Favorite Unit Reflection:
Orchard Hideout:
The central problem of the unit “Orchard Hideout” was two people, Maddie and Clyde have planned a circular orchard with a little hideout at the center. At every point was a tree, the trees would grow to the size so that there would have been no line of sight left from the center. We had to figure out where the last line of sight would be through all the trees and what the area of the closest trees to the line would have to be before it was completely covered up. This unit compiled many mathematical ideas and types. Some of these were Geometry, Algebra, Trigonometry, and the Pythagorean Theorem. All of these ideas helped us grow an understanding of how to properly use all of them effectively to answer one main problem. This unit started with identifying radiuses and telling whether or not certain points were within the radius of a circle on a graph, or not. Pythagorean Theorem would help us here in the beginning. If we had to identify the radius, we would be given two lines that would if given the length of the hypotenuse, would form a right triangle. We would use the equation a2+b2=c2. From there we could identify which points would be out of range or not. We would use circumference to distinguish which points would be exactly on the edge of the circle The Distance Formula helped us find the distance between two points. Yeah, we could just count, but we would not have gotten an accurate answer. The formula for distance is d=(x1-x2)2 + (y1-y2)2. if you were given two points, they each have an x integer and y integer. You would both x’s from each other and square it. You would do the same for the y’s, and get the square root of those added. This answer would sometimes even work if you count along the x-axis and y-axis in between the two points. This formula could have also helped us find the length of the radius of different circles we were creating. The Midpoint Formula helped us find the middle in between two points. The equation for this was x1+ x22 , y1+ y22. This formula would provide us with the point that would lie directly in between the given two points. The area played a vital role in this unit where what we mainly had to figure out was the area of a small circle, and what the radius would be if the circumference of the circle touched the edge on a special line. Trigonometry or inverse Trig would help us find the length of two lines on a right triangle or help us find the angle of the triangle. Trigonometry wasn't as important then inverse Trig. All of these key points played a big role in figuring out the central problem. |
Unit Test: |