Problem Statement:
A rectangle has a corner on the graph of Y=16 - X2 , another at the origin and a third on the positive Y axis and a fourth on the positive X axis. If the area of the rectangle is a function of X, what values of X yields the largest area of the rectangle.
A rectangle has a corner on the graph of Y=16 - X2 , another at the origin and a third on the positive Y axis and a fourth on the positive X axis. If the area of the rectangle is a function of X, what values of X yields the largest area of the rectangle.
Process and Solution:
My initial attempt for drawing the maximum rectangle diagram actually first started by my group and I creating an X and Y table , we used random numbers for X and we also used our original equation from the problem statement and plugged it into y.
after getting the random points and plugging them into the original equation we solved it out and we got the final points, we decided to use a graph to create a parabola and after creating it with our point we tried fitting as many rectangles possible in the parabola.
Our group's final diagram was a parabola with points plotted from 0 x to 16 y in all of the space we were only able to fit 3 fully rectangles one that went from 0,15 another that went from 0,12 and the last one from 0,5.
Area
In order to find the area we knew that the original way to find the area for any shape or rectangle on this case was x times y so we took 16 minus x squared because that was y and multiplied x (16-x to the second) our final answer for the area was 16x - x to the third power.
Perimeter
How my group and i knew that the equation was correct was by plugging in the original value for y and solving it out.
In order to find the perimeter you do x + y times 2 so what we decided to do was to plug in what we already had for y witch was 16-x squared and we plugged it into y the second step was multiply x by 2 and than y by 2 in this case 16-x squared times 2 so than we got 2x for x and 32-2x squared for y.
Group Test/Individual Test:
The way the group prepared for the quiz was always keep the same pace so that no one was left behind and everyone understood what was going on, also we would always check on each other, asking how we were doing if something didn't make sense we communicated very well and that was something that helped us on the actual test.
I feel like my group and I worked pretty well during the test because we would always check on each other and ask how we were doing i feel like that was help full to every one, an example would be how we always asking questions when something did not made sense for example when our groups was creating an x and y table to find the points that we were gonna plug to our graph, it was some what complicated for me to understand why we were getting the points we were getting. So i decided to ask Beto (Group member) How to find those points, and he explained that the way we got those points was by plugging them in to the original equation, the one that was first given to us , and that made sense to me, after plugging the points to the original equation and solving them out we got the final points to plug and we followed the pattern and it turned into a parabola. Basically the way for us to prepare for the group test was just working together and communicating so that when something didn't make sense explained it to each other and maybe build off of the explanation to keep going.
My ability for the individual quiz was okay because of all of the stuff we did before, i paid close attention and it helped me understand the subject more, something that also helped my ability was the group quiz, it refreshed my memory a bit so it was helpful, in nek how to use the graph to find the points and plugged them and from there work with those points. The only thing that wa negative was the short amount of time we had it took me like 5 min for the first portion of the individual quiz and we only had about 10 min, but other than that i feel it made sense to me and i understood the problem.
I think that for me the overall experience for the group quiz didn't really changed because we most of the time work with each other and support each other to understand the problem , but something that really helped me and i really liked was the way the group was willing to keep the same pace in order for me or for someone else to understand where we were at and not only copy to get to the same spot the group was on.
Evaluation and Reflection:
the thing that most pushed my thinking was looking at how the group was willing to help each other to understand the problem, it made me want to think deperr on the problem and made me wanna explain more my opinion and my ideas, I feel like the thing i got the most out of was actually trying my hardest to understand the problem and support my team , the thing that i struggled with the most was the x and y table, after the group quiz i felt stronger when it came to creating a table , so that is one other thing i really got out of the problem.If i were to grade myself on this unit i would give myself a solid A because of the fact that i really tried to help myself and helped my team by asking questions and sharing my thoughts. Also because i actually learned more of something that i don't really know how to do wich was the x and y table.
My initial attempt for drawing the maximum rectangle diagram actually first started by my group and I creating an X and Y table , we used random numbers for X and we also used our original equation from the problem statement and plugged it into y.
after getting the random points and plugging them into the original equation we solved it out and we got the final points, we decided to use a graph to create a parabola and after creating it with our point we tried fitting as many rectangles possible in the parabola.
Our group's final diagram was a parabola with points plotted from 0 x to 16 y in all of the space we were only able to fit 3 fully rectangles one that went from 0,15 another that went from 0,12 and the last one from 0,5.
Area
In order to find the area we knew that the original way to find the area for any shape or rectangle on this case was x times y so we took 16 minus x squared because that was y and multiplied x (16-x to the second) our final answer for the area was 16x - x to the third power.
Perimeter
How my group and i knew that the equation was correct was by plugging in the original value for y and solving it out.
In order to find the perimeter you do x + y times 2 so what we decided to do was to plug in what we already had for y witch was 16-x squared and we plugged it into y the second step was multiply x by 2 and than y by 2 in this case 16-x squared times 2 so than we got 2x for x and 32-2x squared for y.
Group Test/Individual Test:
The way the group prepared for the quiz was always keep the same pace so that no one was left behind and everyone understood what was going on, also we would always check on each other, asking how we were doing if something didn't make sense we communicated very well and that was something that helped us on the actual test.
I feel like my group and I worked pretty well during the test because we would always check on each other and ask how we were doing i feel like that was help full to every one, an example would be how we always asking questions when something did not made sense for example when our groups was creating an x and y table to find the points that we were gonna plug to our graph, it was some what complicated for me to understand why we were getting the points we were getting. So i decided to ask Beto (Group member) How to find those points, and he explained that the way we got those points was by plugging them in to the original equation, the one that was first given to us , and that made sense to me, after plugging the points to the original equation and solving them out we got the final points to plug and we followed the pattern and it turned into a parabola. Basically the way for us to prepare for the group test was just working together and communicating so that when something didn't make sense explained it to each other and maybe build off of the explanation to keep going.
My ability for the individual quiz was okay because of all of the stuff we did before, i paid close attention and it helped me understand the subject more, something that also helped my ability was the group quiz, it refreshed my memory a bit so it was helpful, in nek how to use the graph to find the points and plugged them and from there work with those points. The only thing that wa negative was the short amount of time we had it took me like 5 min for the first portion of the individual quiz and we only had about 10 min, but other than that i feel it made sense to me and i understood the problem.
I think that for me the overall experience for the group quiz didn't really changed because we most of the time work with each other and support each other to understand the problem , but something that really helped me and i really liked was the way the group was willing to keep the same pace in order for me or for someone else to understand where we were at and not only copy to get to the same spot the group was on.
Evaluation and Reflection:
the thing that most pushed my thinking was looking at how the group was willing to help each other to understand the problem, it made me want to think deperr on the problem and made me wanna explain more my opinion and my ideas, I feel like the thing i got the most out of was actually trying my hardest to understand the problem and support my team , the thing that i struggled with the most was the x and y table, after the group quiz i felt stronger when it came to creating a table , so that is one other thing i really got out of the problem.If i were to grade myself on this unit i would give myself a solid A because of the fact that i really tried to help myself and helped my team by asking questions and sharing my thoughts. Also because i actually learned more of something that i don't really know how to do wich was the x and y table.