Problem Of the Week #3
Problems:
River city is having their big fourth of July concert. the band leader, Kevin, is an overachiever and wants to make this year the year to remember. He plans to have baton twirlers standing in the back on big ol’ platforms for all to see. Because the twirlers will be passing the batons to each other in the air, he wants the difference in the height of the platforms to be even. He needs to decide how many platforms he will need which obviously depends on how many twirlers make the cut. Also, he needs to decide on the height of the shortest platform. Lastly, he needs to decide what the difference will be between each platform. Camilla, his friend/assistant is in charge of building the platforms. She needs to know how tall the tallest platform will be for a permit from the government. Being that she too is an overachiever, she wants to decorate it with cute strips of material. She needs to know the height of all of the platforms so that she can get the right of material. Because Camilla is impatient, she is getting all stressed out and asked me to create an two formulas that will give her all the measurements she needs as soon as indecisive Kevster makes up his mind.
Process and solution(sorry for the inconvenience):
the first thing i needed to do was find the height of the tallest platform. i created a list of variables; H represented the number of platforms, H1 represented the height of the first platform, H2 represented the tallest platform, and D represented the difference in height between each platform. i used trial and error to craft up a spiffy formula that used all these variables. i came up with H2=N(D)+H1 at first, but after inputting a few options i realized it was a failure. so i went back to the start and, using most likely black magic, created H2=D(N-1)+H1. this was flawless. it worked no matter what number i threw at it. you can see how i tested this formula a couple times in the picture at the bottom. the second formula, to find out how much material is needed, was fairly simple. i thought, well its just the total of all the heights, so the rate of increase between each platform is the same. i’m basically taking the average of the first and last platform. this being said using the great tools like friendship and survival of the fittest, i came up with the formula of (X/2)(H1+H2)=M.
evaluation/self assesment:
I'm not really sure if we are supposed to claim that we used a HOHAM or not but I would say i used cooperation among others because i worked with others to both develop formulas and solve quarries. I do know we are supposed to give our self a grade and i’d have to say that out of ten, i should get a 7 or 8 because i know my grammar and punctuation in this is that of maybe a three year old and i’m turning it in super late but i put full effort into it and i actually enjoyed the problem.
River city is having their big fourth of July concert. the band leader, Kevin, is an overachiever and wants to make this year the year to remember. He plans to have baton twirlers standing in the back on big ol’ platforms for all to see. Because the twirlers will be passing the batons to each other in the air, he wants the difference in the height of the platforms to be even. He needs to decide how many platforms he will need which obviously depends on how many twirlers make the cut. Also, he needs to decide on the height of the shortest platform. Lastly, he needs to decide what the difference will be between each platform. Camilla, his friend/assistant is in charge of building the platforms. She needs to know how tall the tallest platform will be for a permit from the government. Being that she too is an overachiever, she wants to decorate it with cute strips of material. She needs to know the height of all of the platforms so that she can get the right of material. Because Camilla is impatient, she is getting all stressed out and asked me to create an two formulas that will give her all the measurements she needs as soon as indecisive Kevster makes up his mind.
Process and solution(sorry for the inconvenience):
the first thing i needed to do was find the height of the tallest platform. i created a list of variables; H represented the number of platforms, H1 represented the height of the first platform, H2 represented the tallest platform, and D represented the difference in height between each platform. i used trial and error to craft up a spiffy formula that used all these variables. i came up with H2=N(D)+H1 at first, but after inputting a few options i realized it was a failure. so i went back to the start and, using most likely black magic, created H2=D(N-1)+H1. this was flawless. it worked no matter what number i threw at it. you can see how i tested this formula a couple times in the picture at the bottom. the second formula, to find out how much material is needed, was fairly simple. i thought, well its just the total of all the heights, so the rate of increase between each platform is the same. i’m basically taking the average of the first and last platform. this being said using the great tools like friendship and survival of the fittest, i came up with the formula of (X/2)(H1+H2)=M.
evaluation/self assesment:
I'm not really sure if we are supposed to claim that we used a HOHAM or not but I would say i used cooperation among others because i worked with others to both develop formulas and solve quarries. I do know we are supposed to give our self a grade and i’d have to say that out of ten, i should get a 7 or 8 because i know my grammar and punctuation in this is that of maybe a three year old and i’m turning it in super late but i put full effort into it and i actually enjoyed the problem.
SMALL WORLD PORTFOLIO
We started out the year and the unit with a seemingly small yet very challenging question: How many people could fit on the planet earth before it was completely full? We started out this problem by figuring out how many people could fit into a couple square feet and then using a formula and research, multiplied that out to the square footage off the world giving us 1.6x10^15 people. i’d say thats a lot of people. Then we moved on to what really mattered. how long it would take for us to reach this insane number. We touched on constants and learned about slopes in curved lines which proved to be harder than I expected. Then we learned a very very important formula: Y=K(E^(CX)). When we had trouble finding the exponents necessary, we learned about finding the log of a number. This was somewhat simple since the calculator did all the hard work. Towards the end of the unit, we were finally given a graph that had the corresponding times for certain populations. This helped quite a bit in helping us find how long it would get until we were 1.6x10^15 strong.
Selected Assignments
The first assignment I have in cluded is the assignment that got it all started. Labeled as just “Small World Isn’t It?”, it is definitely significant to this unit because it explained what we would be doing and what we would be finding.
The next assignment was “Return To Small World Isn't It”. I think this one was important because it was a little bit of a recap and a reminder of what we had done over the span of the unit so that we could appropriately begin the final assignment.
The last assignment is the final one. This was obviously important because it was the wrap up for the project besides this portfolio.
I will also include all the actual papers pictured here since they are really small along with other assignments.
Last is my reflection and personal growth. during the unit I learned quite a bit. I didn't really know about logs before this. I always was wondering what those buttons meant on the “big fancy“ calculators and now I know. I also learned about finding the slope in a curved line. I thought this would be easy but it wasn't because you have to break it down into tiny little parts and then add the slopes all back up and its quite tedious.
Selected Assignments
The first assignment I have in cluded is the assignment that got it all started. Labeled as just “Small World Isn’t It?”, it is definitely significant to this unit because it explained what we would be doing and what we would be finding.
The next assignment was “Return To Small World Isn't It”. I think this one was important because it was a little bit of a recap and a reminder of what we had done over the span of the unit so that we could appropriately begin the final assignment.
The last assignment is the final one. This was obviously important because it was the wrap up for the project besides this portfolio.
I will also include all the actual papers pictured here since they are really small along with other assignments.
Last is my reflection and personal growth. during the unit I learned quite a bit. I didn't really know about logs before this. I always was wondering what those buttons meant on the “big fancy“ calculators and now I know. I also learned about finding the slope in a curved line. I thought this would be easy but it wasn't because you have to break it down into tiny little parts and then add the slopes all back up and its quite tedious.