Measure Your World (Project)
When beginning this unit we were assigned 9-10 worksheets that were mainly focused on finding the area and volume of different shapes beginning with triangles and moving onto polygons. We also needed to find the right equations to solve for them. The majority of these worksheets were taking apart and putting back together the problems and we were able to make connections between the previous content we learned on how to solve problems. Another habit of a mathematician we used for when we worked on these packets was looking for patterns because working on one page to another, each page helped us for what was coming ahead of us, changing from learning distance to area and to volume. We first started this unit by reviewing the Pythagorean Theorem, because it helped us learn the quick basics before throwing ourselves in this new work. This led us to the equation of a circle (x^2 + y^2 = 1), which we used to find points of a circle using right triangles. It helped us understand right triangle trigonometry, including the definitions of ; sine, cosine, and tangent. We learned and used for trigonometry equations such as opposite/hypotenuse = sine to solve for missing sides on a triangle. Once we had this information down, we solved for the area of different polygons. We did this by taking apart and putting back together the shapes into triangles which we could solve for. Then used what we knew about these shapes to find the equation for area of a circle. From there, we moved into volume equations, where w started by finding the equation for the volume of a cylinder (area of the base x height). Later on we created yangmas, three pyramids cut from a single cube. Since we knew that each of these pyramids were 1/3 the volume of the cube, we used Cavalieri's Principle to shift the pyramid to the center in order to find the equation for the volume of pyramids and cones (area of the base x height x 1/3).
Design Your Own Project
Description-
For this project we had to find an object that we wanted to measure and find the volume of, it didn't have to be a small object, it could've been something huge like a building or boat. But we all had one job and it was to find the volume of it using the angles and circumference to find the volume. We were allowed to work in groups of 2-3 people, so I decided to work with Gillian. Someone I had not worked with on any math projects with. After talking about some ideas we had we decided to measure a minion, a animated character from a children's movie. I had a small plush doll that we thought would be perfect for this project.
The shape of this minion is a right cylinder and it was what we were learning to measure the day of the project launch so we thought it would be perfect because it was fresh in our mind. We thought that measuring the body would just be too simple so we also measured the eye which also is a right cylinder so we were able to use the same formula as the we used for the body.
Math-
Below
Reflection-
I enjoyed working on this short project because it captured all of the work we had been working on since we began this unit in math. Wrapping this unit up in with a project that we could make into what we wanted was a great idea since it allowed us to bring in our creativity into what we measured. Something that helped me throughout this project was being able to look back at the habits of a mathematician to get through the project. One that really helped me was collaborating and listening to my partner because she had different ideas on how it would be easiest to measure the minion for our project. This technique helped me because when beginning this project I wanted to measure something fairly easy and simple, but after listening to my partners thoughts she persuaded me to measure the minion which would be more fun. Another habit of a mathematician I used for this project was seek and prove why, this helped me in the long run because when I began to measure and use formulas I wasn't sure why these certain formulas worked, I knew that they had to be used to solve it but it didn't make much sense to me. No one could really explain the formulas to me except Abby because she broke it down for me and tried to give me a very hands on explanation, it really did help me after that because I felt more comfortable with what I was working with.
Measure Your World (Reflection)
What I enjoyed the most about this project was knowing that all the content we were learning can and will be used in life and even some daily things. There is significance from within all the work we did, the 20-30 pages we worked on did give me a full understanding on this unit we worked on. I feel that the pace we worked at was great because it wasn't too slow to the point where it would become boring but also not too fast where I would feel left behind. I feel that these last couple of weeks have really been productive because we have half the period to go through the lessons and the other half period to work on the sheets we had for the packets. Another thing that I liked about this unit is how all the worksheets we had in the weekly packet they would all relate to each other for example when we did the measuring the corral problems we had 6-7 sheets on how to measure the areas of different shapes that could be made into a corral and then finishing the packet the last page would really tie in all the work by explaining the patterns within the shapes.
