Entry 4: week 5

The Fiestas 
     This week we had science two classes, and not a lot went on the first day, other than I flunked a test. Apparently, it isn't that difficult to miscount if you are under pressure. It's not that I didn't know how to convert the units it's just I got really panicky towards the end. However, the funny part is I did best on the stuff I thought I royally messed up on, that would be estimating/using powers of 10. I got only one wrong there, but on the super easy converting of like units and unlike units (i.e. metric to metric, standard to standard, and metric to standard) I only got three right. There was a small light at the end of the tunnel though, I can retest on that material and I know where I went wrong.
     On the same note of tests, we got our second test back on Tuesday. I did much better, getting all threes except on one standard. It had to do with identifying a directly proportional equation that was not linear. My first instinct was a linear equation, but the directions excluded that one, therefore I put an inversely proportional graph instead. In retrospect I now see how that is wrong, an inverse equation never even touches the axises and goes up down on one axis and up on the other, both of which contradict the definition of a proportional graph. The answers I could have put down could include a quadratic or exponential graph. The hard part of this mess of though was that both of these were in my notes and in my blog post from two weeks ago. I am kicking myself for not remembering that...

Pre-lab
On the second day we finally got out of our lecturing/discussion rut and did a lab. This lab was aimed at the relationship between the position of a buggy from a fixed point and how long it ran. We did however have an introduction to this concept on Tuesday. This was when our teacher kept having us explain were he was in relation to a fixed tile. From this we learned that a person can't just say "seven tiles from the counter", they have to give the distance the object moved, the direction it moved in, and it should be done in three different dimensions. It also showed that without a reference point it is very difficult to notice movement. Finally, the discussion also produced two definitions:

Reference point: A fixed object that is used to describe were another object is.

Position: Where an object is in relationship to the reference point and how the object moved, is oriented, and where the object is in relationship to other objects/space.

These definitions helped us in the lab that we did the next day.

The set-up

     In the lab that was done on Thursday we first had to measure how far a buggy traveled in a set amount of time in relationship to its starting position. Now, there was a lot of grey areas that the teacher let us to decide. For instance, how to measure the actual distance, where we measured on the car, how  many intervals of time we had, and how fast our buggy was going. Each of these factors were different from each group. For instance, while most groups used a piece of tape and premeasured the lengths my group decided to mark where the buggy was as it rode down the hallway. Another difference was the speed of the buggy. There was a pretty even split between the fast setting and the slow setting (I was in a slow group). The only thing that the class did consistently was measure the front of the buggy. We later found out though that we should have measured the back end. This is because every time the group had to mark the buggy's position we had to partially stop it which skewed our data.
        After the base line data was collected the next step was actually different from group to group. For instance, my group had to just redo the same experiment as mentioned above, but with the buggy going at top speed. Then there was another group who just had to alter the starting point.
    
The results
      At the end of the day we just put  the data on the whiteboards. This was extremely difficult for my group because we took a lot longer to just the equations. This is because instead of measuring the full length the buggy traveled we measured the distance from point to point. Therefore we had to convert those findings into an accumulative distance. In the end my group got an equation of y=6.4*x+.6 for the slow run. The equation above got an r squared value of .9999 and our five percent rule was .1%. This equation was also very consistent with other equations from other groups too. Then, on the fast test we got an equation of y=25*x+23.2. This had an r squared value of .9996 and a 5% rule of only 1%.  The only issue was that this test seemed to have been different from the other equations.
     In all the results from our version of the experiment seems really conclusive. The statement of  "if the buggy is going at a set speed then its position will increase proportionately" is supported a lot, however, all conclusions should be saved for after the whole class shares their findings.

Things that could be improved
We could try and improve how we actually measure the distance car went by using some high tech in order to eliminate the systematic error which was rampant throughout the experiment. A way to accomplish this is by having sensors that are synchronized with a timer mark how far the buggy ahs gone. We also might want to replace the batteries after each test in order to get the same amount of power from test to test. Finally, the path of the buggy should be fixed with the addition of some barriers.

 

Entry 3: week 4

Overview:
This week we expanded on the rest of our standards, which included estimating powers of ten, converting metric/non-metric units, and we did something that wasn't on our list, which was learn about dimensional analysis. We learned these concepts with lectures and some more white boarding.

The week in detail:
This week my hour was lucky because even though we switched days only once (because of some field trips) we still had science twice (the people who have science on B days has it only once). Now that's not to say that we caught up to those people. That was because the momentum that we gained last class was pretty much non-existent this time. That meant the first day was almost wasted by constant talking, which seemed to upset the teacher (not that I can blame him). Therefore he moved seats in the second class. This seems like it  really helped so far. The group I'm paired with also seems to be really good with understanding the concepts, we just need to come out of our shells and begin to talk. That was pretty much the last social change of the week.

