, and it was easy to read and follow what I thought back then.

Paper rocket

Project Description.

In this project, we have learned how to make a paper rocket by using a pencil and other materials. We have watched the video together, doing it step-by-step with my classmate. We must make 3 rockets; they all need to be different, and they can be different in any way. We need to use a straw to blow the paper rocket out and record. Put it in the tracker to calculate the intercept form.

School Values: Global Citizenship - Appreciation of Difference

When we were making the paper rocket, I saw that the other group was using different ways to lets the rocket fly more differently. I saw that other people are putting different material on the rocket, using a different type of pen to make the body of the rocket. These differences are making the rocket flight path different. These new ideas made my teammate and me want to also add some changes to one of our rockets. At last we are using different paper to make other rockets; we are using the paper that still has our exit ticket on it. We think that these papers are harder; through the air resistance, they will get smoother, and it really do.

Finding the equation in root form either mathematically or using desmos

Description.

To find the equation in root, first we need to base on tracker data, locate the two x-intercepts, write it as a base intercept form: y=a(x-r1)(x-r2).Then we need to locate the vertex, use the tracker to find the highest point of the parabola, which lies at the midpoint of the roots.Nest solve the a, substitute x,y into the equation toe solve a.Last to rewrite the equation, just replace a to the number you hace calculate.

Angry bird proejct

Project description

In this project we need to making a angry game on the paper, we need to draw the pig and the bird out.And make a parabola of each 6 birds.We need to calculate the equation of the parabola.And how vertex and different numbers connect to the equation and parabola.

Critical Thinking – Connection to Other Classwork

This project has been connected to our physics project before. In that project, we need to stick an apple on a string, and drop the apple, then the apple will make a parabola that is facing up. The apple will get slower and slower when it swings. In that project we need to calculate the speed in each second and where at each second. It was very similar to our Angry Birds project. In this project, we need to base our drawing on the equation to draw a parabola curve, but it is negative. For drawing the curve, we also need to find where the point is in each second to make sure the parabola is accurate. And also connect to my art project before, in that art project, we need to draw a golden radio art, we need to calculate where the point is to make a perfect golden radio art. In that project, I have made a chameleon, I have turned the tail and the body to spin around to make a golden radio shape. It connects to Angry Birds; we need to calculate the parabola to make it accurate.

Growth -Collaboration/Feedback

When I did this project, my teammates gave us a lot of good feedback. For example, I already calculated all the parabola equations and am going to start to draw the parabola for each Angry Bird. But my teammate has found out the problem with my equation. He said we'd better have some parabolas that hit the pigs or structure, but I don't have it at the start. So I need to change some of the equations to make sure they're hitting the structure. And all the parabolas are pretty average, so it's kind of hard to see which parabola has the highest vertex, so my teammate told me to change one vertex to a number that was very different from the others. He also let me change all the equations, but it helped me to write more easily in my reflection and findings. Next time, I will first see the rubric, then see the reflection to find which things we need the most and pay more attention to these points.

Global Citizenship – Identification of Global Issue

This project can connect to war. In the war there are mortars; they will shoot the things like cannonballs, but they need to be accurate or they could waste the bullets or maybe endanger some innocent lives. In this project I use quadratic equations to calculate precise bird flight paths and hitting the target; that is, shooting could use the same math to plan mortar in the place that we calculated. A small change in the variable can affect a lot in the graph; for example, the "a" in the parabola has a big place in the equation. If you have a small change in "a," the graph will change very differently. So calculating the right number for the variable is very important. It's important in math, science, or the place that has a variable in the equation.

Angle of Depression/Elevation Comic Project

Project description

In this project, we need to base it on the question that the teacher gives us, using the different angle to form a triangle. First we can choose a theme out of three of them: Hawaiian Vacation, Spiderman, and also Babies' Day at the Park. Every question will give us the math and also the theme of that frame. All the triangles need to be correct with the number that the question gives and the correct direction. There also needs to be at least 2 thought/word bubbles.

School Values: Critical Thinking - Identification of Changes

I identified several areas where I could improve my work for future projects. I realized that I need to be more careful when labeling right triangles, especially clearly marking the right angle and correctly identifying which sides are opposite and adjacent to the given angle. I also learned that adding a small diagram next to each problem in my written work would make my reasoning clearer and help me catch mistakes earlier. These changes will make my mathematical work more accurate and easier to follow.

Growth: Vertical Growth

This unit extended my prior knowledge of right triangles into a deeper understanding of trigonometric ratios. I went from just knowing how to find missing sides using the Pythagorean theorem to being able to find missing angles and solve real-world problems using sine, cosine, and tangent. I showed clear progress by mastering these new skills and applying them to 6 different playground scenarios in my comic strip.

Class-specific 1: Conceptual Understanding of Mathematics

I deeply understood the difference between angles of elevation and depression and how they relate to right triangles. I could explain that an angle of elevation is measured from the horizontal up to an object, while an angle of depression is measured from the horizontal down to an object, and that these angles are equal because they are alternate interior angles. Most importantly, I mastered the SOH-CAH-TOA mnemonic that helps us remember the three basic trigonometric ratios. My diagrams clearly labeled the opposite, adjacent, and hypotenuse sides relative to each given angle, demonstrating a strong conceptual understanding of how these ratios work.

Growth: Work/ Study Habits

I stayed organized by breaking the project into smaller tasks: first writing the storyline about Payton's day at the park, then creating the math problems, then drawing the diagrams, and finally solving each problem using SOH-CAH-TOA. I used the provided rubric as a checklist to make sure I included all the required elements, like 6 animations and 2 speech bubbles. I also double-checked all my calculations by cross-referencing with the Pythagorean theorem where possible. These habits helped me complete the project on time and to a high standard.

Growth: Connection to Future Plans

Understanding trigonometry and the SOH-CAH-TOA ratios is essential for many careers I am interested in, including engineering, architecture, and computer graphics. If I become an engineer, I will use angles of elevation and depression every day to design safe playgrounds, ramps, and other public structures. Even if I choose a different career, the problem-solving skills I developed in this project will help me in any field. This project showed me how math is used in real-world professions that affect our daily lives.

School Values: Global Citizenship - Identification of Local/ Regional Issue

I connected this project to local issues in Taiwan, where earthquakes are common. Architects and engineers use trigonometry to design earthquake-resistant buildings by calculating the angles at which forces act on structures. Trigonometry is also used to measure the height of mountains and monitor volcanic activity, which is important for public safety in our region. This made me realize how math is used to protect people in my community.

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