Math Blog #3

Before the Experiments

The day of the Bungee Jumping experiments was finally here. My group and I were nervous, yet we were confident about our equations. We first began class when Ms. Ange told us each to tell our equations and how we got it. Every group except us, had about the same numbers and the same structure of equation. When we came to our equation, which was not only in inches, but different than the others, everyone was curious to find out how we came to these conclusions. Our first equation was  RB = ((h - 12) / 8) -2. We got this by pure logic. H represented the height of wherever we were going to throw it off. The number 12 was how tall our barbie was, and we subtracted that by the height. We then divided it by 8, the amount the rubber bands stretched, and subtracted that all by two. We subtracted it all by two because after multiple experiments we noticed that out rubber band wrapped around our barbie's leg wasn't tight (we always wrapped it 6 times around), so a part of it stretched too. Therefore we came to our random equation, that was actually reliable. Our second equation was y = .11x - 2.3.  We got this as everyone else did - we found a slope, found two points, then created an equation. Ours was different then others, because as I said before, ours was in inches rather than in centimeters. Furthermore, Ms. Ange was curious to know how we had two equations that weren't equal to each other. We weren't sure how to explain this, but all we knew was that every time we plugged a number into each of the equations, it would come out with the approximately the same answer. I say approximately because when we plug a number in, the answer isn't usually a whole number. It has many decimals, and when we plug a number into both of these equations, the decimals are slightly different. But this is okay because whether we round up or down (because we cant have .25 of a rubber band) it comes up to the same whole number.

Experiment #1

Afterwards we began conducting the experiments. We first went down to the lower school near the playground. The height was fairly small, which didn't seem very difficult. The total height was 104 inches. We then plugged it into both of our equations and came up with our final rubber band amount - 9 rubber bands. We were the first to volunteer, so everyone's eyes were on us. Will and I have always been pushing and holding the Barbie, so we were the ones up on the ledge while Lauren was recording. We pushed our Barbie off, and it didn't hit the ground, in fact it was very close to it. Furthermore, we tried it a second time, because we had the time, and the Barbie came even closer to the ground which was great. Other groups went, and succeeded as well, and all I could think about was how amazing this was. We all came up with such different equations yet we all got the same amount of rubber bands.

Attempt #2

Attempt #1

Experiment #2

We then continued to our next height which was near the lower school as well. It was off the third story. Everyone seemed to be nervous for this one because it was such a high height. The total height was 224.5 inches. We then plugged it into our equation and we were very surprised. Both of our equations had different answers. For example, for one of our equations the solution was about 26 rubber bands, while the other one came to about 22-23. We didn't know what to do at first, but we decided to go with the 22 rubber bands because it was better to be safe than sorry. We went up first, again, and stood on the ledge hoping that it will work. We dropped the barbie off the balcony and it did not hit. Unfortunately our first try was a bit far from the ground, so Will and I wanted to try something different - we wanted to throw the Barbie. On the second time Will tossed the barbie down, and we were informed that it was very close to the ground. We were very surprised by this turn, and we were very happy. Because of our equations, we were still surprised though. We came up with the solution that our first equation that we came up with was only useful with small heights. This is because when we were testing it out, we only tested with smaller heights - we never exceeded 15 feet.

Attempt #2

Attempt #1

Experiment #3

We then went onto our 3rd place, since we still had time. This was located up in the art center where we would throw the barbie off to the floor below. This was definitely much higher than anything we did before, but we weren't scared. We knew that we could do it. The total height was 324 inches. We plugged it into our equation, but this time only in the second one. We then added the amount of rubber bands which was about 33. We went third this time, as we eagerly ran up the stairs. Me, being afraid of heights, was shaking while holding the rubber bands when Will was about to drop it; I was so terrified of looking down. Will then dropped our Barbie and it was very close to the ground. We were really happy about this, and then we tried it a second time. We then slightly tossed it off again and it once again almost hit the floor, but not quite.

Attempt #1

Attempt #2

Conclusion

We were overall really happy with our project. I think that we had a lot of problems within our group but in the end we worked together to make this project fun and a learning experience. If I were to work on this project again I would definitely put more work into it, because I know that would've really helped our group a lot more. I would definitely take it more seriously, because it wasn't a good feeling to leave it until the day before the experiments. Furthermore, I think the one thing that didn't work with our group was that we didn't come up with an exact plan. While everyone was out experimenting, we were inside looking for exact measurements, which didn't help us in the end. What did help us was finding the amount of rubber bands for higher places. In the future, I would definitely want to do this project again because I thought it was really fun and suspenseful.

Math Blog Post

This Class
Today, we worked on finalizing our equation and testing higher heights. In the beginning of the class we worked on at what point the third rubber band would hit. We stacked more books on top of where the rubber band #2 hit (Book 7) and used a trial and error method. We came up with a conclusion then established an equation for it. Our equation may not be fully correct but it's still something. Our equation was RB = (h - 12) / 8 then all of that subtracted by two. We then went outside and tested heights that were much larger than a couple of books on a desk. We tested out our equation, but then we realized that we missed a component so we added to the equation (the minus two) . Furthermore, we tried only two heights yet with the new equation it worked fine, though we still need to finalize.

