Math write up:geometry Unit
Two Iron Rails Problem, Geometry Unit: Station work
Problem Statement: Just as Santa Claus was about to get on his sleigh on Christmas Eve he noticed something different about the North Pole. He realized that the temperature went up, which means that the coldness is slowly fading away. He looked to his right, then to his left, Santa saw two thin glaciers that he used as his ramps for his sleigh to jump off the ground both 50 ft long. For some reason the heat that was coming from an unknown place made each rail increase by 0.04%. He started brainstorming things to do next because time was of the essence. He looked closer to those two glaciers and was shocked to see them connected, with no space between them. Well, the only thing Santa could do was get his reindeers and elves to help him fix his rails so he can deliver his presents! In all the time they were looking for supplies and gathering ideas to fix the rails, it had already been to late because the mysterious heat, wherever it was coming from, had made the two rails rise up. Please help Santa by figuring out, what was the measurement of the joint that rose?
Process: First, I drew a before and after picture of the rails. Then, I labeled each side of the triangle. I decided to add 50+0.04% and then multiply 50, but before I could do that I had to convert the percentage into a decimal by moving the decimal point on the percentage two times to the left because 100 has two zeros at the end so in other words I divided 4 by 100. After, I restated my problem which looked like, 50+0.0004 (50) so then I multiplied 0.0004 by 50 which gave me 0.02. The next step was adding 50 + 0.02 = 50.02 ft and that was the final length of each rail. I then had to use the Pythagorean theorem to find out How long the joint is. The formula is a2 + b2 = c2, so I incorporated the measurements which gave me 50 squared + h(stands for height) squared = 50.02 squared. Which gave me 2500 + h squared = 2502, to get h alone I subtracted 2500 by both sides and my answer was 2. The square root of h squared is 2 squared and that gave me my final answer, h = 1.4
Solution: The distance of the joint buckled up is 1.4. All I did was convert the percentage to a decimal and used the Pythagorean Theorem for the second part. Evaluation: This problem seemed really complicated at first and I couldn't figure it out, but I didn't give up on trying to solve it. Then we went over it in class and I spoke to some of my classmates about it and this helped me by guiding me in the right direction. I then noticed my little mistakes that effect the answer majorly. When I finished the problem I felt so good about myself and had a healthy and positive understanding towards the logic in this problem. It was middle ranged for me, not to easy and not to hard. A habit of a mathematician I used was collaborate and listen. I listened to the methods of people who received different answers than what I came up with.
Problem Statement: Just as Santa Claus was about to get on his sleigh on Christmas Eve he noticed something different about the North Pole. He realized that the temperature went up, which means that the coldness is slowly fading away. He looked to his right, then to his left, Santa saw two thin glaciers that he used as his ramps for his sleigh to jump off the ground both 50 ft long. For some reason the heat that was coming from an unknown place made each rail increase by 0.04%. He started brainstorming things to do next because time was of the essence. He looked closer to those two glaciers and was shocked to see them connected, with no space between them. Well, the only thing Santa could do was get his reindeers and elves to help him fix his rails so he can deliver his presents! In all the time they were looking for supplies and gathering ideas to fix the rails, it had already been to late because the mysterious heat, wherever it was coming from, had made the two rails rise up. Please help Santa by figuring out, what was the measurement of the joint that rose?
Process: First, I drew a before and after picture of the rails. Then, I labeled each side of the triangle. I decided to add 50+0.04% and then multiply 50, but before I could do that I had to convert the percentage into a decimal by moving the decimal point on the percentage two times to the left because 100 has two zeros at the end so in other words I divided 4 by 100. After, I restated my problem which looked like, 50+0.0004 (50) so then I multiplied 0.0004 by 50 which gave me 0.02. The next step was adding 50 + 0.02 = 50.02 ft and that was the final length of each rail. I then had to use the Pythagorean theorem to find out How long the joint is. The formula is a2 + b2 = c2, so I incorporated the measurements which gave me 50 squared + h(stands for height) squared = 50.02 squared. Which gave me 2500 + h squared = 2502, to get h alone I subtracted 2500 by both sides and my answer was 2. The square root of h squared is 2 squared and that gave me my final answer, h = 1.4
Solution: The distance of the joint buckled up is 1.4. All I did was convert the percentage to a decimal and used the Pythagorean Theorem for the second part. Evaluation: This problem seemed really complicated at first and I couldn't figure it out, but I didn't give up on trying to solve it. Then we went over it in class and I spoke to some of my classmates about it and this helped me by guiding me in the right direction. I then noticed my little mistakes that effect the answer majorly. When I finished the problem I felt so good about myself and had a healthy and positive understanding towards the logic in this problem. It was middle ranged for me, not to easy and not to hard. A habit of a mathematician I used was collaborate and listen. I listened to the methods of people who received different answers than what I came up with.