In "Scaling your World", you scaled a real life item up or down. By doing this, you had to have the proportions even to one and other. The purpose of this project was to teach students how to properly scale while allowing them to have the freedom of choice of what they want to scale. It ended up being a little more complicated than it seemed at first. By building a three dimensional object it was very clear when proportions were off. We started this project by brainstorming as a class. Once brainstormed, we split into groups and made posters. This was very helpful for me because I was unaware of a lot of the vocabulary involved. I was the presenter for my groups poster so, I had to become extremely familiar with my mathematical concepts. By being an engaged listener throughout the presentation process, I picked up on a lot of new vocabulary. This helped me going into the next project. We then did a worksheet called "Billy Bear". In "Billy Bear", we were scaling a bear at a constant rate. Each week "Billy Bear" would grow the same amount. We had to figure out the area and perimeter for multiple weeks. The perimeter was the easy part. The perimeter was an obvious pattern so, you could plug in the variable for it to equal the constant rate if change. I struggled more with the area. The area was a more complex pattern but a pattern none the less. We then talked about dilation. We learned about dilation by tying two rubber bands together. At first, I was extremely confused by the process of dilation. We were working on this in groups so, after collaboration my partners and I were able to figure it out. The final thing we did was our scaled model. In my opinion, the scaled model was the most fun project. I worked with Brittney and Katie to create a scaled down volleyball court. Our first step was to go outside and take measurements of the volleyball court out front of High Tech High North County. After that, we divided all of those measurements by 45 in order to get them to a shoe box size. Even though we had our struggles with building, in the end our volleyball court looked extremely aesthetically pleasing. May group stayed very on task for this project which was very beneficial with getting quality results. The benchmarks helped my group stay on task for this project. Benchmark #1 was basically pitching our idea. We had to explain to Dr.Drew what we wanted to scale down and who was in our group. We had to explain the steps for creating our model and how we would pick our scale factor. Benchmark #2 was where the math was involved. In benchmark #2, we had to show Dr.Drew two diagrams that would explain our scaling. At first, my group got a B on benchmark #2 but, then we revised to an A. Benchmark #3 was the actual building of the model (which in my opinion was the fun part. After this unit I can proudly say I understand congruence and triangle congruence, definition of similarity, ratios and proportions, including solving proportions,proving similarity: congruent angles + proportional sides, dilation, including scale factors and centers of dilation, dilation: affect on distance and area. Congruence is a synonym for compatibility. Triangle concurrency is when two triangles are the same shape and size with corresponding angles even if they are not appearing to be the exact same because they are flipped.
Similarity is when two things are similar. Two similar things are often mirror images of each other. Thing are similar if all corresponding angles are the same.
Ratio is the relationship between two numbers. Often times, people want their ratios proportional to one and other. Ratios can be scaled down as long as the proportions stay the same. For example, If you start with 10/20, you can scale down to 5/10 because it does not effect the overall ratio. This was key to the scaling our world project because what my group struggled with was keeping the ratios in tact even when changing proportions. When you put ratios into an equation, it is known as a proportion. Proportions are the equation that makes ratios. Ratios are equal proportions. Ratios and proportions go hand and hand with each other. Ratio and proportions were the biggest factor in my scaling your world project. You solve a proportion by stating the ratios as fractions then, cross multiplying.
In order to prove similarity, you have to prove angle-angle (AA), proportional sides (SSS), and two sides and a angle (SAS). Triangles are congruent if all angles have the same measurement even if the triangle is flipped. Though they don't always reflect one and other. Walled reflective triangles. When the triangles create a mirror image that is called reflective triangles.
In order to determine angles are congruent, you have to be sure that the angles have the same degree. For example, if you have a square all of the angles would be congruent because they would all be right angles. Proportional sides is when two triangles of different sizes still are proportional to one other. In other words, you could have a scaled down model. As long as the ratios are the same, those are similar triangles.
Dilation is the transformation of shape from one size to another while still keeping it proportional to the original shape. In order to learn this process, we used two rubber bands and two pencils. I was partners with Katie. This was very fun hands on experiment which really helped me understand the concept of dilation. At first, my mind was blown. I could not process how this worked but then, after collaborating with Katie and talking to Dr.Drew I was able to understand the concept. In order to use dilation, you have to know the center point. A scale factor is a number which scales. Scale factors are often not displayed as a number. They are often displayed as a variable (a letter).While dilating, it is extremely important to take into consideration the distance and area in between the two things you are dilating.
I enjoyed this unit a lot. I feel as if I have grown a lot as a mathematician. Through this unit, I feel as if I have became a more strong of a group member. Before this, I struggled with group work because I am new to High Tech High so group work was a new thing to me. I was also introverted when it came to getting my work done because, I would want to get it done fast and often times collaborating will not be as efficient even though you get a better result. This unit pushed me outside my comfort zone and forced me to collaborate with my peers. By the end of the unit, I can say my peers helped me learn important information and vocabulary.