Planning Platforms
This problem is all about platforms. In the problem, there is a party where Kevin wants baton twirlers on top of platforms. There are four platforms on the diagram, each with a baton twirler on top. They are steadily increasing, the last platform the tallest. Kevin has to decide on how tall the first platform is, the number of platforms he wants, and the difference in height from each platform to the next. then, Camilla wants to hang ribbon from each platform to the ground on one side. The task that we were to complete is to form an equation using variables to determine the tallest platform and the total of all of the heights added up.
What I first did, was form an equation to determine any height of the platform. h=x+(cz) where h=height, x=height of first platform, c=case #, and z=the difference between cases. The case number is basically the number in order of which platform it is. I knew that I could use this to find any height, but now necessarily the tallest platform. My group partner found that equation: t=z(n-1)+x, where all of the variable mean the same thing, t=tallest platform height. Once we had found these equations, I started to work on an equation to solve the total length. Again, my table partner found an equation: L=(x+t)(.5n) where L=the total length of all platform heights added up. this equation works, only you can't have a situation of .5ft tall, you would need to convert it to 6 inches. The equation that I came up with is L=nx+nz. This equation is very interesting because it works with the first three platforms, but not for any other number.
Let's say the platform heights go 2,4,6. 2 would be x, and t would be 6. In my equation the x (2), would be multiplied by n, which would be three. z would also be 2, because the difference between all of the numbers is 2. The equation would equal L=(3*2) + (3*2) which would total 12. 2+4+6 = 12. This proves that it would work for the first three cases. Let's extend the platform number total to 4 instead, the series of numbers being 2,4,6,8. The equation would be L=(4*2)+(4*2) which would equal 16. 2+4+6+8=20, therefore the equation doesn't work.
The two formulas I have would be t=z(n-1)+x and L=(x+t)*(.5n), both of which were found by my partner. If we use the platform number that I used above, you can see these equations work. t=2(3)+2 which would equal eight, the tallest in the four number case. L=(2+8)(.5*4) which would equal (10)(2) which would equal 20. Both of these equations are right and work well.
Two habits of a mathematician that I used would be persistence and seek why/prove. I used persistence because even though my equation didn't work, I kept looking what was wrong and how I could fix it or start a new equation.
I felt that I did a lot of work on this problem. if you look at my work on the paper, I have a lot of equations I was trying and came up with new ones and there are a lot of scribbles all over the page. I didn't use organization as well as I could have, but I really worked hard on this problem. I also liked this problem a bit because it was a little more of a challenge because I didn't get the answer right at first. I would say i should get a 10/10 just because I worked really hard to complete this problem and understand it. I might not have been paying attention to the teacher the entire time, but I was thinking about math and working on it the entire time which I was proud of because usually I zone off sometimes when I get bored.
What I first did, was form an equation to determine any height of the platform. h=x+(cz) where h=height, x=height of first platform, c=case #, and z=the difference between cases. The case number is basically the number in order of which platform it is. I knew that I could use this to find any height, but now necessarily the tallest platform. My group partner found that equation: t=z(n-1)+x, where all of the variable mean the same thing, t=tallest platform height. Once we had found these equations, I started to work on an equation to solve the total length. Again, my table partner found an equation: L=(x+t)(.5n) where L=the total length of all platform heights added up. this equation works, only you can't have a situation of .5ft tall, you would need to convert it to 6 inches. The equation that I came up with is L=nx+nz. This equation is very interesting because it works with the first three platforms, but not for any other number.
Let's say the platform heights go 2,4,6. 2 would be x, and t would be 6. In my equation the x (2), would be multiplied by n, which would be three. z would also be 2, because the difference between all of the numbers is 2. The equation would equal L=(3*2) + (3*2) which would total 12. 2+4+6 = 12. This proves that it would work for the first three cases. Let's extend the platform number total to 4 instead, the series of numbers being 2,4,6,8. The equation would be L=(4*2)+(4*2) which would equal 16. 2+4+6+8=20, therefore the equation doesn't work.
The two formulas I have would be t=z(n-1)+x and L=(x+t)*(.5n), both of which were found by my partner. If we use the platform number that I used above, you can see these equations work. t=2(3)+2 which would equal eight, the tallest in the four number case. L=(2+8)(.5*4) which would equal (10)(2) which would equal 20. Both of these equations are right and work well.
Two habits of a mathematician that I used would be persistence and seek why/prove. I used persistence because even though my equation didn't work, I kept looking what was wrong and how I could fix it or start a new equation.
I felt that I did a lot of work on this problem. if you look at my work on the paper, I have a lot of equations I was trying and came up with new ones and there are a lot of scribbles all over the page. I didn't use organization as well as I could have, but I really worked hard on this problem. I also liked this problem a bit because it was a little more of a challenge because I didn't get the answer right at first. I would say i should get a 10/10 just because I worked really hard to complete this problem and understand it. I might not have been paying attention to the teacher the entire time, but I was thinking about math and working on it the entire time which I was proud of because usually I zone off sometimes when I get bored.