Project DescriptionThe purpose of this project was to obtain information about dilation and how to apply it to real scenarios. Within the project, we were taught different mathematical skills such as: congruence and triangle congruence, the definition of similarity, ratios and proportions, proving similarity, scale factors, and dilation. We put these to the test by making a scale model of anything we wanted, with specific dimensions that we decided on, and relayed them to our work in class.The beginning of the project was very slow - we designed posters for each of the following terms: Congruence, Triangle Congruence, Similarity, Ratios, and Proportions. After these presentations, the teacher went into deeper elaboration on each topic, then we were assigned worksheets for each topic. We had about 30-45 minutes each day in class to complete them, and then we’d discuss as a class our different approaches to solving each and every issue. After finishing about ten sheets through two weeks, we were assigned the final step in this: The project itself. For the project, called “Scaling Your World”, We had to take any object in the world, or our universe, and either scale it smaller, or scale it larger, in time for an exhibition near the end of the year of 2016. Below, I will elaborate more on each section of the paragraphs above.
Mathematical Concepts1. Congruence and Triangle CongruenceDefinition: (of figures) identical in form; coinciding exactly when superimposed.
2. SimilarityDefinition: Two objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.3. Ratios and ProportionsIn the sense of triangles, equal ratios = proportional Exhibition
Benchmark #1: For the first third of this project, we had to assemble ourselves into a group, and within this group decide what we will do for our project - what shall we scale down, with what measurements, etc; and then submit our plans to Dr. Drew for approval. Once approved, we moved onto Benchmark Two. We decided we’d take the scale of the sun in relation to Earth.
Benchmark #2: For this benchmark, we had to figure out the math for our project. Our first step was to figure out the actual dimensions of the Sun, then the actual dimensions of the Earth. Since Earth is so small in relation to the sun, we had to figure out what we’d do to represent Earth, which I will explain later. Our first step was to find the numbers - so we did a bit of research. We eventually ended up with some important facts - for the info relating to the size of the Sun as compared to Earth. The Sun has a diameter of about 1,392,000 km (~865,000 miles). Earth's diameter is 12,742 km (7,917.5 miles). Therefore, we ended up with the fact that the Sun is about 109 times greater in diameter than the Earth. To scale this down was mighty difficult, and I shall explain that in the next part.
Benchmark #3:
This benchmark centered around the physical creation of the product. My partner and I both knew we wanted to have a sphere of some kind in relation to the Sun and Earth, so we bought a ten inch styrofoam ball. We both knew that we wanted to decorate it with acrylic paint, so we went to our school’s art room, and spent about an hour painting the whole thing various shades of red and orange. Halfway through the painting we ran out of the orange paint we we’re using, so we painted the other half red. The math involved was complicated for the scale factor, so I will not relay it back here, but the end result was having to represent Earth in relation to the 10 Inch ball with a scale size of 0.09. Knowing this was complicated, we decided to have more elaboration at our booth during the exhibition, which I will upload photos of when the time comes. We chose to do this both for the challenge and to see how far we could go without asking the Dr. for help, which i’m surprised as for the math component that we did not need to.
ReflectionOverall, I think this project went really well! I was worried that I had chosen something far too complicated, but the end result really paid off, and our scale model is looking great! Needless to say, the math and all other benchmarks are completed, and the writeup for this portfolio is looking pretty swell too. If I could change one thing, it would to be find a 20 Inch ball, so that we could represent Earth better, but this will be fixed if I ever do a project like this again. This project pushed the limits of my thinking, for a bit, I was worried I may have to change the project we were doing to something else, as the scaling part become very difficult. All in all, this project made me really happy that I again show that I can work under stress.
Mathematical Concepts1. Congruence and Triangle CongruenceDefinition: (of figures) identical in form; coinciding exactly when superimposed.
2. SimilarityDefinition: Two objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.3. Ratios and ProportionsIn the sense of triangles, equal ratios = proportional Exhibition
Benchmark #1: For the first third of this project, we had to assemble ourselves into a group, and within this group decide what we will do for our project - what shall we scale down, with what measurements, etc; and then submit our plans to Dr. Drew for approval. Once approved, we moved onto Benchmark Two. We decided we’d take the scale of the sun in relation to Earth.
Benchmark #2: For this benchmark, we had to figure out the math for our project. Our first step was to figure out the actual dimensions of the Sun, then the actual dimensions of the Earth. Since Earth is so small in relation to the sun, we had to figure out what we’d do to represent Earth, which I will explain later. Our first step was to find the numbers - so we did a bit of research. We eventually ended up with some important facts - for the info relating to the size of the Sun as compared to Earth. The Sun has a diameter of about 1,392,000 km (~865,000 miles). Earth's diameter is 12,742 km (7,917.5 miles). Therefore, we ended up with the fact that the Sun is about 109 times greater in diameter than the Earth. To scale this down was mighty difficult, and I shall explain that in the next part.
Benchmark #3:
This benchmark centered around the physical creation of the product. My partner and I both knew we wanted to have a sphere of some kind in relation to the Sun and Earth, so we bought a ten inch styrofoam ball. We both knew that we wanted to decorate it with acrylic paint, so we went to our school’s art room, and spent about an hour painting the whole thing various shades of red and orange. Halfway through the painting we ran out of the orange paint we we’re using, so we painted the other half red. The math involved was complicated for the scale factor, so I will not relay it back here, but the end result was having to represent Earth in relation to the 10 Inch ball with a scale size of 0.09. Knowing this was complicated, we decided to have more elaboration at our booth during the exhibition, which I will upload photos of when the time comes. We chose to do this both for the challenge and to see how far we could go without asking the Dr. for help, which i’m surprised as for the math component that we did not need to.
ReflectionOverall, I think this project went really well! I was worried that I had chosen something far too complicated, but the end result really paid off, and our scale model is looking great! Needless to say, the math and all other benchmarks are completed, and the writeup for this portfolio is looking pretty swell too. If I could change one thing, it would to be find a 20 Inch ball, so that we could represent Earth better, but this will be fixed if I ever do a project like this again. This project pushed the limits of my thinking, for a bit, I was worried I may have to change the project we were doing to something else, as the scaling part become very difficult. All in all, this project made me really happy that I again show that I can work under stress.