Project description
The purpose of this project was to improve our understanding of mostly dilation and similarity. We started this project by brainstorming as a class what we already knew about this topic so that we better understood what we needed and were trying to learn. Somewhere in the middle of this project we did a "mini project" in my opinion. For this we got into small groups and made posters about the definition of a math word we were given. We later had to explain this class. Another thing we did, was take a lot of notes through this, which unlike most, I actually quite enjoyed. A large part of how we finished this project was, we were instructed to make models of an object that we ether dilated up or dilated down. (Made larger or smaller) Their were six main mathematical concepts things that we learned about during this project, which I will take about more further down on this page.
MATHEMATICAL concepts
Congruence and triangle congruence:
The definition of congruence for me was hard to separate from similarity, as they are very close in my opinion. Congruence is when two things are of the same proportions. So for example these two triangles would be congruent (picture to the right) This shows that for something to be congruent, the sides can and angles need to be the same but they are allowed to be rotated differently, or placed down differently. Definition of similarity: The definition of similarity is when this sides and angles are the same, but the size can be different. (as shown to the right) Similarity and proportions can be "mashed together" in math as you can use proportions to find lengths of similar triangles. I learned this can be difficult to do, but once you understand how to solve proportions it becomes easier. Similarity also connects with dilation because, dilation works with similar triangles, so It is important to understand the basics of similarity before learning about dilation. Ratios and proportions: Proportions are just equations that express an equality between two ratios. An example of this could be 12/5 = 24/10. Proportions don't just only, always have numbers, they can also involve variables. So this is also a proportion: 5/2 = x/4. Like I said earlier, when given 2 similar triangles you can also use proportions to figure out the lengths of the sides. Proving Similarity-Congruent angles & Similar sides: Their was a section we learned about on how to prove that sides and angles of triangles were similar/congruent. I had a difficult time understand the proper way to do this, and through this section I mostly just eyed the problem to get an answer. (Trying to visually tell is triangles were similar or different) I do know, that for solving, if angles are similar, you first need to find out the angle measures. You can do this by using angles that are given to you to solve, knowing that overall, all of the angles must equal 180%. Dilation (scale factors): We did two sections on dilation, but to simplify, I decided to combine them both in this section. First, dilation is a transformation that produces the same shape or size as the original, only the size will be different. (Example to the right) It can be describes with scale factor ( Defined as "K") and center of dilation, which is a point in space. Their are two types of dilation, you are ether scaling up/ expanding your shape, or shrinking it down/ making it smaller. |
Exhibition
In our final project, which was making a scale model of something we chose to ether scale up or scale down, included four benchmarks. I will be talking about three of them, as this page is the fourth in itself. The first benchmark, was basically a layout of us setting up our projects. We had to know who we were working with if we decided to group up, what is was we were going to scale up, how it will be constructed, and how we were going to scale it. I worked with my friend on this project, and we scaled down the tallest tree in the world currently and a bike, for size comparison. For our benchmark #2, we needed to sketch out what our project was going to look like, and we had to write along with it the significant dimensions. This was a struggle for us, as our tree scaled down still ended up being almost five feet tall, so we needed a lot of paper. Last, for benchmark #3 we had to ring into class our scale model.
Reflection
Overall, this project was difficult for my mostly during the middle of it, as their are a lot of definitions we needed to learn and understand all at once to complete our end project properly. It was helpful when we took notes on some of the things we learned, because I could reference it when I needed help, rather than looking it up. Another part of this I struggles with was using equations to solve things like the sides and angles of triangles. Something we did during this project that I think I did well on was dilation, because it was one of the few things I remember learning years before this. It was nice because I already understood it ahead of time. I also Think I did good with understanding different patterns that occurred during this project.