Day 1:

During this day we again didn't really get all that much done. All we did was go over the non-metric stuff, that included pounds, grams, inches, and so forth. I learned very quickly that the metric system is the way to go. That is because with the English system there are very weird conversion rates that aren't constant and off the wall. For instance, two cups equals one pint, four pints equals one quart, and four quarts equals one gallon. Even though it was a little confusing, that wasn't the only problem that I personally had. Another issue that was only had to do with me was the fact that after a while I was convinced that I had the answer that I closed out all other theories and logic. However, that wasn't the worst the part. The worst was when I discovered that I confused the conversion rates. That was a very humiliating time for me and I hope I never shut our all logic that again.

Another thing that we learned was this thing called dimensional analysis. It is an easier way to organize our thoughts when it came to converting multiple/ unlike units. This method involved listing all of the units and conversion factors, canceling out some units, and multiplying all of the numbers together. This seems complicated but in actuality is was quite simple. I mean my math teacher in 6th grade already taught us this.

Day 2:
On this day there was of course the move, which I had been  looking forward to for a long time. In addition to that there was the standards which we learned. It was how to estimate things using the powers of ten. This lesson was slightly difficult especially when the numbers were extremely close to the half-way point. Some of the actual concepts we learned were that with powers of ten there is a large difference between the degrees, even one. For instance, 10 to the 2nd power is a hundred but 10 to the 3rd power is a thousand. This realization led to our next finding, which was that powers of ten must be ranges, especially when estimating. After that, we learned that the half way point for a power of ten isn't 5 but it is 3.16.... and just keeps of going. That took most of us by surprise.

After we learned how to estimate we had real world questions. For instance, "how many basketballs would fit in the gym"? We of course used dimensional analysis, conversion rates, and all of the other skills we learned yesterday, but there was a debate about how to measure the ball itself. One person suggested that we measure the sphere like it was in a box because that is how the balls would fit into the gym, but one kid said that that method would skew the data by "skimping out" on potential room for more basketballs in an already smaller room. The other suggestion was to actually calculate the volume and estimate it accordingly. However, a lot of kids forgot that formula, which was a problem. In the end we settled by saying that the person could choose whichever method they wanted as long as there was a range given.

General likes/dislikes
I personally liked how we went through all of the conversion rates and how we handled the estimating portions. However, it seemed to me that we again went a little slow for my taste. Another thing that I liked was again the moving of seats, I believe that will help my class stay on topic a lot more. After that, another couple of things I would like to change would be keeping the far fetched problems but do a couple of real world situations. In addition to that I would like to in cooperate the use of half powers too. That would have made the calculations much easier. Finally, I liked how the teacher said just run with the problem and good luck. He left it up to the class to decide how to do the problems.

Entry 3: week 4

Overview of the week:
Well this week was the week. We finally finished talking about all of our lab-o-rama labs. We did this by having only two groups white-board a particular lab. The progress of getting stuff done was also due to the fact that my class was actually able to focus on what they were doing, coupled with the fact that my teacher also set  some more boundaries it was inevitable. Lets just hope we can keep this up...

Specific views of the Labs:

The first lab was the pendulum lab. In that lab we had to find out the relationship of a pendulum's period (how long it takes to swing back and forth one time) and the mass on the pendulum. My first graph

suggested that no line would fit the data. However, that idea was challenged when two other groups found that a straight line going across the x axis fit that data extremely well. One culprit I can think of that effected my results was that I had used extremely small units on my Y axis and as a  result everything looked scattered, but the other groups did a much broader scale of .5 seconds instead of .1. That seemed to really help. Just this realization of what type of correlation took us a long time because we could not decide the name of the relationship. It turned out that there was no relationship. That led us to dicuss how many times we retsted the data, just because it seemed like something had to be wrong. Finally, we tried to come up with a 5% rule for that data but no conclusion was made.

Next, was the tile lab. In this lab we had to find the correlation of a piece of carpet's mass and its area. The discussion that took place in this lab was extremely difficult for me to participate in because my group did not get to that lab. This lab did however produce something interesting. One group had a polynomial graph and the other had a linear one. In addition to that issue, the group with the polynomial equation had a small outlier, that raised some questions. To find a solution we disscussed eaxh graph extensively, talking about the correlation coefficient, 5% rule, and common sense. Each correlation coefficient each was relatively close, 95% or higher, but the same could not be said for each group's 5% rule. Both groups had a high percentage, being within tenths of the cut off amount.
The linear result was however very slightly lower. The final nail in the polynomial vs. linear coffin came with common sense. My class did not expect a quadratic result, it didn't make sense that the mass would increase so sharply as time went on. It also didn't make sense for a negative amount of carpet (which is already impossible) to have the same mass as a physical piece of carpet. This lead us to the conclusion a of a linear correlation between the area and surface mass of the carpet.  The slope was .19 and the y-intercept was .18. As for the outlier in the polynomial group, that was said to be the result of rushing, which also could have caused them to have a polynomial.

