Scaling Your World Project
Isabella Norton
Math
November 8, 2016
Project Description
The 10th grade project “Scaling Your World” had many topics of math that were used to advance our skill set. For example, similarity and congruency, Proportional Reasoning and the Algebra of Proportions, Polygons and Angles, Logical Reasoning and Proof, Experiments and Data Analysis, and Mathematical Modeling. We overall wanted to develop the clear skill of similarity and the geometric transformation; dilation. We developed this through understanding mathematical modeling, similarity and dilation, whilst creating physical models. For the scaling your world project Dr.Drew had several worksheets that were used to solve problems involving similarity, dilation, ratios, and fully understanding proportions. The physical model aspect of the project was something that I really utilized, including all of the work we put into it. However, I learned a lot about these math topics from the class worksheets, that I will always utilize. Overall, from starting this project documenting onto posters our previous knowledge of congruency and similarity, then to wrapping up the concept of dilation, with a physical model displaying the mathematical concepts we learned over the course of this project, I can definitely take a lot away from this “Scaling Your World” project. Without the activities, I would not have the understanding for the concepts in this project that it obtains because of how they covered the concepts of ratios and how to find the unknown dimensions (inventing rules and similar problems worksheet), while going over the concepts of dilations (repeated dilations worksheet) and the scale factor each shape obtained. Another activity that definitely foreshadowed the purpose of dilations was the Billy Bear worksheet because Billy grew by a scale factor of 2, week three had increased by a scale factor of three, and we had to figure out the future weeks size from the reoccurring scale trend. There were some challenges while trying to understand these activities from the beginning, but I became accustomed to this concept as the activities continued, and with collaborations/ asking key questions.
Mathematical Concepts
The mathematical concepts we learned during this project are foreshadowing the main concept of similarity, dilation, and proportion. Similarity and proportion are two mathematical concepts that depend on each other because similarity is if two objects have the same shape or has the same shape in the mirror. For example, one can be obtained from the other by uniformly scaling, with another rotation or reflection. While a proportion is mathematically comparing two set of numbers, to see if you can determine unknown dimensions from a similar shape. The relationship between dilation and similarity is dilation is producing a different size, with the same shape, of an image, with the scale factor. While, similarity is having two images with different scale factors, but a similar shape. An example that corresponds with these subjects is in benchmark #2 and my group and I found the scale factor for Mount Everest and the Mariana Trench, to scale the original proportion smaller (two feet) while obtaining the same or similar shape. Another connection is when in benchmark #3, my group and I made the physical models for our scaled trench and mountains because we had to make sure the two models were proportional towards each other, so the scaling looked correspondent. I took a lot of mathematical concepts from this project and I believe I took away an equal amount of knowledge from each one. For dilation I learned how to find a scale factor, the steps towards making a proportional and similar shape physical representation for my subjects. For example, the mountain and trench were originally 29,029 ft by 29,029 ft and 226,378 ft by 35,814 ft. Originally my group and I wanted to scale our subjects to 2 feet, but because of the mathematical scaling transition towards physical models, we decided 6 inches would be easier to model. Once we found the scale factor for the trench and mountain, 0.000017224 in. and 0.00002067 in, we consequently received for the mountain width and height, .5 in by .5 in and then for the ocean it was .5 in by .4 in. We were definitely happy with the mathematical results because this made the building process easier. I will always utilize what I learned from this project because scale factors come quicker for me to approach. When making the physical models it definitely helped me determine proportions better and how to make similar models look proportional.
