Problem Statement
This is the problem we were given; A rectangle has one corner on the graph of y=16-x^, another at the origin, a third on the positive y axis and the fourth on the positive Y axis. If the area of the rectangle is a function of x, what value of x yields the largest area for the rectangle?
Wordy, right? Our class started by writing questions about the problem or ideas on how to solve it. The questions I asked were,
Wordy, right? Our class started by writing questions about the problem or ideas on how to solve it. The questions I asked were,
- What is the origin?
- How do I graph y=16-x^2 ?
- How do I find a function of x that shows the area of the rectangle?
- Which function of x do I use?
Process/Solution
Finding the Area
Finding the Largest Perimeter
Recap
- The largest perimeter is 32.5, and it is rational
- The largest area is not going to be one solid number, but can be rounded to 2.31
- Using the equation given, and the basic formulas for perimeter and area, you can find the area or perimeter for any point on the graph
Group test/Individual Test
My group prepared for the group quiz by solving a practice problem that Mr.B gave us. He gave us the equation y=4+x^2 so we found the largest area and perimeter of that equation. Going into the test, I thought I had a really good group! I was almost excited, because I knew that I worked well with the two people in my group, and we were all hard workers with the goal of getting the best grade. Once we read the problem on the group quiz, we were a bit stunned. This was similar to the problems we worked on in this unit, but now we had to account for the negative side of the graph. I was convinced that there was only one rectangle that had the biggest perimeter and area, and that we did not have to go into the decimals. My group was unsure of my observations and we spent the majority of the time allotted for the group test arguing about whether we should go into the decimal range. We eventually received some clarification from Mr.B and we figured out our mistake. We did not end up finishing the group test, but we were very close from getting the right answer. We ended up getting a 70/80 which is not a bad score!
On the individual portion of the test, I understood all of the questions and process to get the answers. The honors questions were the ones I struggled with in previous quizzes, but I prepared myself by studying the concepts used in this unit on Khan Academy. I got a 30/30.
The overall experience of the group test was more positive than negative. I think that I did prevent my group from completing the test because I was set on one answer. I appreciate my group for pushing me and questioning the answer I proposed.
On the individual portion of the test, I understood all of the questions and process to get the answers. The honors questions were the ones I struggled with in previous quizzes, but I prepared myself by studying the concepts used in this unit on Khan Academy. I got a 30/30.
The overall experience of the group test was more positive than negative. I think that I did prevent my group from completing the test because I was set on one answer. I appreciate my group for pushing me and questioning the answer I proposed.
Evaluation/Reflection
The concept that most pushed my thinking was how to know what parts of the work problem to utilize in the steps to the solution. When I first read this problem, I was confused as to what points to plot, and exactly how to find the rectangles within those points. As my class worked through the problem, I understood the process completely and the rest of the problem was a breeze. If I were to give myself a grade on this unit, I would give myself an A, because I worked hard on making sure that I understood the material and took time outside of class to study on Khan.