## Meadows or Malls?

Jade Robbins Orchard Hideout Portfolio:

The Orchard Hideout Problem is a problem that at its core revolves around the pythagorean theorem, and equations of circles. The initial question was, how long will it take in an orchard with a radius of 50, for the last line of sight to be diminished, and the center of the orchard to become a true hideout. In the beginning of this unit, we were so confused as to how to solve this problem without knowing the starting area of a tree, and the speed at which it grew. But throughout this unit, we learned so many complex ideas through the idea that this orchard needed a hideout. We learned the distance formula, and how to find the midpoint of two points, and we learned how to find the radius of the trees with the pythagorean theorem.

For example, on the simple worksheet, Circle WS #1, we found equations for problems we would solve later on, and I completely had no idea what I was doing. As the unit progressed, I saw why this assignment was so important, and found out that the process for these problems were fairly easy. On page 75, we learned how to use the distance formula to find if a tree fell exactly on the circumference of our circular orchard, before we even knew what the distance formula was. And on page 81, where we found the midpoint formula by calculating where the snack in the middle would be held. All throughout this unit, we have been learning concepts that are so much more solidified than they would be if we had just looked them up. In the beginning of this unit, I was too confident in my skills, and thought the work we were doing was too easy, but as the work continued, it became more and more challenging.

The second quiz we took, I didn’t get the score I was hoping for, and as I worked on getting that grade up, I accidentally learned the concepts necessary for the future of this unit. By the time I came to the unit assessment, which was a compilation of all of these ideas, I was happily surprised that I found it really reasonable, and just challenging enough. I think the most important pow I completed was the first one, Equally Watered, because it outlined the root of this problem in an extremely simple way. I was able to understand how to complete this problem, with the simple ideas of multiple flowers, and I re-learned how to put together a POW. Page 114 is where we found out a simple way to solve the ultimate problem, with an orchard with a radius of 3, and Willa and I used the pythagorean theorem, not trigonometry to solve this. All of these assignments lead up to page 119. I originally tried to solve this by graphing it, and found this impossible, as the angle was so small. And when I realised I could solve this just like on page 114, everything clicked. I found that the radius of the trees, and the last line of sight, the pythagorean theorem, distance formula, and every other concept we used were about to help me solve this problem. And, it was a lot easier than I expected with the strong foundation of the frustrating work before this. The answer to the unit problem, is only 11.7 years. But the process was so much more than that.

The Orchard Hideout Problem is a problem that at its core revolves around the pythagorean theorem, and equations of circles. The initial question was, how long will it take in an orchard with a radius of 50, for the last line of sight to be diminished, and the center of the orchard to become a true hideout. In the beginning of this unit, we were so confused as to how to solve this problem without knowing the starting area of a tree, and the speed at which it grew. But throughout this unit, we learned so many complex ideas through the idea that this orchard needed a hideout. We learned the distance formula, and how to find the midpoint of two points, and we learned how to find the radius of the trees with the pythagorean theorem.

For example, on the simple worksheet, Circle WS #1, we found equations for problems we would solve later on, and I completely had no idea what I was doing. As the unit progressed, I saw why this assignment was so important, and found out that the process for these problems were fairly easy. On page 75, we learned how to use the distance formula to find if a tree fell exactly on the circumference of our circular orchard, before we even knew what the distance formula was. And on page 81, where we found the midpoint formula by calculating where the snack in the middle would be held. All throughout this unit, we have been learning concepts that are so much more solidified than they would be if we had just looked them up. In the beginning of this unit, I was too confident in my skills, and thought the work we were doing was too easy, but as the work continued, it became more and more challenging.

The second quiz we took, I didn’t get the score I was hoping for, and as I worked on getting that grade up, I accidentally learned the concepts necessary for the future of this unit. By the time I came to the unit assessment, which was a compilation of all of these ideas, I was happily surprised that I found it really reasonable, and just challenging enough. I think the most important pow I completed was the first one, Equally Watered, because it outlined the root of this problem in an extremely simple way. I was able to understand how to complete this problem, with the simple ideas of multiple flowers, and I re-learned how to put together a POW. Page 114 is where we found out a simple way to solve the ultimate problem, with an orchard with a radius of 3, and Willa and I used the pythagorean theorem, not trigonometry to solve this. All of these assignments lead up to page 119. I originally tried to solve this by graphing it, and found this impossible, as the angle was so small. And when I realised I could solve this just like on page 114, everything clicked. I found that the radius of the trees, and the last line of sight, the pythagorean theorem, distance formula, and every other concept we used were about to help me solve this problem. And, it was a lot easier than I expected with the strong foundation of the frustrating work before this. The answer to the unit problem, is only 11.7 years. But the process was so much more than that.

