Project Description:
We began learning about scaling in class. We focused on many topics all revolving around scaling as a central topic. We learned forms of transferring as well as congruence. We focused on this because we began a project that centered around this term. We gathered our ideas if large or minuscule objects and were able to do the math to change it to a semi-normal size. For our final products we were able to actually construct these and prepare them to be presented. Scaling is a very important skill that can be used regularly in our lives. To begin this project, we did a class brainstorm about everything we knew about congruence. To challenge our thinking, we were asked to research and present a poster about a given topic to the rest of the class. The various topics assigned were: congruence, similarity, ratios and proportions, as well as topics about dilation. After learning these, we focused more on dilation and extended further on the topic. We then got to create our own products to exhibit our learning of dilation and scaling. This included doing the math to get practice scaling and creating work we wish to display.
Mathematical Content:
During this project, we went over many concepts revolving around scaling. They were the focus of this project and fully understanding them was critical. Congruence and triangle congruence is when two triangles are congruent if the corresponding side of another is equal in length. Which means the corresponding sides will be equal in size as well. Complete congruence is equivalent sides and lengths. There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS, HL. Side, Side, Side (SSS) means a three sided triangle is completely equal in side and length. Side, Angle, Side (SAS) is the case of knowing two triangles where we know two sides and the included angle are equal. Angle, Side, Angle (ASA) is knowing two triangles where we know two angles and the included side are equal. Angle, Angle, Side (AAS) is two triangles where we know two angles and the non-included side are equal. Hypotenuse, leg is two right-angled triangles that share the same length hypotenuse and same length for one of the three legs. The definition of similarity is when two similar triangle that only differ in size. Completely identical in length, but quite different when it comes to the size of it. Ratios and proportions are a way to solve an equation. Proportions are equal ratios. Meaning it can be used to solve problems involving ratios.To solve ratios and proportions you must first state the ratios as fractions. From there you are able to cross multiply making proportions able to be used. Proving similarity is the comparison between two triangles and their angles. Similar angles means similar shapes. Dilation is similar shapes as well, but with the use of a scale factor. By multiplying every side of a shape by a scale factor, you will get the dilated shape. Every scale factor has a center of dilation which is the point where the shape would be if the scale factor were zero. Dilation effect of distance and area is when a shape remains in the same place, but changes in size.
Exhibition:
To complete this project, we had to got through various benchmarks in order to fully understand the idea of scaling. For our first benchmark, we began a project proposal. We paired up in groups, brainstorming the ideas for this project. My group proposed the idea of scaling the highest point in the world, Mount Everest and the lowest point in the world, Mariana Trench. Benchmark #2 was to actually figure out the math behind our scaling. We calculated the exact height and depth then scaled them both to one foot. Benchmark #3 was the construction of the final product. We created miniature versions of a mountain and the ocean.
Reflection:
I faced many challenges in this project with my group members. We went through many processes of our final product. To begin our second benchmark, we had a different scale factor. We scaled our project down to two feet which caused many different problems. We couldn’t find anything to accommodate to our scale factor so we were forced to change it. After changing it, we had to redo all of our math and first products. After changing it however, we were finally able to create final products that we were content with. I wish I could have knew that our original factor would result in all of the difficulties we faced and if I were to do this project again, I would think harder about my scale factor. The habit of mathematician I used in this project the most was taking apart and putting back together. I used this the most in the math portion of this project as I was often trying to break down each part of the math. I found it difficult to solve and this skill definitely helped me. Overall, I felt that this project was a major success. I had lots of fun and I ended up very proud of my work.