Exhibition
For benchmark one each student had to determine, with group if in one, what object/item they were going to scale, determine what the scale factor is, and a solid idea for your physical model to exhibit your work. Then for benchmark two, individually every student, had to sketch two similar diagrams of the chosen objects you are going to scale. In this diagram we had to label the specific dimensions and in the second we label the dimensions on the dilated object. We must then submit our mathematical calculations from our dilations. Finally for benchmark three we had to bring our physical models that displayed our mathematical learning subjects we explored during this project into class, to get it checked off. For our scale factor we started off by finding the mountain and trench’s original shapes dimensions and they were originally 29,029 ft by 29,029 ft/ 226,378 ft by 35,814 ft. Originally my group and I wanted to scale our subjects to 2 feet, but because of the mathematical scaling transition towards physical models, we decided 6 inches would be easier to model. Once we found the scale factor for the trench and mountain, 0.000017224 in. and 0.00002067 in, we consequently received for the mountain width and height, .5 in by .5 in and then for the ocean it was .5 in by .4 in. For benchmark three my group and I wanted to utilize all of the concepts we discovered during the course towards our exhibition models being proportional believe we definitely did a good job scaling down and changing the dimension ratios for the mountain and trench, while keeping the original similar shape.
Reflection
I am proud from my group and I's successes from this project and I believe our biggest success was our final physical model to display all of our calculations. I put in a lot of after school time and found solutions to any problems that had occurred, for example if the scaling wasn't exact or needed to be altered. This occurred when my group and I realized that building a half of an inch scale model would benefit us dramatically, instead of creating 2 foot models for exhibition. Also, for our scaled down models I found all the materials at home, when we thought we could not obtain the right materials we needed and made the template of our models after school, so my group and I could finish it all together the next day in school. I was dedicated to also have the appropriate math and make sure everything was scaled right. To make sure everything was correct I asked prudent questions in class and at lunch about our scaling math. Overall, I really wanted to be a problem solver and take initiative with my partners towards building an exact and mathematically correct product. My group and I were definitely using the habit of a mathematician, "Be patient, confident, and persistent," during this project because its very easy to give up when you have made a mistake. But, we never gave up when we came across a difficulty or problem and thats something that showed in our math, products, and overall team collaboration. I definitely felt like I could depend on my partners for collaboration because of how much we learned throughout our activities. Without the activities, I would not have the understanding for the concepts in this project that it obtains.
Math
November 8, 2016
Project Description
The 10th grade project “Scaling Your World” had many topics of math that were used to advance our skill set. For example, similarity and congruency, Proportional Reasoning and the Algebra of Proportions, Polygons and Angles, Logical Reasoning and Proof, Experiments and Data Analysis, and Mathematical Modeling. We overall wanted to develop the clear skill of similarity and the geometric transformation; dilation. We developed this through understanding mathematical modeling, similarity and dilation, whilst creating physical models. For the scaling your world project Dr.Drew had several worksheets that were used to solve problems involving similarity, dilation, ratios, and fully understanding proportions. The physical model aspect of the project was something that I really utilized, including all of the work we put into it. However, I learned a lot about these math topics from the class worksheets, that I will always utilize. Overall, from starting this project documenting onto posters our previous knowledge of congruency and similarity, then to wrapping up the concept of dilation, with a physical model displaying the mathematical concepts we learned over the course of this project, I can definitely take a lot away from this “Scaling Your World” project. Without the activities, I would not have the understanding for the concepts in this project that it obtains because of how they covered the concepts of ratios and how to find the unknown dimensions (inventing rules and similar problems worksheet), while going over the concepts of dilations (repeated dilations worksheet) and the scale factor each shape obtained. Another activity that definitely foreshadowed the purpose of dilations was the Billy Bear worksheet because Billy grew by a scale factor of 2, week three had increased by a scale factor of three, and we had to figure out the future weeks size from the reoccurring scale trend. There were some challenges while trying to understand these activities from the beginning, but I became accustomed to this concept as the activities continued, and with collaborations/ asking key questions.
