Rocket Project
Throughout this project we faced a few challenges while building and testing our rocket. The most difficult challenge was getting our nose cone to stay on enough. We started with our nose cone falling off way too easily, it was too small and did not fit on the top of our rocket. So as it was flying up in the air, it would fall off and our parachute would deploy. Then dragging our rocket back down before it could reach max height. After that we got a bigger top that fit on the rocket extremely snug and would not fall off at max height. The tip would either stay on too much or fall off immediately, we needed a nice balance of both. We fixed this by testing and changing our nose cones. What ended up working the best was having about a one inch piece of transparency paper around the top of the rocket that the nose cone could sit one. It allowed us to make it whatever size we needed to best fit the nose cone. Also after testing our rocket a few times we decided that our fins were too small. To overcome this we just laser cut new fins out of acrylic with the same design, just a few inches larger. Then, we attached them once again and it helped our rocket stay straighter while in flight.
One major success we had during the rocket project was we had enough time to fix and change our rocket if we needed to. In the beginning of the build and test time we built a quality rocket quickly, so we could launch our rocket and see what we needed to adjust to improve it. If we spent an extremely long time on the original design we wouldn't have been able to test and build new rockets. It is vital to test it and fix your projects according to the feedback you receive. Leave yourself enough time for unexpected challenges. Another success we had was our fins and parachute were attached extremely well and rigid. Therefore our fins didn't flap in flight and our parachute always stayed connected. It is important to use proper technique and materials while attaching your elements.
For the first week of building our rocket we had the same rocket body and fins, only making small adjustments to the nose cone. Then on the first day of the second week, during testing, our rocket broke. Therefore we were forced to construct an entirely new rocket. This actually ended up benefiting us in the long run because we redid the way our nose cone was attached and the size of our fins. After making these adjustments, with a new bottle that wasn't as beat up, our rocket was flying the best yet. This was our turning point because our nose cone finally fell off at the right time. Also our rocket stopped turning upside down mid flight. It flew straighter and for longer, with our parachute still deploying as planned. Everything was falling into place.
The biggest takeaway that I got from this project was that you have to create, test, critique, and refine over and over again in order to get the best possible project. The first time you do something it's probably not going to be perfect, but you will find out how to do it better. You can then come at that same problem again until it works just right. That is important to keep in mind throughout life whenever you come across something that you can't figure out. Don't stop trying after one failed attempt. Take what you learned from your practice experience and try again and again. Eventually it will work, as long as you keep making it better.
If I were going to do this project again I would like to try different sized presser chambers. I think it would be interesting to compare a smaller bottle (smart water bottle), a 2 liter bottle, and try to splice a few 2 liter bottles together. For each of the different rockets I would have different fin designs for each bottle. I would love to test different types of rockets and compare. Then for my final rocket I would take the best parts from each rocket and build the best of all worlds. I also think it would be cool to see the difference in each type of pressure chambers and fins.
One major success we had during the rocket project was we had enough time to fix and change our rocket if we needed to. In the beginning of the build and test time we built a quality rocket quickly, so we could launch our rocket and see what we needed to adjust to improve it. If we spent an extremely long time on the original design we wouldn't have been able to test and build new rockets. It is vital to test it and fix your projects according to the feedback you receive. Leave yourself enough time for unexpected challenges. Another success we had was our fins and parachute were attached extremely well and rigid. Therefore our fins didn't flap in flight and our parachute always stayed connected. It is important to use proper technique and materials while attaching your elements.
For the first week of building our rocket we had the same rocket body and fins, only making small adjustments to the nose cone. Then on the first day of the second week, during testing, our rocket broke. Therefore we were forced to construct an entirely new rocket. This actually ended up benefiting us in the long run because we redid the way our nose cone was attached and the size of our fins. After making these adjustments, with a new bottle that wasn't as beat up, our rocket was flying the best yet. This was our turning point because our nose cone finally fell off at the right time. Also our rocket stopped turning upside down mid flight. It flew straighter and for longer, with our parachute still deploying as planned. Everything was falling into place.
