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This project was completed by Jennifer, Bruce, Kyle, and Kevin, in which we produced a little farm. We broke up all of the different parts of our farm accordingly so that everyone basically had the same amount. Jennifer was in charge of the pig, hay bales, hills, and tractor. Kyle was in charge of the barn, along with all of its features and the silo. Kevin was in charge of the sun, hog trough, and stop-sign (which was omitted in our final project). Bruce was in charge of the clouds and fence. Upon collaboration, we were able to determine specific sizes, and we could then scale our different pieces so that everything blended together realistically. We met up one last time to develop all of the procedures, with our main procedure being MAIN and 3 subprocedures being titled PIG, FOOD, and TRACTOR.

Farm Scene

Reflection: While our Terrapin Logo project just appears to be a simple work of art, a lot of mathematics were involved in its production. Everyone had to figure out the size and angles of their objects. This involved a lot of trial and error as well as keeping track of lengths and angle measurements. Kevin even used GeoGebra to figure out the size and angles needed to make the trough. A graphing grid was used to assist in figuring out the location or the coordinates of different items so that everything blended well together. For future mathematics classes, students could solve the necessary angle and line measures with paper and pencil so that they can translate the information into a Terrapin Logo project. If time permitted and the students were interested, teachers could also assign certain programming procedures, like we did for this project, to expand their technological boundaries. Although we don't really envision ourselves using this software regularly in our future classrooms, it is still a viable option in the mathematics classroom.

For the Terrapin Logo [project], Amy, Adam, Dan, and Jane worked together. We decided to make flags for our project. We each chose a unique flag with interesting geometry and worked on the commands separately. Once we finished, we put them all together. In the first quadrant, Jane created the Israeli flag. In the second quadrant, Amy made Jordan's flag. In the third quadrant, Dan replicated South Africa's flag, and in the fourth quadrant, Adam constructed Panama's flag. Each flag is 200x300.

The flag of Jordan is composed of basic geometric shapes such as an equilateral triangle and a rectangle. However, the biggest challenge of this flag was to create the seven-pointed star. I started this flag by creating a rectangle of dimensions 300 by 200 in quadrant I. To create the equilateral triangle, I knew that all the angles were 60 degrees and that all the sides must be 200 units. For the stripes, I had to determine how many units to travel up the sides of the triangle before rotating the turtle to start the stripe. I used trigonometry (the sine function in particular) to determine this. I also had to know that corresponding angles are congruent to determine how far to rotate before starting the stripe. In order to replicate the seven-pointed star I had to find the interior and exterior angles of the star. Although this flag seems fairly simple, there was a lot of geometry in the works to create it. Knowing about complementary angles, corresponding angles, and properties of triangles and rectangles was crucial in creating the flag of Jordan.

The flag of Panama is divided up into four equal quadrants so students have to take the midpoint of each side to create an accurate representation in Logo. To create a five point star students must realize that such a star is created by extending each side of a pentagon until they intersect with each other. Students should find that this creates five congruent triangles that will make up each point of the star. Since each angle in a pentagon is 108 degrees students will be able to use this fact to find that the base angle measures of each triangle are 72 degrees, which from this they can conclude that the point of each star has an angle measure of 36 degrees. Knowing the angle measures of each triangle allows the students to figure out how many degrees to turn the turtle when they move from one leg of a triangle to another leg of a new triangle and also how many degrees to turn so that the point of the star is 36 degrees.

The mathematics behind the Israeli flag was somewhat tricky. It only consisted of two rectangles and two triangles, however the placement of those shapes gave me some trouble. I first started out with the rectangles. I knew my flag was 200x300 so I divided it in half and decided how big I wanted one rectangle to be and made the other one the same. To make the Star of David, I first calculated how much open white space I had. Then I made one triangle pointing up first and decided to make the side lengths a multiple of three so then I could overlap a second triangle more easily. Going into this project, I knew how to make shapes using Logo. The hard part about making a flag is getting the measurements correct. That part took a lot of preplanning with some trial and error.

The most difficult part of creating the South African flag is deciding what angles are need for the shapes and how those angles will affect lengths. To start I saw the the red, blue, and middle parts divided the flag roughly into thirds. Since I knew that the dimensions of the flag were 200x300, I made the top and bottom portions 67 units in width and the middle 66 units. After creating the top trapezoid, I moved outside of it to make a larger trapezoid of roughly the same shape but with longer sides. Afterwards, I saw that the bottom half of the flag was a reflection of the top half, and used the same order of commands but with different directions. To create the triangles, I used equilateral triangles by keeping the all of the angles at 60 degrees and using different side lengths for each triangle, which were based on the distance between their vertices on the left edge of the flag. The most crucial part of this flag was finding the correct angles to use and matching the lengths of the sides of the shapes to those angles.

This project was completed by Zach, Scott, Kasi, and Staci. We set a main procedure to produce a coast line with a boardwalk including a Ferris Wheel. The development of our project was done as an entire group. Staci drew out the sketch of the idea originally and Kasi used her computer to type up the procedure. Zach and Scott were key components in making sure we had the correct angles and measures of the picture. The entire group sat in front of the computer and collaboratively made the procedure together. Our project is one main procedure called TOWN and 3 sub procedures called WHEEL, BOAT, and WAVE.

Reflection: The mathematics used to complete this project was primarily simple geometry applications. Terrapin Logo is a program that requires angle input of supplementary angles. Also with some algebraic manipulation, we were allowed to do computations of the diameters and radii of the circles drawn. The Pythagorean Theorem played a role during the construction of right triangles. Other simple concepts, like knowing the sum of a triangle's angle measures is 180 degrees and relationships of line segment lengths, were also used.

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