Mathematical Concepts
The mathematical concepts we learned during this project are foreshadowing the main concept of similarity, dilation, and proportion. Similarity and proportion are two mathematical concepts that depend on each other because similarity is if two objects have the same shape or has the same shape in the mirror. For example, one can be obtained from the other by uniformly scaling, with another rotation or reflection. While a proportion is mathematically comparing two set of numbers, to see if you can determine unknown dimensions from a similar shape. The relationship between dilation and similarity is dilation is producing a different size, with the same shape, of an image, with the scale factor. While, similarity is having two images with different scale factors, but a similar shape. An example that corresponds with these subjects is in benchmark #2 and my group and I found the scale factor for Mount Everest and the Mariana Trench, to scale the original proportion smaller (two feet) while obtaining the same or similar shape. Another connection is when in benchmark #3, my group and I made the physical models for our scaled trench and mountains because we had to make sure the two models were proportional towards each other, so the scaling looked correspondent. I took a lot of mathematical concepts from this project and I believe I took away an equal amount of knowledge from each one. For dilation I learned how to find a scale factor, the steps towards making a proportional and similar shape physical representation for my subjects. For example, the mountain and trench were originally 29,029 ft by 29,029 ft and 226,378 ft by 35,814 ft. Originally my group and I wanted to scale our subjects to 2 feet, but because of the mathematical scaling transition towards physical models, we decided 6 inches would be easier to model. Once we found the scale factor for the trench and mountain, 0.000017224 in. and 0.00002067 in, we consequently received for the mountain width and height, .5 in by .5 in and then for the ocean it was .5 in by .4 in. We were definitely happy with the mathematical results because this made the building process easier. I will always utilize what I learned from this project because scale factors come quicker for me to approach. When making the physical models it definitely helped me determine proportions better and how to make similar models look proportional.
Exhibition
For benchmark one each student had to determine, with group if in one, what object/item they were going to scale, determine what the scale factor is, and a solid idea for your physical model to exhibit your work. Then for benchmark two, individually every student, had to sketch two similar diagrams of the chosen objects you are going to scale. In this diagram we had to label the specific dimensions and in the second we label the dimensions on the dilated object. We must then submit our mathematical calculations from our dilations. Finally for benchmark three we had to bring our physical models that displayed our mathematical learning subjects we explored during this project into class, to get it checked off. For our scale factor we started off by finding the mountain and trench’s original shapes dimensions and they were originally 29,029 ft by 29,029 ft/ 226,378 ft by 35,814 ft. Originally my group and I wanted to scale our subjects to 2 feet, but because of the mathematical scaling transition towards physical models, we decided 6 inches would be easier to model. Once we found the scale factor for the trench and mountain, 0.000017224 in. and 0.00002067 in, we consequently received for the mountain width and height, .5 in by .5 in and then for the ocean it was .5 in by .4 in. For benchmark three my group and I wanted to utilize all of the concepts we discovered during the course towards our exhibition models being proportional believe we definitely did a good job scaling down and changing the dimension ratios for the mountain and trench, while keeping the original similar shape.
Reflection
I am proud from my group and I's successes from this project and I believe our biggest success was our final physical model to display all of our calculations. I put in a lot of after school time and found solutions to any problems that had occurred, for example if the scaling wasn't exact or needed to be altered. This occurred when my group and I realized that building a half of an inch scale model would benefit us dramatically, instead of creating 2 foot models for exhibition. Also, for our scaled down models I found all the materials at home, when we thought we could not obtain the right materials we needed and made the template of our models after school, so my group and I could finish it all together the next day in school. I was dedicated to also have the appropriate math and make sure everything was scaled right. To make sure everything was correct I asked prudent questions in class and at lunch about our scaling math. Overall, I really wanted to be a problem solver and take initiative with my partners towards building an exact and mathematically correct product. My group and I were definitely using the habit of a mathematician, "Be patient, confident, and persistent," during this project because its very easy to give up when you have made a mistake. But, we never gave up when we came across a difficulty or problem and thats something that showed in our math, products, and overall team collaboration. I definitely felt like I could depend on my partners for collaboration because of how much we learned throughout our activities. Without the activities, I would not have the understanding for the concepts in this project that it obtains.