Calculus; (Yes This Was Difficult)

Hello, and welcome to my first action project for the first unit of my workshop, "Introduction to Calculus". In this class, we learned the basics of calculus by reviewing slope formulas from Algebra. The slope is a formula used to find the steepness between two points on a graph. We learned and practiced derivatives and instantaneous slope, which is the slope at a specific x coordinate. Derivatives or prime is another function that can be used to find the slope at any point. To help us with figuring this out we learned the power rule. The power rule is just simpler equations that show us how to distinguish between form expressions. For this action project, we were instructed to use a nonlinear function incorporating our two random numbers, evaluate our functions, find the derivatives, and use the derivative to estimate the instantaneous slope of our function on a graph and its tangent line. I hope you enjoy my calculus equations down below!

In conclusion to this project, I didn't have too much difficulty solving the equations once I understood the rules and formulas used in calculus. I enjoy calculus and math overall when I have a decent understanding of the formulas and rules involved. I wouldn't do anything different with this project since my equations led me back to my exact derivative. I hope that this class will continue to benefit me after high school when it comes to more advanced mathematics. 

THE UNORTHODOX PODCAST

For this Fall term, I decided to take up the "Podcasting 101" workshop. I've always had a love for interviews and discussions so podcasting lets me enjoy both. In this workshop, I grouped up with my classmates (CH, KE, CH, NL), to create a podcast called The Unorthodox Podcast. We learned editing and recording skills that would be used later in our episodes. I enjoyed working with my classmates on this podcast because our environment was a safe and fun space when making content. In this podcast, we talk about anything. Common questions, random thoughts, perspectives on various topics, and etc. Grab some snacks, relax and vibe out to our wonderful production.

GCE Lab School · The Unorthodox Podcast Trailer

GCE Lab School · The Unorthodox Podcast Episode 1

Reshaping Education Towards Adult Life

Hello and welcome to my final presentation for the Winter term of my Sophomore year (2019-20). This presentation is based on a workshop I had in my STEAM course Disease. My guiding question was inspired by a disaster plan I made starting out Unit III of Disease. My guiding question is, "What skills do students need to survive in the "real world" and how can education systems better prepare them?".  I formed this question from my own and my elders' experience(s). Some feel that they would've thrived earlier in life if they were taught life skills for their future earlier in their education. I started focusing more on survival during a nationwide pandemic but later refined my studies by focusing on life skills that boost the chances of survival. I hope you enjoy.

Housing Discrimination in Chicago: A History of Injustice

This is my action project for my workshop, "Writing Workshop". In this class, we looked at many different examples of writing and reviewed some basic and advanced writing skills. We took the time to either write a research paper about a topic we were interested in, write a personal narrative about ourselves, or write a summary response essay. This workshop challenged me by introducing me to more styles of writing. I chose to do a research paper because I wanted to challenge myself for this last project of my Freshman year. I have spent a lot of time researching housing discrimination. I even reached out to the director of Human Rights Compliance/Fair Housing at the Chicago Commission On Human Relations. I hope you enjoy my research paper.

Representations of: Mathematical Combination and Pascal's Triangle

In my last action project for prove it or lose it, we were looking at combinations.  This action project is for my course "Prove it or Lose It.” In class, we have gone over permutations, combinations, and Pascal's Triangle. We saw how pascal’s triangle it symmetric and how it shows reflections. We also watched videos and saw slideshows on permutations and Pascal’s Triangle. This unit has made me think about how math does relate to things that we wouldn't expect.

A mathematical combination is a selection of things from a group. The order of those things doesn’t matter in combinations, unlike permutations. FOR EXAMPLE: There are 10 marbles in a jar and each marble has a number from 1 to 10 on it. Three marbles are selected at random. How many different ways are there of selecting the three balls?
Formula: (n/r) = n C r. = n!/r! (n-r)!
Answer:
10C3 =10!=10 × 9 × 8= 120
             3! (10 – 3)!3 × 2 × 1
Pascal’s Triangle is a triangular array of numbers. Each next row has one more number than the last row.  Each row has 1's on both sides and every inner number is the sum of two numbers above it. It can span infinitely. The connection between mathematical combinations and Pascal’s Triangle is that the numbers in Pascal's Triangle represent mathematical combinations. If you sum each row, you can see that each row has powers of base 2, beginning with 2⁰=1 and so on.

N.L., (2018) Pascal's Triangle with Powers with the base of 2 

Triangular Numbers

If you start with row 3 and start at 1, the diagonal contains the triangular numbers.

N.L. (2018) Pascal's Triangle with Triangular Numbers

In conclusion to this action project, I learned many things from this project. I learned more about how I can relate reflections to Pascal's triangle and I found different patterns in Pascal's triangle. Some challenges for me during this process were coming up with a question and answer about mathematical combinations and creating my own Pascal’s Triangle. I found completing this action project enlightening because I know I a lot of effort into this action project. Overall I enjoyed doing this action project and I also enjoyed this unit.

Geometry Reflections In Buildings and Structures

This action project is for my course "Prove it or Lose It" and unit on finding reflections in the real world.  We went over what reflections were, how to find reflections, talked about how we can show them in the real world. In this action project, I found reflections and I also found two different ways to measure or quantify the reflection using mathematical terminology. I looked for my geometric reflections in buildings and structures.

The first way to measure the reflections in buildings and structures is using angles.  In the screenshot below, you can see how this building has different angles on its structure. You can also see how I found the angles that the buildings made. To understand this reflection, we can look at the angle of where they are equal. That is an important property of geometric reflections.

O'Neill, McKenna. (2012) Two Buildings. Web: Blogspot 

Another way that you can measure reflections is to measure reflections in buildings and structures is using slope.  In the picture below, you can see window bars. Instead of measuring the angles of the lines, you can find the coordinates of the points on the ends of the triangles on the window bars and calculate the slope of each line.

NL. (2018) Window Bars.

Using the slope formula, we find:
SLOPE of AD: (-6.5+-1.6) / (8 - 2.7) = (4.9) / (5.3) = 0.92
SLOPE of ED:  (-6.5+-1.6) / (13.5-8) = (4.9) / (5.5) = 0.89

My slope is off by a decimal of 0.3 but we can see that the slopes of the two lines are about the same.

This action project was challenging for me because I had a difficult time figuring out how I was going to include some mathematical terminology to show and measure reflections. Overall I enjoyed this action project and I hope that my skills with measuring reflections have increased because of this project.