For this project, everyone had to choose an object or thing that we had to scale to a bigger size, or a smaller size. For example, I chose to shrink down an Orca Whale to 1/26 it's size. Throughout the project, there would be 4 benchmarks that had to be completed. Those are what we would be graded on, along with the product of our work (which is basically benchmark 3).
Mathematical Concept
Topics we worked on: 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)
My understanding of the topics we learned varies. For example, I understood most of the dilation, like the Billy Bear assignment, but I didn't understand the kind of dilation that looks like this:
Although, I did understand the relationships between different concepts. The relationship between similarity and proportion is that similarity needs proportional sides, and proportional sides (two ratios that are equal) make up similarity. You can't have one without the other. We used these two things to create the measurements for our project. For mine, if one fluke was a different shape than the other whale's fluke, then it wouldn't involve similarity because it doesn't have the right proportions. The relationship between dilation and similarity is a dilation is similar to the original object, just a different size. This is also used in our project because our objects were just a dilation of the actual object.
Exhibition
As said previously, there were 4 benchmarks for the project. Benchmark #1: This was the benchmark for the brainstorming of the project. The class entered a post in edmodo saying who they were going to partner with (if partnering with anyone), what you were planning on scaling, what your scale factor was, and how will your object be constructed and shown for exhibition. Benchmark #2: In this benchmark, everyone had to make a rough sketch of what their object was and get the measurements for the life-size object. For me, I chose a Killer Whale/Orca. It took me quiet a while to find all the measurements, and when I finally got them all near the end, I realized that they wouldn't work. My original image was seen from a side angle, making all the measurements incorrect. My solution was to change the viewpoint of the image. My final decision was to do a drawing of the bottom of the Orca. Benchmark #3: For this benchmark, we took our rough sketch and turned it into our final piece. Some people make actual models of their object, but for me since I love to draw, I chose to stick to drawing it out. Benchmark #4: Once you were done with all the previous benchmarks, you moved on to creating the "Exit slip" basically. Writing the project description, mathematical concepts, benchmark overview, and the reflection is all part of benchmark 4.
Reflection
Overall I think I did well on this project. I really enjoyed shrinking down the Killer Whale and drawing it out. It really shows how huge the world is when you look at it like this. An Orca whale, 1/26 it's size, is a bit bigger than a regular piece of printer paper. A success I had was definitely doing the actual drawing. I had the most fun doing this portion of the project, since I love to draw. Of course, it was a bit challenging because I would accidentally look at the wrong measurements, then have to go back and erase all of what I did for the section. I think my end product turned out well, also. It does look what you'd think an Orca whale would look when shrinked down to 1/26 it's size.