There are three separate plots of land that the city can do whatever they wish with. Mr. goodfellow has a 300 acre plot, the U.S. army closed a 100 acre plot, and a mining company gave 150 acres of land. Altogether, this makes up 550 acres of land that the city can use in any way. Each plot of land costs a different amount to modify, and a different amount to modify for both recreation, and development. There are many constraints, 6 to be exact, which means this problem is a system of equations. Our task was to find a way to seperate the land, and satisfy the constraints. Throughout this unit we explored solving systems of equations with substitution, eleminiation, graphing, and matrices. We first learned how to do this with equations with only two variables, and slowly made our way up to six through small activities, and assignments. In this portfolio you will see both of the pages we used to solve the final unit problem, how we learned how to solve matrices, an assignment I am proud of, a pow that pertains to the problem solving, and an assignment that shows how we first learned to solve linear equations. Enjoy!

Personal Growth

This unit was extremely complicated for me. I left for a week in the beginning of this unit, and that was a rocky start, but eventually, the mathematical topics I understood trumped the difficulty of this unit. I learned how to use matrices to figure out otherwise extremely complicated problems. I learned how to visually conceptualise a graph with more than two axises. We learned how to solve systems of equations with substitution, eleminiation, graphing, and matrices, and that will be so helpful in the future with more complicated algebra. Personally, the part that was most difficult for me was understanding the three or four axis graph. I felt as though I was able to keep up though, and if I had any questions or frustrations, I was able to work through them.

If I were to give any advice to someone going into this unit, I would say that there are many takeaways from the cookie unit that will be very useful for this. Multiple variables, very conceptual work, and visual graphing will be necessary moving forward. I obviously doodle a lot, and it’s very hard for me to pay attention for an entire class period, but I think that this unit helped me persevere through that well.

## Orchard Hideout Portfolio!

The Orchard Hideout Problem is a problem that at its core revolves around the pythagorean theorem, and equations of circles. The initial question was, how long will it take in an orchard with a radius of 50, for the last line of sight to be diminished, and the center of the orchard to become a true hideout. In the beginning of this unit, we were so confused as to how to solve this problem without knowing the starting area of a tree, and the speed at which it grew. But throughout this unit, we learned so many complex ideas through the idea that this orchard needed a hideout. We learned the distance formula, and how to find the midpoint of two points, and we learned how to find the radius of the trees with the pythagorean theorem.

For example, on the simple worksheet, Circle WS #1, we found equations for problems we would solve later on, and I completely had no idea what I was doing. As the unit progressed, I saw why this assignment was so important, and found out that the process for these problems were fairly easy. On page 75, we learned how to use the distance formula to find if a tree fell exactly on the circumference of our circular orchard, before we even knew what the distance formula was. And on page 81, where we found the midpoint formula by calculating where the snack in the middle would be held. All throughout this unit, we have been learning concepts that are so much more solidified than they would be if we had just looked them up. In the beginning of this unit, I was too confident in my skills, and thought the work we were doing was too easy, but as the work continued, it became more and more challenging.

The second quiz we took, I didn’t get the score I was hoping for, and as I worked on getting that grade up, I accidentally learned the concepts necessary for the future of this unit. By the time I came to the unit assessment, which was a compilation of all of these ideas, I was happily surprised that I found it really reasonable, and just challenging enough. I think the most important pow I completed was the first one, Equally Watered, because it outlined the root of this problem in an extremely simple way. I was able to understand how to complete this problem, with the simple ideas of multiple flowers, and I re-learned how to put together a POW. Page 114 is where we found out a simple way to solve the ultimate problem, with an orchard with a radius of 3, and Willa and I used the pythagorean theorem, not trigonometry to solve this. All of these assignments lead up to page 119. I originally tried to solve this by graphing it, and found this impossible, as the angle was so small. And when I realised I could solve this just like on page 114, everything clicked. I found that the radius of the trees, and the last line of sight, the pythagorean theorem, distance formula, and every other concept we used were about to help me solve this problem. And, it was a lot easier than I expected with the strong foundation of the frustrating work before this. The answer to the unit problem, is only 11.7 years. But the process was so much more than that.

