Unit Two:
The Orchard Hideout:
Here is my portfolio for this unit.
The Orchard Hideout
Cover Letter:
In this unit we covered three main topics. The pythagorean theorem/coordinate geometry, circles and the square cube law, and proof. Something we did was studying the distance from a point to a line, and when we finished that up we went on to finding the best/last line of sight. The last line of sight was very important to solving the unit problem because in order to find out how much the trees need to grow and to also find the radius of the trees, you had to find out the best line of sight. The next step in this process was knowing that the orchard is a coordinate plane, and this led to things like distance and midpoints. Because it is a coordinate plane, we used distance to find how far a coordinate point was, or with midpoint we were able to find a point using multiple fixed points. The distance formula which was so key, is d=(x2-x1)2+(y2-y1)2, and a piece of work where I used this was Proving With Distance.
This led into the pythagorean theorem because we were able to find the distance of a side of a triangle. We worked with triangles a lot this semester, and one of the most important formulas we used was A2+ B2 =C2. This was an essential formula because in the final steps of the problem, we had to find the lengths of the sides of the smaller triangle within the last line of sight. After we worked on finding the lengths of a triangles side or what not, we started learning about finding area, volume, etc… Area would become a really important step to finding the answer to the unit question. We had to find the area of the first tree in order to see how much they needed to grow.
Another part of finding the area was the square cube law. The square cube law basically stated that when the size of a shape increases the volume then increases more than the surface area. We used the square cube law when trying to find how the trees grow because the growth affects the last line of sight. A piece of work where I used this was The Square Cube Law and Unpacking the Article. Going deeper into the coordinate geometry, another thing we learned about was angle and perpendicular bisectors. The angle bisector is when a line starts at the vertex of an angle and splits it into two equal angles. The perpendicular bisector is simply when a line intersects with another line at 90 degrees and bisects the first line. We used these when trying to find the angles of the lines in the last line of sight.
Introduction: There is a couple that want to plant trees in a circular lot and allow the trees to grow enough so there is no possible way to see out of the orchard from the center. They plan on making their orchard with a radius of 50 trees. The unit question is “How soon after they planted the orchard would the center of the lot become a true orchard hideout?” We are given the information that the cross section of the tree trunks increase by 1.5 square inches per year. The starting trees have a circumference of 2.5 inches. The trees are planted 1 unit away from each other, and 1 unit=10 feet.
Solution: First thing I did was I found the last line of sight using the distance formula. This was a line that passed through (25,½). I then was left with a triangle, with two sides which lengths we know, 50 and 1. Using the pythagorean theorem, I had to find the remaining side. I then figured out the area of the first tree, and then found the area of the triangle. I subtracted the area of the first tree (0.49 inches) to the area of the triangle (18.9 inches) and got an answer of 17.6 inches. Once I got this piece of information, I divided this number by how much the trees grow per year, (1.5 inches), and got my final answer of 11.7. So, it will take 11.7 years for the orchard to become a proper hideout.
Selection of Work:
Reflection:
Over the last semester in math, I learned a lot about math and about myself as a student. Math concept wise, it was quite a challenging unit. I had a hard time learning the concepts, but I also struggled to find interest in the work we were doing. One thing I struggled with a lot was finding the solution to the unit problem. Using all of the concepts we used in class and applying them was very hard. This is because of my lack of interest in the work. I didn’t pay attention as much as I should have when we were learning about important concepts in class. Because of this, the work I created wasn’t work I was super proud of. But I can also say that because some of these concepts were super challenging to me, when I finally understood something that was taking some time to do, it felt super rewarding. Reflecting on my semester as a student, I know there are some changes I need to make coming into the future. With math especially, I need to really lock it down and give more of my attention to class and the work we are doing. Doing online math has been a huge challenge, but that doesn’t mean I can’t perform at my best.
Over this unit Julian has done a good job mixing the topics of algebra and geometry. It was interesting to see how you could find an algebraic solution or equation when working with geometry. I enjoyed learning about measuring space and area inside geometric shapes. To me, that was one of the topics that made most sense to me. I just realized that with the work that we were doing especially, it went hand in hand.
