June 14, 2010

1. This year's math class helped me complete my PBAT. All the activities and projects we did was very helpful. This math class made me realize that I can use what i learned in the real world. I also think that becuase of this math class i become better at math than what i used to be.

2. Yes i want to send my letter to the company i wrote to.

3. I think that this class was well organized, and you helped us alot Wan. I dont think you should change anything for next year. I liked blogger and google docs. It kepted all our documents well organized.

Exit Slip 5/6/10

The overall task of today's lesson was to graph the new surface area and the minimum surface area.
It is necessary because we want to reduce the Surface Area, but keep the same volume, so the use of a graph will help us find the smallest surface area.

Exit Slip 5/4/10

The way my new surface area function will be used for this PBAT is by me substituting my can values into the new surface area function. The ultimate goal of finding this new surface area function is finding the smallest surface area.

The way I would use this function to visually represent the relationship bewtween the height and the surface area of my can is by me making a new design or can.

Exit Slip 5/3/2010

I think it is necessary for us to combine two formulas because the task is to eliminate the height in the surface area function and leave the radius as the only independent variable. This will allow me to find the minimum surface area with r being the independent variable and SA being the dependent variable.

I would need to simplify the the volume and surface area of a cylinder. I would also need to Solve for Height, so that I can substitute it into the surface area formula. When doing all of this I would need to Justify all the steps I did to solve for height and simplify the SA formula. Last thing I would need to do is apply my units when i'm done solving everything.

Exit Slip 4/30/10

The name of this PBAt is called the Can Project. The overall task of this PBAT is to minimize the material being used for cans or cylinder containers because the company of my choice is being pressured by consumers. Basically my task is to write a letter to the company of my choice presenting the dimensions of my old and new can. I have to make two physical models of my can before and after pictures. I must try to make the can cheaper by still using the same materials, but still keeping the same amount of content of the can. Inorder to do this I must keep the same volume of the can but make the surface area smaller. Then we must find the radius, and height of the can as well.

Exit Slip

The important concept of today's lesson was solving for the height of your can. Also putting the calculations from our can into a spreadsheet and labeling the columns. Another important concept was making a graph using our calculations from our can and labeling the graph as well.

The mathematical tool I used to today was a calculator. The calculator helped me calculate the height for all of the radiis. This mathematical tool made it easier for me because I just has to plug in my values into the calculator to get my answers and didnt have to use scrap paper.

Exit Slip 4/23/10

Today I helped some of my peers. I helped Ellen by explaining to her what was being asked of us. I also helped Sha'Eika find the Volume and Surface Area of her can.Today I was able to accomplish many things. I found all the measurements to my can by using a ruler. Also, I found the Surface Area and Volume of my can. The skills I learned today were how to find the height and diameter of a can or cylinder. I would use these skills when I want to build a cylinder model or in college when I have to do a project based on cylinders. For the moment I dont have any questions to ask because I understand everything that we are going to be doing for our PBAT.

Extra Credit.

The results from the two calculations are shown in Table 1. The first function is y1=4x^3+5 and the second function is y2=7x^3+100.

The first column contains some values for the independent variable x. The domain of these values: -25 to 25 were chosen randomly, first. I just wanted to make sure that when the graph is made the important parts would show. Some examples of the important parts are: the vertex, the roots, the local minimum, the local maximum, etc. The scale is set to 5.

These x-values were substituted into the function y1, and the results are displayed in the second column. Since y1 is a third degree polynomial or cubic function, the y-values first increase as the x-values increase from negative numbers to positive numbers. There is no vertex because this is a third degree polynomial. It is hard to tell the coordinates of the local minimum and maximum without a graph.

The y-values for y2=7x^3+100 are shown in the third column of Table 1. The y-values also increase as the x-values increase from negative to positive numbers.

Graphs Exit Slip

• The curvature of y2 compared to y1 is narrower, meanwhile y1 is wider. This is not a reflection on the x-axis. The reason why it is not a reflection is because the coeffiecients are different. The coefficient for y1 is 3 and the coefficient for y2 is -5.


• Compared to y1, y2's graph is shifted downward vertically, while y1 is shifted upward vertically. I see this in the graph by noting that the minimum point of y1 is (0,100) and the maximum point of y2 is (0,-100).
• There is no horizontal shift because the lines have the same pattern horizontally. Also the minimum and maximum line up at x=0.

Exit Slip

We can compare and contrast two functions in many ways, but I chose to compare and contrast my two functions by creating a graph. The two expressions I used were 2X^4 and -2X^4. Then I created a spreadsheet, which helped me a lot. In the spreadsheet one column was (X), the next one was Y1 and then Y2. The great thing about the spreadsheet was that when you went to a column all you had to do was drag the first number in the cell all the way down and the numbers were calculated for you. When that was done I had to graph my numbers, which was easy to do. After graphing the two functions I realzied that function y1 and y2 was a reflection of one another. Once the numbers were graphed I labeled my graph. I put the title, and labeled the x and y axis. I also had to change y1 and y2 to its functions. For example, for y1 I put 2*A2^4 and for y2 I put -2*A2^4. Once I plugged in those functions I then had to create a table on Google Docs. The table had the two functions, the highest , lowest, and constant term for each as well. For example, like for function y1 for the hghest term I put 2x^4 and then for y2 I put -2x^4. The next degree term and contant degree term was 0 for each functions.
In essence, by looking at my graph and table you can compare and contrast the two functions.

Exit Slip

1.One major thing i learned today was that i can create a graph on my Google spreadsheet. I think creating this Google spreadsheet makes it easier for me to do my graphs and plug in my functions.

