The Scaling Your World project was a chance to understand the concept of scaling by using objects that we use in our day to day lives. We took something that was foreign to us and tied it to something we were familiar with. This project was broken up into 4 benchmarks. The first being a description of the object that we we're scaling up or down. This was a moment to work with out partners to figure out what we wanted our final outcome to be. I had to partners that brought up the idea of doing a human heart. I was really excited about the idea and pushed it to be our final project.
We all turned in our bench mark explaining how we would find our scale factors and what products we could use to model it. For our second benchmark we used the internet to help us find the exact size of the average human heart. There are multiple parts of the human heart (i.e the right and left atrium) so finding the numbers were more difficult than anticipated. We decided to scale our heart up. We explained this by drawing pictures and labeling lengths on the heart. For the third benchmark we did an analysis of our personal growth and our partners. In that I explained how I felt that I could avoid some of the problems that occurred during this project. Also how amazing my partners are.
This is our final benchmark, going over every part of the project. In between these benchmarks was building time. My partners brought in materials such as balloons, glue, and paper towel rolls. With these we shaped each part of the heart. We covered the balloons in glue then small pieces of paper and then let them dry on strings. We attached the pieces of the heart together and then added paper towel rolls to the areas where the values of the heart are. Then painted it red. When we started this project I was really confused with all the mathematical information, but now that we related it to our daily lives I can say that I can understand the concepts we learned.
We started learning about Congruence and Triangle Congruence. In the beginning my idea of congruency was to things being exactly the same. I thought that was going to b some difference in was it came to triangle congruence, but really it's just a congruent shape. Congruence is when two figures or objects have the same shape and size, or if one has the same shape and size as the mirror image of the other. Triangle Congruence is When two triangles have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position.
When we started going over Similarity I had no clue what the definition was. I knew that it had to do with shapes being similar, but I didn’t know if that meant in the size or shape. I thought that it meant that it was a different shape, but same dimensions. Similarity is when two shapes that have the same shape or is a mirror image of one another. The difference between Congruence and Similarity is congruent shapes have the same measurements for both shapes, but similar shapes can have a different scale.
Ratios are a relation between two amounts showing the number of time one value can contain or is contained within the other. A Proportion is two equal ratios and to solve for it you start with stating your ratios as fractions. You make your two fractions equal to each other. Then cross multiply and solve the resulting equation. When we first started solving proportions in class I was very rusty to cross multiplying. I had to work a bit harder then my friends had to into order to understand the concept fully. Now I can say that I really understand how to solve for proportion comfortably.
Before we started talking about any of these concepts we got into groups and made posters explaining each of these different concepts then presented them in front of the class. My concept was how we can prove similarity. We can prove similarity by proving you have angle’s(AA), proportional sides (SSS), and two sides and angle (SAS) on a triangle. Triangles will be congruent if all the angles are the same measurement even when flipped. When two triangle are different sizes, but still have the same ratios they are till a similar triangle due to its proportional sides. With these steps I came to understand this concept.
Dilation is the transformation of a figure growing larger. How we grasped this concept was using a pencil, paper, and rubber bands. We started by tying two rubber band together at there ends. Then we placed a pencil in the last end of the rubber bands then our finger in the first. We placed the pencil middle west section of the paper and sketched a circle. Then using the ball in the middle of the two bands over the circle, we sketched another one using the ball as a guide. This was so fascinating to me and Dr. Drew explained that we scaled the circle us using the elastic potential energy in the band and also the middle ball. Dilation is decreasing the sides of an object by a scale factor. The sides get bigger or smaller by a certain length.
This project was full of material that helped me grow as a mathematician. One habit that I feel that I really expanded was my communication. We went over a lot of subjects and I wanted to make sure I had everything understood. I would question my partners and peers constantly even for the most simple questions. A few other areas that I feel I grew in was my understanding of choosing the right group, importance of benchmarks, and organization. I want to push myself to start projects more organized so I can get everything that I need turned in. I started this project very disorganized and about half way through I had to shape up and get everything organized. After that I was getting the things I needed turned in. Overall this project was a time to grow and understand how my peers work and understand.
