Cover letter:

During this unit we covered three main topics or ideas. The Pythagorean Theorem & Coordinate Geometry, Circles & the Square-Cube Law and Proof. For the pythagorean theorem and coordinate geometry we learned about the distance and midpoint formulas. This helped us go find distances between two points. Distance =(x2-x1)2+(y2-y1)2 It could also help us find areas and volumes circumferences ect…

The square cube law states that when a shape increases in size the volume will increase more than its surface area. We used this when comparing tree sizes and how they grow. This growth affects our last line of sight. The activity that helped me the most with this was the square cube law and unpacking the article.

The final important thing that we studied was the proof. I had never worked very much into this in past math classes so it was very hard for me to understand it. We had to find out the answer and then find another way to prove that our answer was correct. This involved all of the math equations that we had worked on all year. The assignment that helped me the most on this was proving the distance part 2. I was able to do all the work on the paper and that helped me find the proof.

Introduction:

Maddie and Clyde have a 50 unit circular orchard. They are wondering how long it will take for the center of the orchard to become a hideout meaning they can't see out or in. What we know is that the trees are planted 1 unit away from each other. 1 unit = 10 feet. The cross section area of the tree increases by 1.5 square inches per year. We also know that all the tree trunks have a circumference of 2.5 inches.

Process and Justification:

The first thing that needs to be done is to find the last line of sight. I found that this is a line passing through the point (25,½). I found this with the distance from a point to a line. We now have a triangle that we know the length of two sides. 50 and 1. Now we must find the last side using the pythagorean theorem. Then we find the area of the triangle and that is 18.09. We then subtract the area of the first tree and that is 0.49. You then get 17.6. Then divide that by how much the area increases each year with is 1.5. And you get 11.7.

Solution:

The orchard will take 11.7 years for the orchard to become a complete hideout.

Reflection:

During this unit I feel that I learned alot about algebra and geometry. Before this unit I would see a letter in an equation and just think, “Oh jeez I can't solve that.” During this unit I became much more comfortable and confident in many algebraic equations. I also became more confident in geometry and how we can use geometry, algebra, and many other equations to solve the unit problem and many others. My biggest takeaway from this unit was the midpoint and distance formulas. I understood them more than anything else we studied. I don't know why this is it may be because I see it as a us in my life where the other equations I don't see myself using.

The biggest struggle that I have with this unit is I feel like I have learned a lot but I am having trouble remembering it all. Directly after the assignment I think ok I understand what we just did and I could do It again. Now that I am trying to write my portfolio that is a different story. I am having lots of trouble trying to write out the ideas of the unit and explain how we solved each. I don't know why this happened. Maybe I didn't practice the equations enough or they just didn't stick with me from the beginning.

During this unit we covered three main topics or ideas. The Pythagorean Theorem & Coordinate Geometry, Circles & the Square-Cube Law and Proof. For the pythagorean theorem and coordinate geometry we learned about the distance and midpoint formulas. This helped us go find distances between two points. Distance =(x2-x1)2+(y2-y1)2 It could also help us find areas and volumes circumferences ect…

The square cube law states that when a shape increases in size the volume will increase more than its surface area. We used this when comparing tree sizes and how they grow. This growth affects our last line of sight. The activity that helped me the most with this was the square cube law and unpacking the article.

The final important thing that we studied was the proof. I had never worked very much into this in past math classes so it was very hard for me to understand it. We had to find out the answer and then find another way to prove that our answer was correct. This involved all of the math equations that we had worked on all year. The assignment that helped me the most on this was proving the distance part 2. I was able to do all the work on the paper and that helped me find the proof.

Introduction:

Maddie and Clyde have a 50 unit circular orchard. They are wondering how long it will take for the center of the orchard to become a hideout meaning they can't see out or in. What we know is that the trees are planted 1 unit away from each other. 1 unit = 10 feet. The cross section area of the tree increases by 1.5 square inches per year. We also know that all the tree trunks have a circumference of 2.5 inches.

Process and Justification:

The first thing that needs to be done is to find the last line of sight. I found that this is a line passing through the point (25,½). I found this with the distance from a point to a line. We now have a triangle that we know the length of two sides. 50 and 1. Now we must find the last side using the pythagorean theorem. Then we find the area of the triangle and that is 18.09. We then subtract the area of the first tree and that is 0.49. You then get 17.6. Then divide that by how much the area increases each year with is 1.5. And you get 11.7.

Solution:

The orchard will take 11.7 years for the orchard to become a complete hideout.

Reflection:

During this unit I feel that I learned alot about algebra and geometry. Before this unit I would see a letter in an equation and just think, “Oh jeez I can't solve that.” During this unit I became much more comfortable and confident in many algebraic equations. I also became more confident in geometry and how we can use geometry, algebra, and many other equations to solve the unit problem and many others. My biggest takeaway from this unit was the midpoint and distance formulas. I understood them more than anything else we studied. I don't know why this is it may be because I see it as a us in my life where the other equations I don't see myself using.

The biggest struggle that I have with this unit is I feel like I have learned a lot but I am having trouble remembering it all. Directly after the assignment I think ok I understand what we just did and I could do It again. Now that I am trying to write my portfolio that is a different story. I am having lots of trouble trying to write out the ideas of the unit and explain how we solved each. I don't know why this happened. Maybe I didn't practice the equations enough or they just didn't stick with me from the beginning.