Our Big Find
The equation that we established as the final equation was a large finding for us. It worked really well, and we are proud of it. Though we do need to test it a few more times, it is allowing the barbie to reach very close to the ground without touching it which is great.

Our problem
I think this class we didn't work as efficiently as we could've. All the other groups were working hard and going outside while we were still in the same position as the last class, which isn't good. The overall group dynamic of our groups isn't working, which is strange because each of us are friends. I think because we aren't ready, therefore I will stay after school on Tuesday to finalize our project, and hopefully it will work better. 

Next Class
Regarding next class, I am very nervous. I don't believe my group is ready to do such a large task, especially since it is a summative assessment. As I said before I will stay after school to fix it and finalize it. I do believe over the days that we worked on this project, if we worked better we wouldn't have been in this situation, but you cannot go back in time. You have to move and try to do the best you can.

This is a trial we did in the classroom.

UPDATE - After School Lauren, Will, and I stayed after school because we felt as if we were very behind on our project. We got our barbie and many rubber bands and went to Mr. Oksness's class since he had tape measurers. When we got there we didn't find him, but we found another group that had a tape measure. While we were waiting, Lauren was problem solving different ways of coming up with an equation, while making a data table. During Lauren was doing this, Will and I were testing out our previous equation with different heights in the classroom. Each time (we did about 3 trials), the older equation would work. Lauren then found a new pattern through her work and developed the idea to make a new equation. We tried it many times but the answer would change every time we added a new number. We were only using two of the trials we did, when we should've plugged in more. It was definitely an unreliable equation that we would never use. We talked to other people from other groups, and they said they found their equation by creating a linear function. We then added more of our trials into a graphing calculator, and came to an equation. At first, we thought it wouldn't work but after trying it multiple times it worked perfectly. The new equation was y = .11x - 2.3. Therefore we had two different equations that worked perfectly. I am feeling so much better about this project and I cannot wait to show off our barbie tomorrow in class!

These are two trials that we did at the same place. I believe one of them hit the ground, while the other was very close to hitting it. 

Barbie Bungee Jumping Task

Introduction
In the last few weeks of school we are working on a task called Barbie Bungee Jumping. In this task we are seeing how much rubber bands are needed from a certain amount of height, and coming up with a conclusion. Then in one of the last few classes she will tell us to throw the barbie off a certain height, and we need to adapt to it. My group consists of three other people: Will, Lauren, and Ian. I believe we all have strengths that when combined will be really good.

What we did
We started out by finding the height of the desk and seeing if one or two rubber bands would work. Only one rubber band worked, so then we tried to make it higher. Then, we found out the height of a math book and see if there are any changes to the results, there wasn't. Then we added two books, three books, etc. Each book was a small amount which will be a good thing once we come up with our equation. We ended up finding a difference between when the rubber bands would touch and tried to come up with a solution, though I don't believe we have.

Consistencies
We tried each of the stages multiple times to ensure we have an accurate results. To be consistent we have decided to keep the barbie doll's hand down. This is because we don't want to take any chances with it touching the ground. Furthermore, when making a table we did not count the rubber band tied around the doll's feet because we didn't believe it contributed a great amount, plus we need to be repetitive.

What we found
We have found out that even an inch of extra inch will make a difference. Between book 7 and 6 there are a few inches different, yet the three rubber bands work on book 7, while it doesn't work on Book 6. Book 6 was the point where the switch off between two rubber bands, to three. Our next step is to see when one rubber band doesn't work. We also found out that working together is much better, since I believe that in the beginning of the class we weren't communicating. Furthermore when we came up with what we were going to do we got a lot of work done.

What we will do 
Though we worked slowly, I believe we did achieve a lot, and we did find out a lot of things in our research. I believe that for the next class we should begin testing out our theories with larger heights rather than a few feet. We have not found a pattern yet, so we must try to look at our data and analyze it. Also, we should construct a graph with all of our findings and see if there are any patterns. Additionally, I do believe we should also try to come up with a formula because it would help us immensely.

This video is one of our trials in slow motion. As you can see the barbie hit the floor, which means that the amount of rubber bands was more than needed. 

These two pictures represent how we organized our data as well as what we did last class. 

Stacking Cups

Stacking Cups - Act 1 from Mr.Stadel on Vimeo.


For this activity we had to figure out many things.

Questions

When does the white cup pass the blue? When are both the blue and white cups equal? What is an equation for this scenario?

What We Did

My group and I tried many methods but we almost immediately found out how to do it. We needed to multiply the amount of cups to the excess amount that would be left on each of the cups, subtracted by one. This is because on the first cup the amount of excess was already included in the height, therefore it was unnecessary to add it in. For the white cup (which has a smaller height) we were given the dimensions 9.2 for the height. The excess amount of 'cup' would be 1.3. For the blue cup the height was 12.1 while the excess amount was .8.

Formula 

The equation that we came up with was R(N-1)+H.

R = Rim
N = Number of cups
H = Height

Conclusion

After we came up with the equation, everything else became simple. We began guessing and checking and we finally came up to a conclusion. The cups will become equal at 7 cups each. The white cup will then pass the blue cup at 8 cups.