The biggest takeaway that I got from this project was that you have to create, test, critique, and refine over and over again in order to get the best possible project. The first time you do something it's probably not going to be perfect, but you will find out how to do it better. You can then come at that same problem again until it works just right. That is important to keep in mind throughout life whenever you come across something that you can't figure out. Don't stop trying after one failed attempt. Take what you learned from your practice experience and try again and again. Eventually it will work, as long as you keep making it better.
If I were going to do this project again I would like to try different sized presser chambers. I think it would be interesting to compare a smaller bottle (smart water bottle), a 2 liter bottle, and try to splice a few 2 liter bottles together. For each of the different rockets I would have different fin designs for each bottle. I would love to test different types of rockets and compare. Then for my final rocket I would take the best parts from each rocket and build the best of all worlds. I also think it would be cool to see the difference in each type of pressure chambers and fins.
Chi-Squared Calculations
Over the course of this semester students dove in to statistics using different tools to look at the data that they have collected. They mainly used what is called chi-squared, a formula that we can use to determine if the data we collected and compared is in anyway significant. Students selected a group and a metric from our survey of AHS students to ask a question about the population. I was wondering if having instagram or not effected a students GPA, I found that it does.
Cookies Project Reflection
- In what ways has the cookies project helped you gain perspective on doing real world mathematics?
While working on the cookies projects it has made me realize how wrapped up math is in the real world around me. Also how helpful math can be when planning what you want to sell to make the most profit. When completing the cookies project we were tasked with choosing two different baked goods and finding out how we can make the most profit. This made us work with the cost of bulk goods, profit, expenses, time, markup, budgeting, planning, labor costs; everything that goes into the books of running a business. Normally when I am doing math it feels like the numbers don't have any deeper meaning. Although with the cookies project it attached a value to them, I had to make sure all of the pieces fit together with the most profit. Showing me that the solutions I was coming up with have consequences that can affect business in either a positive or negative way.
Tessellation Project Write UP
Question: Describe the concept of area and volume in terms of efficiency. What is the most efficient shape and why? How can we measure efficiency?
Efficiency is measured by how we can maximize one thing, and minimize another. For example if I am building a bridge I would want to maximize the strength of it and minimize cost. When we talk about effectively in area and volume, circles and spheres will always be the best.
Efficiency is measured by how we can maximize one thing, and minimize another. For example if I am building a bridge I would want to maximize the strength of it and minimize cost. When we talk about effectively in area and volume, circles and spheres will always be the best.
If you have all of these shapes in a circle, the hexagon has the least wasted space. With the triangle having the most. The most efficient shape in terms of area would be the circle because it has no wasted space. Giving the most amount of area with the least amount of perimeter.
Question: Explain how we can prove two triangles are similar
Two triangles are similar when they can be flipped, turned, slid, or resized and still have similar values.
1. Two triangles are similar if two of the angles are the same, or by default all three. Even through these triangles are different they are similar because they share the same interior angels.
Two triangles are similar when they can be flipped, turned, slid, or resized and still have similar values.
1. Two triangles are similar if two of the angles are the same, or by default all three. Even through these triangles are different they are similar because they share the same interior angels.
2. Two triangles are similar if you can multiply the side lengths of one of the triangles into the other one
3. Two triangles are similar if two of the side lengths are the same algon with one of the angles.
4. Two triangles are similar if all of the side lengths are equal.
Project Reflection
Question: How do you think you have grown in your understanding of geometry?
Throughout the unit my understanding of geometry has depended, I see shapes in a new light. I have learned how to construct shapes and see how they interact with each other. With both virtual tools like desmos, and by hand on paper using a compassas or ruler. A compas is such and important tool in geometry because it can both make circles and measure distance. Now I understand shapes relationships with one another, their importance to each other and how they interact. I notice how geometry affects the world around me such as in buildings I am in or the nature that surrounds me. For example, seeing how bees used the most efficient shape, a hexagon to store their honey. Also how leaves maximized space to get the most sunlight using the fibonacci sequence. When we were constructing our final tessellations, I kept running into the problem of my compass and lines not matching up. This was quite frustrating to me because I wanted to get it perfect. Then I noticed that my measurements were a little off for my smaller flowers. After realizing this, it clicked in me that I should put the stabby part of my compass on the last line I made. It is important to preserve proper distance when making a tessellation to make sure everything lines up and tessellates correctly. This showed me that every shape affects the other in a tessellation.