Cover Letter:
In this unit we covered three main topics. The pythagorean theorem/coordinate geometry, circles and the square cube law, and proof. Something we did was studying the distance from a point to a line, and when we finished that up we went on to finding the best/last line of sight. The last line of sight was very important to solving the unit problem because in order to find out how much the trees need to grow and to also find the radius of the trees, you had to find out the best line of sight. The next step in this process was knowing that the orchard is a coordinate plane, and this led to things like distance and midpoints. Because it is a coordinate plane, we used distance to find how far a coordinate point was, or with midpoint we were able to find a point using multiple fixed points. The distance formula which was so key, is d=(x2-x1)2+(y2-y1)2, and a piece of work where I used this was Proving With Distance.
This led into the pythagorean theorem because we were able to find the distance of a side of a triangle. We worked with triangles a lot this semester, and one of the most important formulas we used was A2+ B2 =C2. This was an essential formula because in the final steps of the problem, we had to find the lengths of the sides of the smaller triangle within the last line of sight. After we worked on finding the lengths of a triangles side or what not, we started learning about finding area, volume, etc… Area would become a really important step to finding the answer to the unit question. We had to find the area of the first tree in order to see how much they needed to grow.
Another part of finding the area was the square cube law. The square cube law basically stated that when the size of a shape increases the volume then increases more than the surface area. We used the square cube law when trying to find how the trees grow because the growth affects the last line of sight. A piece of work where I used this was The Square Cube Law and Unpacking the Article. Going deeper into the coordinate geometry, another thing we learned about was angle and perpendicular bisectors. The angle bisector is when a line starts at the vertex of an angle and splits it into two equal angles. The perpendicular bisector is simply when a line intersects with another line at 90 degrees and bisects the first line. We used these when trying to find the angles of the lines in the last line of sight.
Introduction: There is a couple that want to plant trees in a circular lot and allow the trees to grow enough so there is no possible way to see out of the orchard from the center. They plan on making their orchard with a radius of 50 trees. The unit question is “How soon after they planted the orchard would the center of the lot become a true orchard hideout?” We are given the information that the cross section of the tree trunks increase by 1.5 square inches per year. The starting trees have a circumference of 2.5 inches. The trees are planted 1 unit away from each other, and 1 unit=10 feet.
Solution: First thing I did was I found the last line of sight using the distance formula. This was a line that passed through (25,½). I then was left with a triangle, with two sides which lengths we know, 50 and 1. Using the pythagorean theorem, I had to find the remaining side. I then figured out the area of the first tree, and then found the area of the triangle. I subtracted the area of the first tree (0.49 inches) to the area of the triangle (18.9 inches) and got an answer of 17.6 inches. Once I got this piece of information, I divided this number by how much the trees grow per year, (1.5 inches), and got my final answer of 11.7. So, it will take 11.7 years for the orchard to become a proper hideout.
Selection of Work:
- Another kind of Bisector
- Pow 1
- Proving with Distance PT 2
- The Square Cube Law and Unpacking the Article
- Proving with Distance
- Hiding in the Orchard
Reflection:
Over the last semester in math, I learned a lot about math and about myself as a student. Math concept wise, it was quite a challenging unit. I had a hard time learning the concepts, but I also struggled to find interest in the work we were doing. One thing I struggled with a lot was finding the solution to the unit problem. Using all of the concepts we used in class and applying them was very hard. This is because of my lack of interest in the work. I didn’t pay attention as much as I should have when we were learning about important concepts in class. Because of this, the work I created wasn’t work I was super proud of. But I can also say that because some of these concepts were super challenging to me, when I finally understood something that was taking some time to do, it felt super rewarding. Reflecting on my semester as a student, I know there are some changes I need to make coming into the future. With math especially, I need to really lock it down and give more of my attention to class and the work we are doing. Doing online math has been a huge challenge, but that doesn’t mean I can’t perform at my best.
Over this unit Julian has done a good job mixing the topics of algebra and geometry. It was interesting to see how you could find an algebraic solution or equation when working with geometry. I enjoyed learning about measuring space and area inside geometric shapes. To me, that was one of the topics that made most sense to me. I just realized that with the work that we were doing especially, it went hand in hand.