We all turned in our bench mark explaining how we would find our scale factors and what products we could use to model it. For our second benchmark we used the internet to help us find the exact size of the average human heart. There are multiple parts of the human heart (i.e the right and left atrium) so finding the numbers were more difficult than anticipated. We decided to scale our heart up. We explained this by drawing pictures and labeling lengths on the heart. For the third benchmark we did an analysis of our personal growth and our partners. In that I explained how I felt that I could avoid some of the problems that occurred during this project. Also how amazing my partners are.
This is our final benchmark, going over every part of the project. In between these benchmarks was building time. My partners brought in materials such as balloons, glue, and paper towel rolls. With these we shaped each part of the heart. We covered the balloons in glue then small pieces of paper and then let them dry on strings. We attached the pieces of the heart together and then added paper towel rolls to the areas where the values of the heart are. Then painted it red. When we started this project I was really confused with all the mathematical information, but now that we related it to our daily lives I can say that I can understand the concepts we learned.
We started learning about Congruence and Triangle Congruence. In the beginning my idea of congruency was to things being exactly the same. I thought that was going to b some difference in was it came to triangle congruence, but really it's just a congruent shape. Congruence is when two figures or objects have the same shape and size, or if one has the same shape and size as the mirror image of the other. Triangle Congruence is When two triangles have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position.
When we started going over Similarity I had no clue what the definition was. I knew that it had to do with shapes being similar, but I didn’t know if that meant in the size or shape. I thought that it meant that it was a different shape, but same dimensions. Similarity is when two shapes that have the same shape or is a mirror image of one another. The difference between Congruence and Similarity is congruent shapes have the same measurements for both shapes, but similar shapes can have a different scale.
Ratios are a relation between two amounts showing the number of time one value can contain or is contained within the other. A Proportion is two equal ratios and to solve for it you start with stating your ratios as fractions. You make your two fractions equal to each other. Then cross multiply and solve the resulting equation. When we first started solving proportions in class I was very rusty to cross multiplying. I had to work a bit harder then my friends had to into order to understand the concept fully. Now I can say that I really understand how to solve for proportion comfortably.
Before we started talking about any of these concepts we got into groups and made posters explaining each of these different concepts then presented them in front of the class. My concept was how we can prove similarity. We can prove similarity by proving you have angle’s(AA), proportional sides (SSS), and two sides and angle (SAS) on a triangle. Triangles will be congruent if all the angles are the same measurement even when flipped. When two triangle are different sizes, but still have the same ratios they are till a similar triangle due to its proportional sides. With these steps I came to understand this concept.
Dilation is the transformation of a figure growing larger. How we grasped this concept was using a pencil, paper, and rubber bands. We started by tying two rubber band together at there ends. Then we placed a pencil in the last end of the rubber bands then our finger in the first. We placed the pencil middle west section of the paper and sketched a circle. Then using the ball in the middle of the two bands over the circle, we sketched another one using the ball as a guide. This was so fascinating to me and Dr. Drew explained that we scaled the circle us using the elastic potential energy in the band and also the middle ball. Dilation is decreasing the sides of an object by a scale factor. The sides get bigger or smaller by a certain length.
This project was full of material that helped me grow as a mathematician. One habit that I feel that I really expanded was my communication. We went over a lot of subjects and I wanted to make sure I had everything understood. I would question my partners and peers constantly even for the most simple questions. A few other areas that I feel I grew in was my understanding of choosing the right group, importance of benchmarks, and organization. I want to push myself to start projects more organized so I can get everything that I need turned in. I started this project very disorganized and about half way through I had to shape up and get everything organized. After that I was getting the things I needed turned in. Overall this project was a time to grow and understand how my peers work and understand.