Intermediate Secondary Mathematics

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

Description

You can use the intercept form of a quadratic equation to track the arc, start, end, and highest point of the rocket. y=a(x-p)(x-q). P and Q are x-intercepts. 

Growth: Connection to Future Plans

I want to be able to use my knowledge I have learnt in these math classes to be able to efficiently calculate all of the statistics of my  bottle rocket.

Learning and using the software to track parabolas (process)

Description

Our teacher led us to the download link and helped each of us to download the tracker application. After this, he taught us the basics of using the tracker app, with us following along with him to a prebuilt video in the tracker app of a person throwing a ball. The process is to insert a video that we want to graph. After this, we want to insert a calibration stick to make our graph accurate to the distance. After this, we will put in a coordinate axis to mark the starting point for the graph. Finally, we will track the object we want to analyze. This will automatically create a graph that we can find the parabola of. After this, we filmed a video of ourselves throwing a ball and did the same process to make a graph. Finally, we moved on to paper rockets. 

School Values: Critical Thinking - Connection to Other Classwork

Using a new application like this was similar to when I used Unity and DaVinci Resolve for PBL. I like that the school is introducing me to these unique applications and that it continues to challenge me with different concepts. The teachers do a good job at teaching how to use them, and it sets me up to use similar applications in the future. 

Paper rockets (process, launch, and recording)

Description

We made the paper rockets by wrapping a sheet of construction paper around a pencil, taping it around it, making wings to tape to the end of the rocket and then finally either twisting the top part to make the nose cone or taping a new piece on. While launching, we blew air into the rocket using a straw and recorded it using a phone. I found that standing far back worked better to record the full flight and that the more airtight your rocket was, the more it would use the energy from the air to blow forward. 

School Values: Critical Thinking - Identification of Changes

I can use what I have learned from changes I could have made to my paper rockets to apply to my bottle rockets. For example, I should weigh my bottle rocket down less because of the large amount of t    ape that I used on the paper rocket that weighed it down. I also need to make my bottle rocket more airtight so that all of the "fuel" I am using on it doesn't escape.

Finding the equation in root form either mathematically or using desmos

Description

I learnt that you have to find the x intercepts, plug in a point from the graph, simplify the equation to find a, and then plug in all of the variables into the root form.

Growth: Vertical Growth

This concept was used in our paper rocket launch where we calculated the root form of the arc of our rocket.

Angry Birds Project

Growth: Work/Study Habits

While making the Angry Birds Project, I was able to complete it on time without requiring any work from home. I hope I will be able to continue this, so I can focus more on the actual homework that is assigned to me at home rather than work that can be finished in class. To do this, I will try to stay on task as much as I can in class rather than getting sidetracked on other homework assignments. I know this will always be feasible, as our teachers always give us enough time to finish what is assigned to us as classwork. 

The Angry Birds Project was completed on time without requiring working from home. 

• Complete the Angry Birds project without working at home

• Time was managed well with my teammate, splitting up responsibilities

• Continue this, as teachers always give us enough time to work on classwork to finish it

• Apply this to other classes

• Focus on homework at home

• Less stress

• Avoid getting sidetracked

• Make sure everybody is on the same page/Good communication with teammates

• PBL needs better communication

• Don't underestimate how much time projects will take

• Start using a calendar to organize my time (I've been meaning to do this)

Growth: Collaboration/Feedback

While working with my partner on this project, I got a ton of good feedback. By splitting up the work with my partner, we each worked on our parts while also giving feedback on what we thought should be changed in theirs. For example, adding the sun, the pillar's colour palette, and the birds' vertex was all based on feedback from my partner. The most important feedback I got was when we were graphing the parabolas of the birds; my partner gave me feedback on the math worksheet I was working on, correcting me about whether or not the blue bird would hit the tower or not. This led me to change one of the questions asking about whether all birds hit the tower and what birds didn't hit the tower, and why. I definitely should have made the bluebird's vertex lower, as it just barely hit the tower while graphing. The final piece of minor feedback was when printing the birds and the pigs, we both realized they may have been too large for our project, causing us to reprint them in a smaller size. However, even after printing them smaller, we still could not fit them into the small hole we covered, as you can see in the image. As a result of this, my partner gave me feedback on what we should do by covering the hole up with the colour that was surrounding it, making it seem like it was never there.