Algebra and geometry are concepts that most definitely go hand in hand. Each time you want to solve a real life problem that has to do with space and logic, you have to use both of these concepts. Especially when it comes to understanding ideas like distance, and anything that can be graphed. This unit was frustrating to me because I felt like what we were learning wasn’t getting me any closer to the final problem, and then we were just given all the dimensions we needed, and I was able to figure it out so quickly. I realised, that without all of the work leading up to it, I would have had such a hard time understanding how to solve this problem. Throughout this process we found every component along with these given variables, like the last line of sight, and different methods to solve this. I feel like I grew in my ability to stick with a frustrating problem, and persevere through many assignments that had me upset. I don’t think I grew as much as I could have, because I dismissed a lot of this work as busy work, and did not try to fully understand the underlying purpose of the assignment. If I had, the entire unit, done my work at my maximum level, I would have learned so much more. But as a student in highschool, I definitely do look for the easiest way to do things. I found that I work much better with a partner, and math is surprisingly interesting when it comes to real world application. I As I am maturing I am just starting to understand that math is just as important to my future in the artistic realm as science, and humanities, which has made me much more able to do my work with purpose.

For example, on the simple worksheet, Circle WS #1, we found equations for problems we would solve later on, and I completely had no idea what I was doing. As the unit progressed, I saw why this assignment was so important, and found out that the process for these problems were fairly easy. On page 75, we learned how to use the distance formula to find if a tree fell exactly on the circumference of our circular orchard, before we even knew what the distance formula was. And on page 81, where we found the midpoint formula by calculating where the snack in the middle would be held. All throughout this unit, we have been learning concepts that are so much more solidified than they would be if we had just looked them up. In the beginning of this unit, I was too confident in my skills, and thought the work we were doing was too easy, but as the work continued, it became more and more challenging.

The second quiz we took, I didn’t get the score I was hoping for, and as I worked on getting that grade up, I accidentally learned the concepts necessary for the future of this unit. By the time I came to the unit assessment, which was a compilation of all of these ideas, I was happily surprised that I found it really reasonable, and just challenging enough. I think the most important pow I completed was the first one, Equally Watered, because it outlined the root of this problem in an extremely simple way. I was able to understand how to complete this problem, with the simple ideas of multiple flowers, and I re-learned how to put together a POW. Page 114 is where we found out a simple way to solve the ultimate problem, with an orchard with a radius of 3, and Willa and I used the pythagorean theorem, not trigonometry to solve this. All of these assignments lead up to page 119. I originally tried to solve this by graphing it, and found this impossible, as the angle was so small. And when I realised I could solve this just like on page 114, everything clicked. I found that the radius of the trees, and the last line of sight, the pythagorean theorem, distance formula, and every other concept we used were about to help me solve this problem. And, it was a lot easier than I expected with the strong foundation of the frustrating work before this. The answer to the unit problem, is only 11.7 years. But the process was so much more than that.

Algebra and geometry are concepts that most definitely go hand in hand. Each time you want to solve a real life problem that has to do with space and logic, you have to use both of these concepts. Especially when it comes to understanding ideas like distance, and anything that can be graphed. This unit was frustrating to me because I felt like what we were learning wasn’t getting me any closer to the final problem, and then we were just given all the dimensions we needed, and I was able to figure it out so quickly. I realised, that without all of the work leading up to it, I would have had such a hard time understanding how to solve this problem. Throughout this process we found every component along with these given variables, like the last line of sight, and different methods to solve this. I feel like I grew in my ability to stick with a frustrating problem, and persevere through many assignments that had me upset. I don’t think I grew as much as I could have, because I dismissed a lot of this work as busy work, and did not try to fully understand the underlying purpose of the assignment. If I had, the entire unit, done my work at my maximum level, I would have learned so much more. But as a student in highschool, I definitely do look for the easiest way to do things. I found that I work much better with a partner, and math is surprisingly interesting when it comes to real world application. I As I am maturing I am just starting to understand that math is just as important to my future in the artistic realm as science, and humanities, which has made me much more able to do my work with purpose.