1 Point and 2 Point Perspective Geogebra Lab
3-D project
For this project, each student assembled their own 3-D image with orthographic and isometric drawings of slice forms and geometric nets as seen below.
Anamorphic Drawing Project
1. Anamorphic is a 3-D image that is intentionally distorted to make only one perspective of the image displayed 3-D. Below is an anamorphic drawing, and you can only see this image from the view the photo was taken from. The drawing would be very stretched out and distorted if it wasn’t at the correct view. Image URL: http://www.moillusions.com/wp-content/uploads/2009/09/LIENZ_3D04-580x325.jpg
2. The supplies we used were the picture of our image, a visa vi marker, the glass from a picture frame, a box, a yard stick, pencil, a white poster board, a good eraser, a sharpie, and colored pencils.
3. The image we created is a projection because we plotted points onto the poster based off of matching points on the glass sheet. One person in the group would figure out where the points went based off of the drawing on the glass sheet, lining up the original drawing with that on the poster. The points were plotted based on the perspective of the person looking through the glass sheet, creating a projection of the original drawing.
4. My partner and I were challenged during the projection part of the project. Since neither of us had a laser pointer, we had to almost guess where a point on the poster matched up with the image on the glass. It took a lot of erasing and matching up to make sure the projected image matched in the one on the glass on the table. We overcame that challenge by getting a yard stick, and matching lines up with the yard stick. Since we had a rubix cube, we only had straight lines. So the yard stick helped us find all of the lines, and when we found the lines, it made it a lot easier to find the dots on the lines.
2. The supplies we used were the picture of our image, a visa vi marker, the glass from a picture frame, a box, a yard stick, pencil, a white poster board, a good eraser, a sharpie, and colored pencils.
3. The image we created is a projection because we plotted points onto the poster based off of matching points on the glass sheet. One person in the group would figure out where the points went based off of the drawing on the glass sheet, lining up the original drawing with that on the poster. The points were plotted based on the perspective of the person looking through the glass sheet, creating a projection of the original drawing.
4. My partner and I were challenged during the projection part of the project. Since neither of us had a laser pointer, we had to almost guess where a point on the poster matched up with the image on the glass. It took a lot of erasing and matching up to make sure the projected image matched in the one on the glass on the table. We overcame that challenge by getting a yard stick, and matching lines up with the yard stick. Since we had a rubix cube, we only had straight lines. So the yard stick helped us find all of the lines, and when we found the lines, it made it a lot easier to find the dots on the lines.
Determining Heights
For this mini project, the class went outside and measured the heights of things like poles, light posts, and tops of mountains and trees. To do this, we used trigonometric ratios. The variable H stands for height and the variable X stands for the remaining distance between the object and the distance measured.
Hexaflexagon
Description:
In the hexaflexagon project we used both rotational symmetry and line reflection. When I was creating my hexaflexagon, I reflected multiple patterns to create a good design. In the pictures, few of the patterns and shapes I created reflect across a line onto each other, and many of the designs withhold rotational symmetry when the hexaflexagon was flexed. Reflection: A feature of my hexaflexagon I am most proud of is. To refine the symmetry design in my hexaflexagon, I would definitely have colored each triangle a specific pattern to match the column it was lined up in. Instead I tried to be more creative and color each triangle a different design, so my outcome was not as good as I hoped. Through making the hexaflexagon, I have learned that I tend to challenge myself in projects and classwork that is meant to be more simple. I tried to go above and beyond and make mine stand out, but instead I ended up making it worse and spending too much time on it. I also learned that art is not my best way to express my learning because I am not very good at drawing, therefore the hexaflexagon did not turn out as creative looking as I intended it to. |
Snail Trail Graffiti Lab
Description:
When everyone in the class made an image like the one seen on the left, several concepts from geometry had to be
used. Although this lab mainly represented reflection. In the
process, we created six points. This was done by reflecting one point
over and over again across six different lines. These points created,
were turned into multiple colors to make it look more creative, and the trace tool was turned on so when you moved them, they left a trail. When you moved the original point, all of the
other points moved with it, creating interesting lines and pictures, as seen on the left.
