The purpose of this project in my opinion was to teach us not only math skills such as dilations, ratios and proportions, similarity and congruence and other types of math that lead up to and help us while trying to scale large of small models But It also taught us critical thinking techniques and habits of a mathematicians while learning to scale and object using several drafts. When we first launches this project Dr.Drew showed our class an absolutely amazing video about a group of friends who scaled the solar system in the desert. This video blew me away and I loved it more than words could explain. I love film and found it so fascinating how they accurately scaled something as big as our solar system from what we know down to the size of marbles. My favorite part of this video was when they held up the sun and it was as big as the sun actually was in the sky from our perspective down here on earth. After watching that video I immediately knew that this was going to be a project I would really enjoy. I chose to start small like mathematician and build on my ideas from there. With something like an iPhone with a game on the screen. When we were put in table groups one activity/benchmark we did was where we made posters and presented each group one topic. The topic we had was what was similarity. And so because I was the poster illustrator or artist I drew lots of similar shapes and wrote out the definition of similarity means in a way almost any person could understand. When we started brainstorming or board-storming what we knew about congruence and similarity I remembered a lot of things I had learned last year with Dr.Cate about congruence, similarity, rotations, translations, dilations etc. And from the board-storming we used our knowledge and launched into the creative group posters summarizing the mathematical concepts we were given. And then we closed the project with the topic of dilation and then started to move into our actual scale artifacts that will be used for our upcoming exhibition we are all having later in December.
Mathematical Concepts Throughout this entire project we learned a total of six different mathematical concepts. The Concepts we learned were 1. Congruence and Triangle Congruence 2. Definition of Similarity 3. Ratios and Proportions, including solving proportions 4. Proving Similarity: Congruent Angles + Proportional Sides 5. Dilation, including scale factors and centers of dilation 6. Dilation: Affect on distance and area (re: Billy Bear) (we also looked at transversals, vertical angles and corresponding angles) The very first concept we learned was about congruence and triangle congruence. Which in summary means that if two shapes were congruent they would be the exact same shape showing no difference in size or shape. One easy way to check if two shapes are congruent would be to see if they have the same matching angles and side lengths. This leaded into the definition of Similarity. Unlike congruency a similar shape can differ in size . This means that there ratios and proportions match. For example if you had a 4 by 4 square and a 2 by 2 square which have matching ratios and proportions they would be similar even though they are not the same size they are the same shape with the same ratios and proportions. Another way to prove if two shapes are similar would be to measure the angles. If all of the angles are the same and the size is different you could conclude that the two shapes are similar. Dilation in math is known as a similarity transformation where a shape is enlarged or reduced. One cool way to think about dilation is like when you are zooming in or out on a camera. Because even though the shape grows or shrinks it always keeps the same overall shape. All six of these concepts helped me while I was trying to scale my iPhone. I used all of these skills while I was scaling the phone and I especially used measurements proportions and ratios while I was scaling. These six concepts are crucial mathematical skills and each one has helped me immensely during projects such as this current project "Scaling the World". During benchmarks #2 and #3 we used many calculations related to dilation. Every single thing I dilated for my bench marks #2 and #3 so dilation was the most used concept during the process of making these drafts and final drafts in my benchmarks. Because I was just increasing the ratios of proportions of my original model by twice the size so it is technically a similar iPhone. Not congruent though because one is twice as large as the other. If you scroll down to the bottom of the page you can see some of my scaling work with calculations and my original model scale to the model twice as big that I submitted in my benchmarks #2 and #3.
Exhibition
Ourfirst benchmark during this project was to submit a project plan with our ideas of what we were going to scale and who would be in our group. What materials we would need and how we were planning to present our project. I originally was alone and was going to make a video possibly scaling baking but I am very glad I partnered with Jackson and chose to do something different like a cel phone with the game "Flappy bird" as the home screen dilated. For our second benchmark we had to sketch or create somehow two similar diagrams of the actual thing we were going to scale. This diagram had to be labeled with all of the original measurements, dimensions and proportions of the original object that we would scale either larger or smaller. In my group this took a lot of work because I was not familiar dilating anything that wasn't triangular or square. And a lot of the dimensions on the phone were round such as camera, home buttons, edges etc. And I learned a lot about how to dilate objects with just a ruler, pencil and calculator. Our third benchmark or you could just say our final product was our absolute final draft for this project.The math we used behind benchmarks #2 and #3 were the scale factors, calculations and dilations. We chose as a group for the scale factor to be 2 times the size as the original. My final product was a cel phone twice the size of my iPhone 5s and I am proud of our final product other than the fact I could have spent some extra time to add some color so it is not just plain black and white. And finally afterwards we filled out self-assessmet and peer grades for the project.
Reflection
I grew and learned a lot from this project. Going into this project I didn't know to much about scale factors and how to dilate objects or what that even meant to dilate a figure. I would say this project had many challenges but was an overall success. I worked hard and really pushed myself to fully understand what I was learning in the moment before I was eager to just jump to the next step once we were finished with something. In the beginning of this project I did not have a lot of confidence and not a lot of knowledge of how to even start the project. I was sad in the beginning before benchmark #1 because all of my friends partnered up so I was left out. But I ended up making a new close friend Jackson if it wasn't for the project. I had a hard time choosing one idea that was achievable for me to accomplish and within my reach. I'm glad I didn't choose to do something food related because I think that would have been to simple and I wouldn't have challenged myself mathematically or learned as much as I did if I hadn't pushed myself to chose this product. The habit of a mathematician I used the most during this project was to "Be Confident, Patient, and Persistent" if I hadn't been confident, patient and persistent I would never have gotten the final product I have now. I'm glad I chose the route of patience and persistence because even sometimes when it feels like you have hit a brick wall and you want to just give up and you may even just start to get down on yourself and think you are dumb. If you don't think positively you won't move anywhere. I know many times in math I have gotten to that point where I just want to give up but there is always an answer on the other side. It is called a problem for a reason and most times there is almost always a solution. I am so happy with my final product and had such a great time during this project and learned so much!