Scaling A New Dimension
Essential Questions
Scale models are a very important tool used in our modern society in areas such as building and science. Scale models are sometimes used as a plan for a large building or house because then the architects can look at how the building will look and operate once it is built. Scale models are also very helpful because they are very accurate and show the builders how the final building will look. Sometimes, scales models are made of a small thing and made bigger so that researchers can look closer at the object. One example of that is science. In science, when studying small things such as atoms, scientists can make a larger model to show their findings. Scale models are also commonly made to show the environment around us. Geographers might make a scale model of the environment so that they can study how it was formed or how it has changed. Maps are also an example of 2 dimensional scale models of the environment. Maps have been used for a very long time to help people find their way around their environment. Scale models can be very useful, although messing up can cause big problems.
If an architect messed up, even just a little, on a building plan, then it is possible that the whole building would collapse. This is a really big problem because it is very easy to mess up while making a scale model. While I was making my miniature fish tank, I rounded my measurements of the original and once I scaled it down the pieces did not fit together correctly because since it was so small, errors were more noticeable. Scaling down is especially problematic because the the error increases by the scale value. For example my scale was ¼ so if my error piece was wrong by one centimeter on the original, on the scale it looked like it was of by 4 centimeters. It is very important to measure correctly when making a scale model.
The area of a square changes when the square is scaled. I found that the area changes by the scale value squared. I think this is because the area of a square equation is side squared, or side X side. In my demonstration, I used a square with a side length of 5. When the side length of the square was one half of the original, the area was one fourth of the original. That is because the scale value was ½, squared is ¼. When I did a ⅕ scale of the side length, the area was 1/25 of the original area. You can see my calculations in the drawing below.