Hexaflexagon:
To create my hexaflexagon I utilized reflections to make the patterns line up and create a pattern. To do this I made it so the different lines and color changes met up as perfectly as possible.
Reflection:
Looking at my finished hexaflexagon I am really proud of how well my patterns matched up, I took a long time to design every side and love how well it came out. Looking back I would probably change my designs and make them more complex, I think I could have made it a lot more interesting by doing so. During the process of designing and making this I discovered that I really enjoy creating things with lines of symmetry and reflections, I love how things match up and form a bigger picture.
Looking at my finished hexaflexagon I am really proud of how well my patterns matched up, I took a long time to design every side and love how well it came out. Looking back I would probably change my designs and make them more complex, I think I could have made it a lot more interesting by doing so. During the process of designing and making this I discovered that I really enjoy creating things with lines of symmetry and reflections, I love how things match up and form a bigger picture.
Snail Trail Graffiti Lab:
To create the "snail trail" in this geogebra lab I used lines of reflection to create a symmetrical design. An example of a reflection in this piece would be the green onto the blue. Each line spreading out from the center is a line of reflection for the different colors.
During this lab I learned about reflections and it really helped me understand them more. Through my learning in math I have discovered that having a visual aspect really helps me get the material. This lab allowed me to see how reflections work and the colors made it easy to understand and stick with me.
During this lab I learned about reflections and it really helped me understand them more. Through my learning in math I have discovered that having a visual aspect really helps me get the material. This lab allowed me to see how reflections work and the colors made it easy to understand and stick with me.
Two Rivers Geogebra Lab:
A rider is traveling from point D to point E in between a pasture and a river. Before reaching point E the rider wants to stop at both the river, to get water for her horse, and at the pasture, to feed her horse. What route should the rider take to minimize the distance her horse must walk?
This would be a good path choice for the rider because it is the shortest distance for the horse to travel to get both food and water.
This would be a bad path choice for both the horse and the rider because the distance to get from point D to point E and get both food and water has increased resulting in a longer walk for the horse.
The Burning Tent Geogebra Lab:
Returning from a hike a camper sees that her tent has caught fire! The shortest distance from her position to her campsite is a straight line, but, she must run to the river to fill her canteen and run back to put out the fire. What is the shortest path she can take? In this exploration you will investigate the minimal two-part path that goes from a point, to a line, and then to another point.
This path would not work for the camper would have to run far to long to get the fire out. Esentially the camper would have to backtrack to get water and then run a longer distance to her burning tent. In this example the camper would not have a straight path to save her campsite.
This would be a smart path choice because the camper would not need to change directions to get water on the fire. This path allows for the camper to sprint quickly to the river and fill the canteen with water and then run to her tent without missing a beat.