Help Kevin and Camilla Each Find a Formula that Will Help Them Both Plan Out the Platforms!
Gabriel Concepcion
Math 3
September 29, 2012
POW! 3: Planning the Platforms
Problem Statement
In the Planning the Platforms POW, I am going to help Kevin find a formula that will help him plan platforms for baton twirlers. Kevin needs to decide on the total number of platforms, the height of the first platform, and the difference in height between one platform and the next. Because the baton twirlers will be tossing the batons up and down to one another on the platforms, Kevin has decided that the difference in height between the platforms should be the same. I am also going to help Camilla, who will be planning the decorations for the platforms, find a formula that will help her decorate the platforms that Kevin has planned out. She needs to know the height of the tallest platform and also the total length of fabric she will need in order to decorate all of the platforms. In order to help them, I am going to create two formulas. The first formula is going tell me the height of the tallest platform. The second formula is going to tell me the total height of all the platforms combined. The goal of this lab is to create these two formulas in order to help Kevin find the height of the highest platform and to help Camilla find the total height of all the platforms.
Process
I first tried to create the formula for Kevin. I needed to create this formula so that will solve for three things, 1.) The height of the first platform, 2.) The total number of platforms, and 3.) the difference in height of each of the platforms. I figured that, since the difference in height between the platforms is equal, the formula could be a linear equation or y = mx +b. Then, I decided on what the different numbers will be. I decided that “y” would equal the height of the highest platform, “m” would be the difference in height, “x” would be the number of platforms, and “b” plus “m” is the height of the first platform. With this information, I reworded the formula into Tp = D(#p) + Fp. Next, I plugged in numbers into the formula in order to see if I was right. The numbers I plugged in were 2 feet for “m”, 4 platforms for “x” and 1 foot for “b”. When I solved, the tallest platform is going to be 9 feet. I reworked the problem in order to check if the formula was right by solving for “x” or the number of platforms. After I solved it, it says that x is 4 which proved that my answer was correct. This problem would now help Kevin with the platforms. Now I had to create another formula that would help Camilla.
Camilla needs a formula that would help her find the total length of fabric needed. Because Camilla’s formula is dependant on what Kevin’s formula would be, I needed to include some of the variables from Kevin’s formula. I knew that when a new platform is added to the formula, the total length of the fabric would increase by the height of the new platform. This meant that the growth of the total height of all the platforms would be exponential. In order to see if it did grow exponentially, I solved for Kevin’s formula using the numbers I used to test it (m is 2 ft., x is 4, and b is 2) with the exception of x equaling 1. After I solved, I plugged in 2 as x, then 3 and 4. Then I plotted my points on a graph. I found out that Camilla’s formula would be an exponential growth problem or y = mx2 + b. I analyzed how my formula would probably work on a piece of paper. I also tried to find the relationship between the number of platforms and the total length of all of them. In the end, I found a formula that would work with Camilla’s needs.
Solution
The formula I found for Kevin is “Height of the Tallest Platform” equals “The Difference in Height Between the Platforms” times “The Number of Platforms” plus (“The Height of the First Platform” minus “The Difference in Height Between the Platforms”) or
The formula I found for Camilla is “The Total Height of All the Platforms” equals “The Difference in Height Between the Platforms” times “The Number of Platforms” times (1/2 “The Number of Platforms” plus 0.5) or
Reflection
I feel that the second part of the problem was the most challenging part of this POW. I realized a while after getting stuck on the second formula that the formula was a non-linear equation.
Data
On Separate Sheet of Paper
Math 3
September 29, 2012
POW! 3: Planning the Platforms
Problem Statement
In the Planning the Platforms POW, I am going to help Kevin find a formula that will help him plan platforms for baton twirlers. Kevin needs to decide on the total number of platforms, the height of the first platform, and the difference in height between one platform and the next. Because the baton twirlers will be tossing the batons up and down to one another on the platforms, Kevin has decided that the difference in height between the platforms should be the same. I am also going to help Camilla, who will be planning the decorations for the platforms, find a formula that will help her decorate the platforms that Kevin has planned out. She needs to know the height of the tallest platform and also the total length of fabric she will need in order to decorate all of the platforms. In order to help them, I am going to create two formulas. The first formula is going tell me the height of the tallest platform. The second formula is going to tell me the total height of all the platforms combined. The goal of this lab is to create these two formulas in order to help Kevin find the height of the highest platform and to help Camilla find the total height of all the platforms.
Process
I first tried to create the formula for Kevin. I needed to create this formula so that will solve for three things, 1.) The height of the first platform, 2.) The total number of platforms, and 3.) the difference in height of each of the platforms. I figured that, since the difference in height between the platforms is equal, the formula could be a linear equation or y = mx +b. Then, I decided on what the different numbers will be. I decided that “y” would equal the height of the highest platform, “m” would be the difference in height, “x” would be the number of platforms, and “b” plus “m” is the height of the first platform. With this information, I reworded the formula into Tp = D(#p) + Fp. Next, I plugged in numbers into the formula in order to see if I was right. The numbers I plugged in were 2 feet for “m”, 4 platforms for “x” and 1 foot for “b”. When I solved, the tallest platform is going to be 9 feet. I reworked the problem in order to check if the formula was right by solving for “x” or the number of platforms. After I solved it, it says that x is 4 which proved that my answer was correct. This problem would now help Kevin with the platforms. Now I had to create another formula that would help Camilla.
Camilla needs a formula that would help her find the total length of fabric needed. Because Camilla’s formula is dependant on what Kevin’s formula would be, I needed to include some of the variables from Kevin’s formula. I knew that when a new platform is added to the formula, the total length of the fabric would increase by the height of the new platform. This meant that the growth of the total height of all the platforms would be exponential. In order to see if it did grow exponentially, I solved for Kevin’s formula using the numbers I used to test it (m is 2 ft., x is 4, and b is 2) with the exception of x equaling 1. After I solved, I plugged in 2 as x, then 3 and 4. Then I plotted my points on a graph. I found out that Camilla’s formula would be an exponential growth problem or y = mx2 + b. I analyzed how my formula would probably work on a piece of paper. I also tried to find the relationship between the number of platforms and the total length of all of them. In the end, I found a formula that would work with Camilla’s needs.
Solution
The formula I found for Kevin is “Height of the Tallest Platform” equals “The Difference in Height Between the Platforms” times “The Number of Platforms” plus (“The Height of the First Platform” minus “The Difference in Height Between the Platforms”) or
- Tallest Platform = Difference in Height (#Platforms) + (Height of 1st Platform - Difference in Height)
The formula I found for Camilla is “The Total Height of All the Platforms” equals “The Difference in Height Between the Platforms” times “The Number of Platforms” times (1/2 “The Number of Platforms” plus 0.5) or
- Total Height = Difference in Height (#Platforms)(1/2(#Platforms) + 0.5)
Reflection
I feel that the second part of the problem was the most challenging part of this POW. I realized a while after getting stuck on the second formula that the formula was a non-linear equation.
Data
On Separate Sheet of Paper