Reflection:
I learned that I am better at working with technology and expressing my work through it, rather than doing something like the hexaflexagon. I am not as good with expressing my creativity and learning through it with things where it requires artistic talent to have a good outcome. I also learned that I manage my class time well with geogebra because I enjoy doing geogebra rather than work on a piece of paper.
When everyone in the class made an image like the one seen on the left, several concepts from geometry had to be
used. Although this lab mainly represented reflection. In the
process, we created six points. This was done by reflecting one point
over and over again across six different lines. These points created,
were turned into multiple colors to make it look more creative, and the trace tool was turned on so when you moved them, they left a trail. When you moved the original point, all of the
other points moved with it, creating interesting lines and pictures, as seen on the left.
Reflection:
I learned that I am better at working with technology and expressing my work through it, rather than doing something like the hexaflexagon. I am not as good with expressing my creativity and learning through it with things where it requires artistic talent to have a good outcome. I also learned that I manage my class time well with geogebra because I enjoy doing geogebra rather than work on a piece of paper.
Two Rivers Geogebra Lab
Description:
There is a sewage treatment plant where two rivers meet. You want to build your house close by the two rivers upstream from the sewage plant, you want the house to be at least 5 miles from the sewage plant. You go to each of the rivers to go fishing, but you would prefer to minimize the amount of walking you have to do to go fishing at both rivers. You want the sum of the distances from your house to the two rivers to be minimal, in other words, the smallest distance. In geogebra we created a lab following these instructions. These two images are screen shots of the lab we did. Explanation: The scenario on the left would not be correct because the distance from the house to point A on the West river and the distance from the house to point B on the East river isn't equal to the shortest distance possible. This location fits the requirement that the house is out of the sewage zone, but doesn't meet the requirement for the shortest possible distance. The picture below would indeed be the correct scenario because the distance from the house to point A on the West river and the distance from the house to point B on the East makes the shortest possible distance. This location fulfills the requirement that the house must be out of the sewage zone, and is also the shortest path possible |
Burning Tent Geogebra Lab
Description:
A camper out for a hike is going back to his tent. The shortest distance between him and his tent is along a straight line, as he reaches his campsite, he sees that his tent is burning. He has to run to the river to fill a bucket of water, and then run to his tent to put out the fire. In this exploration we studied the minimal two-part path that goes from a point to a line and to another point. This lab analyzed concepts learned from previous geogebra labs using point > line > point ideas
Explanation:
The scenario pictured on the left wouldn't work because the segment between the camper and river doesn't lay on top of the segment between the Camper and TentFire', which is important when figuring out the shortest distance. The incoming and outgoing angles are not equal as well, which is another signal that the distance traveled would not be the shortest in this.
The picture below of the lab would work because the segment between the camper and river lays on top of the segment between the Camper and TentFire', which signals that point river doesn't need to be moved on line AB. The incoming and outgoing angles are equal, which is also a signal that the distance traveled would be the shortest distance possible.
A camper out for a hike is going back to his tent. The shortest distance between him and his tent is along a straight line, as he reaches his campsite, he sees that his tent is burning. He has to run to the river to fill a bucket of water, and then run to his tent to put out the fire. In this exploration we studied the minimal two-part path that goes from a point to a line and to another point. This lab analyzed concepts learned from previous geogebra labs using point > line > point ideas
Explanation:
The scenario pictured on the left wouldn't work because the segment between the camper and river doesn't lay on top of the segment between the Camper and TentFire', which is important when figuring out the shortest distance. The incoming and outgoing angles are not equal as well, which is another signal that the distance traveled would not be the shortest in this.
The picture below of the lab would work because the segment between the camper and river lays on top of the segment between the Camper and TentFire', which signals that point river doesn't need to be moved on line AB. The incoming and outgoing angles are equal, which is also a signal that the distance traveled would be the shortest distance possible.