Banking Blog Post

Bank Policy 
In the past few math classes we have been learning about bank accounts. Traditionally, there are two bank accounts: Checking and savings account. There are also other special accounts that bank offer as a 'super saver'. Within these banks there are two different interests, compound and simple. A compounded interest is when the interest rate is constantly being added on to a new amount.  On the other hand, there is simple interest where the interest rate is constantly added onto the original amount.

Compound vs. Simple
In my opinion, I think compounded interest is a lot better, but in some scenarios simple interest can be a bit better. For example, we watched a video where a man who lived for a thousand years wanted to check  on his bank account. He originally had 20 cents, but with an interest of 2.25% it grew to a larger amount. We weren't told of the new amount, and we had to figure it between ourselves. We originally found the simple interest amount which turned out to be $20. We thought this was a bit low, so we then tried the compounded interest. We then calculated the compounded interest and found that amount was around $4,000,000,000 dollars. There is a huge difference between these two and though, we don't leave our money in the bank for thousands of years, I believe it would still make a difference. Furthermore, I believe that if I were to invest in a bank, I would want to have a compounded interest, as well as a high rate. Moreover, I would also like to keep about a thousand dollars in the bank for emergencies and never touch it. As the years go by, it will grow to a larger amount, which will benefit me.

Citations 
Fox in Flats. "Piggy Bank - Fox In Flats." Fox In Flats RSS. N.p., n.d. Web. 29 Sept. 2014.

Finding the midpoint

We viewed a video about 4 boys who drew two points, and a point in the middle. After that, we had to guess which person had the closest point in the middle. Furthermore, we had to back up these facts with why. I thought it was Chris because I thought his looked a lot more accurate, while the others were less precise.

This is Chris's guess, except without the coordinates. (It comes later) 

In the beginning, if I would want to know the exact midpoint of each one, and who got the closest I would need to know a lot of things. I would want to know the coordinates of each point, and want to measure the distance between each point with a formula. After, we talked about which one would be closest to the middle and why. I was the only person who guessed Chris, and when asked why, I just said that it looked that way. Someone then contradicted me by saying that his was too spread out, and I agreed. 

Afterwards, Ms. Ange showed us the exact coordinates, angles, and lengths, and we had to figure out a way to find the exact midpoint. My first reaction was to look at each information given and just guess to see which one was most accurate. For example, which one had the straightest angle, and which measurements were the most even. Then, when we had access to the internet, I decided to find the midpoint formula, and plug each person's lengths into it. I would then compare and subtract the guess and the actual midpoints, and see which ones were the most accurate. I found that Andrew's and Nathan's were both equally accurate. 

Math Reflection

This year we worked with a system called Acceleration Math. Acceleration Math helped us with our math skills online, at our own pace. If you didn't understand something accelerated math would provide methods and videos that help you. You would complete enough problems to show you understand the objectives and then they are put on a test. You can only print out a test if you have 5 objectives. The test is on paper and you cannot use anything on the internet to complete the tests. You can ask Mr. Swartz for help but you cannot ask the internet. Once you finish the test you scan it and see how much objectives you mastered. The maximum you can get is 5 objectives mastered, but sometimes you only get four.

As you can see I reached the goal of 35 objectives this semester. I am really proud because I finished these objectives in a span of two weeks. Usually its over the span of six, so I was far ahead everyone else. Because I finished acceleration math I understood some lessons before others did as well. I could also work on other subjects without thinking about accelerated math. I actually enjoyed accelerated math because it helped me understand math in a new level. It was also at my pace so it really helped if I wanted a challenge or if I didn't understand something. I actually prefer Acceleration Math over the traditional way because it suits your needs. If you are a better student then the others in class, you can learn more challenging subject, and if you are struggling with some lessons, it will go at the pace you want it.

Math Reflection

This above shows my accelerated math score. Accelerated math has always been hard for me, especially since we had a due date for 40 objectives, and I was always trying my best to be one of the the tops tens. Accelerated Math is a program in which allows you to go on the pace you want, but still has the same problems as other. So for example lets say you do a practice and you get all of them right except you get 3 wrong in one certain area, it gives you those problems on the next practice, to make sure you fully  understand them before you get a test. To get a test you need to have 5 objectives that you have done well on. On the test, you cannot use any source except your calculator or a peer, which is difficult because sometimes you would want to ask your teacher, or look it up on Google. If you do well on the test, and you get no more than 2 wrong, then you get 5 objectives mastered. For our class, you would need 40, so then after you would get 5 you would need 35 more. So as you can see, you would always want 5 so it would be even. So let's say you have 34 objectives mastered you would need 2 more test to complete the goal set out for you.


As you can see, this is a very hard experience. Not only does it take up a lot of your time, it also causes stress onto you, since you have other classes. But actually, I really liked this. It really helped me do better on my tests, and I learned a bunch of new things, and I am so glad that I have. Once, my mom needed help with a problem she saw, and I knew how to do it, and I could tell she was surprised. Furthermore, I would love to do this experience again because it has taught me to be responsible, and risk-taking.