2. I didn't have a major problem today. I understood everything i was doing and i found it to be very easy to create a Google spreadsheet.

okay well today i tried my best in completing this report, due to these circumstances. Im proud of myself.!!

Wan can you please comment our report one more time..thank you!~

Today I got on google docs to continue editing my group's report and I noticed that Michelle was editng the report as well, I was very excited because it goes to show that someone at least cared about helping with the report.
Well today the math report is due. I hope my group's report is great because Michelle and I worked very hard. Michelle and I were very honest in this report and completing every aspect of the report. We tried our very best.

Today i finished editing everything, now im jus waiting for Wan to review the report and let me know if their is anything else to change. Hopefully their is nothing else to change and everything is fine. I tried my best and i hope the report is what was expected.

Well today when i came out of school i fixed all the charts and placed them on the report. Then i started editing, but im still not done. I still have to add in more information in the body, conclusion, and inquiry process. hopefully we'll be done by Monday and everything is ok because i have been working very hard, and so has Michelle and Tyre'

Today i am very upset cuz Wan stood wit one table all day and barely helped anyone else.

Well me and michelle basically did all our group work. We was making sure everyone was on point. Unfortunately Ellen, and Tyre weren't in class today to finish what they were assign to do, so nowMichelle and I muyst take it upon ourselves to do their part. I think we will do well though so it dont matter anyway

So far my group and i are done with our report. We just need to revise and wait for Wan to comment on it.

1.So far all my group members are on point. We already did both our Fed Ex Express (130 inches) and UPS (165 inches) graphs, as well as our tables. We have generalized and checked our volumes, girth, length, width and height using calculators.

The design I used for FedEx Express was the width and the height are the same. This would make the box a square face, which means the formula i used to find the girth was x+x+x+x or 4x. Since i knew that X, the width and the height would be the same all i had to do was find my length. The way i found my length was by subtracting the total by the girth, in this case it would be (130-4x). Now i had to find the volume. The way i found the volume was by multiplying the length, width,and height. I generalization for the volume was (130-4x)x*x.

The design i used for UPS was the width is always 10 inches longer than the height. This design would make the box a rectangular face, which means that the formula i used to find the girth was w+h+w+h or 4x. In this problem my width and height werent the same anymore, but my height and x would always be the same. So in order to find the width i had to add 10 to the height becuase my design said that the width is always 10 inches longer than the height(x+10). now i had to find my length so i did the same thing i did with the FedEx Express box, i subtracted the total from the girth (165-4x). the next thing i had to was find the volume. I found the volume by multiplying the width, length , and height. My generalization for the volume was (x+10)(x)(165-4x) .

My group memebers and i checked all our calculations inoreder to see what our scale on the graph would be. It was very hard at first becuase we werent sure how to scale it, but then it worked out. When we were done i checked my tables first to do the finite differences so that i can see whether my calculations were correct, and to see if when i graphed my points it would be a 3rd degree polynomial. Then i felt i was ready to start graphing. For my FedEx Express graph my y- axis scale was 3,000's and my x -axis scale was 1's. My y-axis was labeled volume and my x-axis was labeled just plane ol (x). As my graph was completed i plugged in my function in the calculator, put in my scale and pressed graph to see whether my graph matched the one on the calculator and it did. Then i pressed 2nd graph on the calculator to see if my maximum point was correct and it was. I didnt use the trace thing on the calculator to find the maximum volume becuase i find that to be very confusing, instead i looked at my table and my graph.

My maximum volume for FedEx Express was 20,328 (22,20328) and for UPS it was 40,227 (23,40227).

The way i organzied was by creating a table. My first two tables had the total, (x), length, width, height, volume , and girth. It also had all my functions for each column. Then i made two T -charts with only x and the volume. I used this chart to check the finite difference. Unfortunately everyone in my group had to create their own tables becuase we all had different designs and the shipping was different as well.

3. When my group members and i were done with all our calculations and graphing we looked at our maximum volume for FedEx Express and UPS. Michelle's and my maximum volume for FedEx Express was 20,328. Tyre's maximum volume was 20,342 and it was the highest. I think his was different because he had a different design from the both of us. Like his design was for FedEx Express was the width is always 6 inches longer than height and mines was the width and the height are the same. For UPS we all had different maximum volumes. My maximum volume was the highest. The reason for this was because we all had different designs for our boxes too. Like my UPS design was the width is always 10 inches longer than the height. Meaning like if my height was 1 then my width would be 11 because i added 10 to 1 (x+10). Since my design was the width is always 10 inches longer than the height, that means the width is longer than the rest of my group members and its more flat.

Today my group and i learned that X and H are always going to be the same nobody whether it is a square face or rectangular face. One of my group memebers also learned that inorder to find the length you must subtract the total from the girth.

Wyclef Jean a celebrity activist who has founded his own foundation named Yele for his country, Haiti. Wyclef Jean has one the NAACP award and says its for his people in Haiti. He was an ex-member of The Fugees, now a solo artist. He also is a songwriter and producer. Wyclef Jean came from a hut, to the projects to a mansion so he feels that anybody can make it theirs no excuses.
"fought for recognition of my country"- Wyclef Jean

1.How are we suppose to find out how much material is required to make each type of box?
2.Will you help us with this project?
3.Can we pick ouor groups?
4.we have to write a big report?
5.will we do this project step by step?

Wan im not sure what is really being asked of me but when i checked the USPS website i noticed that the boxes have different dimensions which means they have a different volume. The post office boxes come in different sizes so that people can buy the box size that they need.

Hey im in my math class learning how 2 follow ppl inorder for me to communicate with others...

This is my first time on my blog..im excited
*community box maker*