Measuring Your World
During this project we worked on measurement. We began by using the Pythagorean Theorem. We learned the formula to find distance and used this formula with different shapes and what they look like if they had the exact same distance from the center point. After this we made a circle and knowing that this circle will always have the exact same distance from each of its points. Something else we learned in this project was points of the x and y axis we learned that they are the same and they intersect with radical lines and when this happens angles are formed. Also, we went over how the sine is the hypotenuse of a triangle. We figured out how to use this with the Pythagorean Theorem. This lead to us learning about how to prove that a tangent of an angle is the same to sine and cosine. Next, we began learning how to work with 30, 45, and 60 degree angles. And then we were given a problem about the position and height of Mount Everest. After this, we began learning polygon equations and how trigonometry was able to be added in this. Also, we figured out that a square could be taken apart into right triangles. Next, we used trigonometry to find areas of equilateral and isosceles triangles. Also, we figured out formulas for hexagons, octagons, octagon, and pentagons. And lastly we learned about volume in 3D shapes and learned how to find the area of those different shapes.
Design Your Own Project
For this project we picked any object we wanted and we had to find the volume of it. My partner and I (Alena) decided to do something pretty simple so we just chose to find the volume of a pen. The math was simple we just plugged in the numbers to each equation and then added them together as you can see in the picture.
Reflection
This project was really interesting to me. There was a lot of challenges we had, First of all we thought a pen would be pretty simple since it was a pretty small item. This ended up being a challenge because the pen had a lot of small parts that we would need to find the volume of. To solve this challenge we decided to generalize and find the volume of the top of the pen and the body of the pen then add those and this made it much more simple. The habit of a mathematician we used is taking apart and putting back together. I realized something really cool during this project. I realized that getting help from my peers is a very helpful option for me. Before this project I was not comfortable doing this math but after getting help and having Alena explain it to me i got much more comfortable with it and I thought that was really cool. Overall this project was really helpful.
During this project we worked on measurement. We began by using the Pythagorean Theorem. We learned the formula to find distance and used this formula with different shapes and what they look like if they had the exact same distance from the center point. After this we made a circle and knowing that this circle will always have the exact same distance from each of its points. Something else we learned in this project was points of the x and y axis we learned that they are the same and they intersect with radical lines and when this happens angles are formed. Also, we went over how the sine is the hypotenuse of a triangle. We figured out how to use this with the Pythagorean Theorem. This lead to us learning about how to prove that a tangent of an angle is the same to sine and cosine. Next, we began learning how to work with 30, 45, and 60 degree angles. And then we were given a problem about the position and height of Mount Everest. After this, we began learning polygon equations and how trigonometry was able to be added in this. Also, we figured out that a square could be taken apart into right triangles. Next, we used trigonometry to find areas of equilateral and isosceles triangles. Also, we figured out formulas for hexagons, octagons, octagon, and pentagons. And lastly we learned about volume in 3D shapes and learned how to find the area of those different shapes.
Design Your Own Project
For this project we picked any object we wanted and we had to find the volume of it. My partner and I (Alena) decided to do something pretty simple so we just chose to find the volume of a pen. The math was simple we just plugged in the numbers to each equation and then added them together as you can see in the picture.
Reflection
This project was really interesting to me. There was a lot of challenges we had, First of all we thought a pen would be pretty simple since it was a pretty small item. This ended up being a challenge because the pen had a lot of small parts that we would need to find the volume of. To solve this challenge we decided to generalize and find the volume of the top of the pen and the body of the pen then add those and this made it much more simple. The habit of a mathematician we used is taking apart and putting back together. I realized something really cool during this project. I realized that getting help from my peers is a very helpful option for me. Before this project I was not comfortable doing this math but after getting help and having Alena explain it to me i got much more comfortable with it and I thought that was really cool. Overall this project was really helpful.