When beginning this unit we were assigned 9-10 worksheets that were mainly focused on finding the area and volume of different shapes beginning with triangles and moving onto polygons. We also needed to find the right equations to solve for them. The majority of these worksheets were taking apart and putting back together the problems and we were able to make connections between the previous content we learned on how to solve problems. Another habit of a mathematician we used for when we worked on these packets was looking for patterns because working on one page to another, each page helped us for what was coming ahead of us, changing from learning distance to area and to volume. We first started this unit by reviewing the Pythagorean Theorem, because it helped us learn the quick basics before throwing ourselves in this new work. This led us to the equation of a circle (x^2 + y^2 = 1), which we used to find points of a circle using right triangles. It helped us understand right triangle trigonometry, including the definitions of ; sine, cosine, and tangent. We learned and used for trigonometry equations such as opposite/hypotenuse = sine to solve for missing sides on a triangle. Once we had this information down, we solved for the area of different polygons. We did this by taking apart and putting back together the shapes into triangles which we could solve for. Then used what we knew about these shapes to find the equation for area of a circle. From there, we moved into volume equations, where w started by finding the equation for the volume of a cylinder (area of the base x height). Later on we created yangmas, three pyramids cut from a single cube. Since we knew that each of these pyramids were 1/3 the volume of the cube, we used Cavalieri's Principle to shift the pyramid to the center in order to find the equation for the volume of pyramids and cones (area of the base x height x 1/3).
Design Your Own Project
Description-
For this project we had to find an object that we wanted to measure and find the volume of, it didn't have to be a small object, it could've been something huge like a building or boat. But we all had one job and it was to find the volume of it using the angles and circumference to find the volume. We were allowed to work in groups of 2-3 people, so I decided to work with Gillian. Someone I had not worked with on any math projects with. After talking about some ideas we had we decided to measure a minion, a animated character from a children's movie. I had a small plush doll that we thought would be perfect for this project.
The shape of this minion is a right cylinder and it was what we were learning to measure the day of the project launch so we thought it would be perfect because it was fresh in our mind. We thought that measuring the body would just be too simple so we also measured the eye which also is a right cylinder so we were able to use the same formula as the we used for the body.
Math-
Below
Reflection-
I enjoyed working on this short project because it captured all of the work we had been working on since we began this unit in math. Wrapping this unit up in with a project that we could make into what we wanted was a great idea since it allowed us to bring in our creativity into what we measured. Something that helped me throughout this project was being able to look back at the habits of a mathematician to get through the project. One that really helped me was collaborating and listening to my partner because she had different ideas on how it would be easiest to measure the minion for our project. This technique helped me because when beginning this project I wanted to measure something fairly easy and simple, but after listening to my partners thoughts she persuaded me to measure the minion which would be more fun. Another habit of a mathematician I used for this project was seek and prove why, this helped me in the long run because when I began to measure and use formulas I wasn't sure why these certain formulas worked, I knew that they had to be used to solve it but it didn't make much sense to me. No one could really explain the formulas to me except Abby because she broke it down for me and tried to give me a very hands on explanation, it really did help me after that because I felt more comfortable with what I was working with.
Measure Your World (Reflection)
What I enjoyed the most about this project was knowing that all the content we were learning can and will be used in life and even some daily things. There is significance from within all the work we did, the 20-30 pages we worked on did give me a full understanding on this unit we worked on. I feel that the pace we worked at was great because it wasn't too slow to the point where it would become boring but also not too fast where I would feel left behind. I feel that these last couple of weeks have really been productive because we have half the period to go through the lessons and the other half period to work on the sheets we had for the packets. Another thing that I liked about this unit is how all the worksheets we had in the weekly packet they would all relate to each other for example when we did the measuring the corral problems we had 6-7 sheets on how to measure the areas of different shapes that could be made into a corral and then finishing the packet the last page would really tie in all the work by explaining the patterns within the shapes.