Project Description: For this project we had to take an object and either scale it up or down. We learned about congruence, dilation, scale factors, proportion and similarity. We started by making posters about the different mathematical topics and presenting them to the class. We also did some work sheets about dilation, and other concepts. We then had our first benchmark, we had to figure out what we were going to scale, and who we were going to work with. After that we had the second benchmark, for that we had to figure out our scale factor and what each dimension would be. The third benchmark was making our scale model. Finally bench mark four was this DP update and our exhibition .
Benchmark #1: For benchmark #1 we had to decide on the object that we wanted to scale. We also had to figure out who we were going to work with and have a rough idea of what kind of scale we were going to use. I decided to take the plane from the show Agents Of SHIELD and scale it down. I wanted to work alone, I also decided that I wanted the length of the planes body to be two feet. To get the dimensions of the original plane I did some searching on line. I was able to find a prop blueprint directly from marvel. I was able to use that and some other measurements I had found online to get a pretty good idea on the sizes.
Benchmark #3: Benchmark #3 was making the final model. I decided to carve my model out of foam. I used a different block of foam for each part. This allowed me to use a smaller knife to add the details. First I carved out the body of the plane, after that I carved both sets of wings. I used dowels to attach the wings on to the plane. I also intended on using foam glue to hold the dowels in place. It ended up taking a while to dry, therefore I started using super glue. Then I started carving the tail and flight stabilizer. I used dowels to make the wings more rigid and hold them on better. I used a ruler to make sure that every piece was following the scale. I then used matte black latex house paint to paint the entire model. After that I used acrylic paint to do the details like the windows and logo on the top of the plane. The latex paint also helped fill in the holes that naturally come in Styrofoam.
Mathematical Concepts: During this project, we learned about many different concepts including congruence, dilation, scale factors, proportion and similarity. Many of them relate to each other. Similarity and proportion depend on each other, for shapes to be similar they need to be proportionate to each other. Another example of the concepts being related to each other are dilation and similarity. If you dilate a shape it will be similar to the shape you started with, they will have the same aspect ratio. We also learned about scale factors, we needed to use a scale factor in benchmark 2 when we were tying to find the dimensions for our scale models. In conclusion we were taking an object and dilating it to a more manageable size, if we decided to scale and object down like I did.
Benchmark #2: For the second benchmark we had to find the dimensions and scale them down. To do this I drew a picture of the plane and labeled it with the original dimensions. I then drew the plane again and labeled it with the new scaled down dimensions. My scale was 250/2 because the original length of the plane was 250 feet, and I wanted it to become 2 feet. My scale factor ended up being 0.008. This means that I multiplied all the original dimensions by .008. Since the measurements of the original objects were written as improper fractions I had to convert them into decimals. This gave me the scaled down dimensions. I then labeled the second diagram.
Reflection: Overall I feel like I did a good job with this project. In the end I was quite proud of the final. It is quite recognizable as a plane and looks really nice. If I had more time I would definitely use a less porous foam so that hopefully it would look more like metal. Other then that I think the final came out looking very nice. I am really glad I decided on making the model on a larger scale then other groups. I think it helped solidify the idea that the original plane is quite large. If I had more time I would have found a way to attach the motors and make it look even more like a plane. I feel like I could have used the habit of a mathematician start small more during benchmark #3. Planning out how I was going to carve the plane, and maybe starting with a smaller model would have helped a lot. Instead I grabbed a knife and began cutting into a block of foam, no planing whatsoever. I feel like that definitely could have backfired, thankfully it didn't. I did end up having to slim the body a bit more than I had anticipated because it wasn't exactly straight. If I had some kind of plan I wouldn't have had to do that extra step. Overall I am very happy with the final product. I think it is one of the best pieces I have produced so far this school year.