• Collaborate with a partner

• Feedback during work on the project

• Split up the work with a partner

• Made changes based on feedback about colouring and graphing

• Colouring of the pillar/sun

• Graphing of the bluebird

• Leads to changes on the math worksheet

• Should have made one of the birds definitely miss, as when graphing, I realized that the bird meant to miss the pillar just barely hit it

• The size of the printed birds and pigs was initially too large

• Placement of the pigs

• Feedback for myself

• Made sure my partner understood the math

School Values: Global Citizenship - Identification of Global Issue

The global issue that the Angry Birds Project can solve is renewable energy generation. This is a global issue because of global warming, rising demand, and the need for universal energy access. Since we are focusing on parabolas, we can focus on a type of solar panel called the solar parabolic dish. How this solar panel works is that it uses its shape as a parabola, coated with a reflective material, to collect sunlight over a large area and reflect it onto a single point. This point captures the solar energy and turns it into heat. This heat can then be turned into electricity or can be used directly for heating. Some benefits of using this specific type of solar panel are its high efficiency, versatility, and reliability. Because of the fact that it's able to focus sunlight onto one single point, this type of solar panel can reach higher temperatures, which in turn causes it to have higher efficiency while converting to energy. A solar parabolic dish is versatile because of its multiple applications, including electricity, heating, and cooking. Finally, it's reliable because of its effectiveness in areas with direct sunlight and its ability to continue generating electricity even on cloudy days.

• Renewable Energy Generation

• Solar Parabolic Dish

• Parabolas

• Solar Energy

• Parabolic Reflector

• Focus sunlight onto a Central Receiver

• Solar Reflector, Receiver, Supporting Structure

• Environmentally Friendly (Little to no water required)

Unit 8 Assessment

Description

The Unit 8 Assessment went over solving triangles using the sine and cosine laws. There were two sections in the test. The solving triangles section and the word problems section. The solving triangles section was just a list of triangles that needed to be solved to the nearest tenth (find all the side lengths and angles). The word problems were more complicated, with 3 of them being provided. Some needed you to draw a triangle from just a word description, and some needed you to solve a specific problem using a triangle provided. Additionally, there was a bonus question that asked you to find two possible lengths of a third side of a triangle using 2 side lengths and the area of the triangle. The parts I struggled most with were the first word problem and the bonus question. For the first word problem, I couldn't understand how to fill in the angles for the triangle, and for the bonus question, I just misread the equation and didn't have enough time left.

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

The concepts I used in this test can be applied to solar energy in Taiwan. Engineers can use trigonometry to maximize energy capture by finding the optimal tilt angle for solar arrays across different cities like Tainan or Taipei. The angle will need to be changed seasonally, and biannual cleaning and inspection will be required. However, despite the upfront investment, long-term savings are still possible with proper maintenance and mathwork. 

Angle of Depression/Elevation Comic Project

Description

For this assignment, we were required to pick a theme and solve the word problems provided in the theme. After that, we made a comic strip that included a picture of each problem. Each word problem was an example of using angles of depression/elevation in real-life situations.  The three themes were a Hawaiian vacation, a baby's day at the park, and Spiderman's adventure. In addition to this, we were given the option to create our own 6 word problems with a mix of depression and elevation and finding angles and sides. After doing this, we were to trade our word problems with another person and make a comic strip for their word problems. 

School Values: Global Citizenship - Appreciation of Difference

I like the way this assignment allows people to interpret the word problems in different ways while drawing them. It also shows the different perspectives and approaches people have for solving math problems. Additionally, the fact that there is a choice between 3 themes and also the choice of creating your own theme allows people to find the way that suits them best when solving the problems.