POW #3 Planning the Platforms
Write-Up
Problem Statement
This Problem of the Week focuses on a dilemma between two people, Kevin and Camilla. Kevin has several decisions to make for a Fourth of July concert. He wants to have baton players standing on different individual platforms while tossing batons from one the the other. He needs to decide on the number of platforms that need to built but is not sure how many baton twirlers will be there. He needs to find out how high the first platform will be but it depends on how tall the first baton twirler is, and that person still has not been decided on. The last thing he needs to decide on is the height difference between each platform, but he cannot because he doesn’t know how high each of the baton twirlers can throw. Camila is in a dilemma because Kevin cannot make the decisions needed for her to do her job. She needs a permit from the city to build the structures, so she needs to know how tall is the highest platform. She is also ordering fabric so she needs to know the total accumulated height of each of the platforms. In this problem, the task is to create two formulas for Camila, one that finds the height of the highest platform and one that finds the total height of each of the platforms. These formulas will be filled in once Kevin has made up his mind.
Process
In order to create the formulas, there needs to be information to plug in or substitute. So I started with the formula y=mx+b then I looked at the problem statement for information that could be represented. Kevin’s decisions could be represented in the problem, which are the number of platforms, the height of the first platform, and the difference in height of each of the platforms. For the first part, the height of the highest platform, I needed to find the height of the highest platform. so in the formula, I represented it with y, since this is the solution that the formula is trying to find. I represented the number of platforms as x since this is the main variable in the problem. The height of the first platform will be represented as b because it will not be multiplied by another number and is a single constant. For the difference in height of each platform, I represented as m. After looking at the formula and the represented variables, I noticed that m should be subtracted by 1, making the formula look like y=m(x-1)+b, This was changed because b represents the first platform and x-1 represents each additional platform after that one.
For the next part, the total accumulated height of the platforms, I started by representing each of the variables in the equation. I started with the total accumulated height of the platforms with y. Then I represented the difference in height with m, the number of baton twirlers with x, and the height of the first platform with b. After organizing each one, I looked at how I would create a formula for this specific problem. I began with having y equal _____ plus b, meaning that y would equal an unknown function plus b. After much trial and error with this function, I learned that by using halves, I could complete the problem. My final function is y=mx(0.5x+0.5+0.5b), or the total accumulated height of the platforms is equal to the difference in height multiplied by the number of baton twirlers which is multiplied by half of the number of baton players plus half of the height of the first platform.
Solution
For the first part, the height of the tallest platform, I found that the formula should be: y=m(x-1)+b; meaning that the height of the tallest platform is equal to the difference in height multiplied by the number of platform minus one plus the height of the first platform.
For the second part, the total accumulated height of the platforms, I found that the formula should be: y=mx(0.5x+0.5+0.5b); meaning that the total accumulated height of the platforms is equal to the difference in height multiplied by the number of baton twirlers which is multiplied by half of the number of baton players plus half of the height of the first platform.
Reflection
This assignment was particularly tough for me. I felt like I used a lot of evidence to prove wrong my formulas. I worked on many different formulas in order to find the correct one.
I tried such formulas as y=mx2+b and then tried to see if it could be proven wrong by adding different variables for m, x, b, and y. Most of the formulas had been correct only with a certain set of numbers but had not been consistently right. Only my final formula was correct for all the variables.
Problem Statement
This Problem of the Week focuses on a dilemma between two people, Kevin and Camilla. Kevin has several decisions to make for a Fourth of July concert. He wants to have baton players standing on different individual platforms while tossing batons from one the the other. He needs to decide on the number of platforms that need to built but is not sure how many baton twirlers will be there. He needs to find out how high the first platform will be but it depends on how tall the first baton twirler is, and that person still has not been decided on. The last thing he needs to decide on is the height difference between each platform, but he cannot because he doesn’t know how high each of the baton twirlers can throw. Camila is in a dilemma because Kevin cannot make the decisions needed for her to do her job. She needs a permit from the city to build the structures, so she needs to know how tall is the highest platform. She is also ordering fabric so she needs to know the total accumulated height of each of the platforms. In this problem, the task is to create two formulas for Camila, one that finds the height of the highest platform and one that finds the total height of each of the platforms. These formulas will be filled in once Kevin has made up his mind.
Process
In order to create the formulas, there needs to be information to plug in or substitute. So I started with the formula y=mx+b then I looked at the problem statement for information that could be represented. Kevin’s decisions could be represented in the problem, which are the number of platforms, the height of the first platform, and the difference in height of each of the platforms. For the first part, the height of the highest platform, I needed to find the height of the highest platform. so in the formula, I represented it with y, since this is the solution that the formula is trying to find. I represented the number of platforms as x since this is the main variable in the problem. The height of the first platform will be represented as b because it will not be multiplied by another number and is a single constant. For the difference in height of each platform, I represented as m. After looking at the formula and the represented variables, I noticed that m should be subtracted by 1, making the formula look like y=m(x-1)+b, This was changed because b represents the first platform and x-1 represents each additional platform after that one.
For the next part, the total accumulated height of the platforms, I started by representing each of the variables in the equation. I started with the total accumulated height of the platforms with y. Then I represented the difference in height with m, the number of baton twirlers with x, and the height of the first platform with b. After organizing each one, I looked at how I would create a formula for this specific problem. I began with having y equal _____ plus b, meaning that y would equal an unknown function plus b. After much trial and error with this function, I learned that by using halves, I could complete the problem. My final function is y=mx(0.5x+0.5+0.5b), or the total accumulated height of the platforms is equal to the difference in height multiplied by the number of baton twirlers which is multiplied by half of the number of baton players plus half of the height of the first platform.
Solution
For the first part, the height of the tallest platform, I found that the formula should be: y=m(x-1)+b; meaning that the height of the tallest platform is equal to the difference in height multiplied by the number of platform minus one plus the height of the first platform.
For the second part, the total accumulated height of the platforms, I found that the formula should be: y=mx(0.5x+0.5+0.5b); meaning that the total accumulated height of the platforms is equal to the difference in height multiplied by the number of baton twirlers which is multiplied by half of the number of baton players plus half of the height of the first platform.
Reflection
This assignment was particularly tough for me. I felt like I used a lot of evidence to prove wrong my formulas. I worked on many different formulas in order to find the correct one.
I tried such formulas as y=mx2+b and then tried to see if it could be proven wrong by adding different variables for m, x, b, and y. Most of the formulas had been correct only with a certain set of numbers but had not been consistently right. Only my final formula was correct for all the variables.