Finally, there was my group's lab, the lever lab. In this lab we had to find the distance from the fulcrum that it would take for varying amounts of mass to balance 300 grams of mass 10 centimeters from the pivot point. This lab discussion was interesting because while my group got an exponential equation I got an inverse equation (this was in addition to the other groups findings which was also an inverse equation). This led to a bunch of discussions, the main one being "who was right". The reasoning for not using the power graph was 1: it wouldn't make sense for the distance to go up that fast, 2; the teacher said that there are very few equation in nature that are exponential, 3: the majority of the class got an inverse equation. Other factors that suppoted an inverse equation include the correlation coefficient on Wed, and common sense. Therefore, the general consensus was that the inverse equation was right. That isn't to say that there wasn't other topics that we talked about. Some include whether my equation was equivilant to the other inverse eqaution (the other group did thiers in inches, mine was in centimeters). It did however indeed match up. Then we discussed  a weird variable in power equation, e. It apparently is a number that appears in nature a lot and is like pi. Finally, we talked about what the end of an inverse line is called. It is called something like an assemetope (this is spelled phonetically because I do not have a spelling for it). We also learned the actual line of an inverse graph is called a hyperbola.

Other things we did.
After that we went over our first"fiesta" ,test,(I know I should have mentioned last week test but I had a bit of a brain fart). In the first test I did pretty well, getting all 2s or 3s, but I did learn a lot. For instance, after the first test I realized that I must make the variables specific to the situation. I also had clarification to the types of graphs there are, like a direct linear graph or an indirect graph (one goes up on both axises and the other has each axis go in different directions). These newly learned skills I took into the next fiesta, and as a result I think I finally got the other standards up to 3s. Finally, after the testing there was a PowerPoint on another standard we have to learn, and that was

conversions. For the most part it was all review, and that might be why I fell to the dark side and started to do stupid things like make towers with markers. That did however change when the teacher put up a measurement with the abbreviation of M. I was at such a loss, and started to panic a little. That is until he gave us the answer, which was that it stood for "mega". For me that was a new measurement and it was the equivalent of 1000 "kilos". That madness apparently went on higher, and that is something I know I must study before the next test.

Entry 2 week 3

What We did This Week.
This week was actually kind of slow. We didn't do any labs but went over one packet that we got last week. This was supposed to only take a day and a half, however, this ended up taking the whole week. This was mainly due to the fact that we could not for the life of us focus on the task at hand. The fact that we are left to our own devices at the beginning of class didn't help, or having some kids go off on random tangents (drawing winter in Hawaii for example) especially when there are few kids wanting order.

Day 1
On the first day it was a standard day, we got in, settled down after a long while and started to discuss the packet. I of course was very nervous because I hadn't fully understood the packet but tried to do it anyways. We discussed the topics in small groups with the people at our table, and from the looks of things, no one else understood what to do either. No one else even completed the packet. The only reason I even guessed was because I remembered some of the things from Algebra 1. This caused major confusion and some heads being butted. Like when the teacher said to talk about the characteristics of a directly proportional line and I said it must go through the origin, while one person disagreed. That was not fun. I believe the teacher could see this confusion because the next day all we did was talk about those equations and their characteristics.

Day 2

On day two the teacher decided to do a type of Socratic Circle, only with a few catches. For instance, there were two different circles and each of them were having a different conversation. One circle was actually talking and the other was communicating via a type of texting website. There were many problems that came with this. For instance, trying to picture the tables in our heads was impossible, trying to keep up with the conversation was difficult, trying to multi-task between texting and listening caused people to get lost, and trying to make connections/ comments about the things being said was just not possible (except in a few places). Although, the conversation that happened during this new experience suggested that most people had the same issue that I did, not understanding. Next is what the first group talked about. They were charged with explaining what would happen in the equation y=a/(bx^2) if each of the variables were doubled while the other two stayed constant. For instance changing a but leaving b and c the same. What they decided would happen is if a doubled so would y, if b doubled then the equation would be halved, and if x was doubled then it would be cut into fourths. The first group explained this in three ways, one was with math and logic, another involved using actual numbers, and finally there were people that just used common sense. The group that explained this stuff was very good because there were no real dominators, they also got the idea to use white boards to show the math, and there was even a girl that after every point explained the concept. Then there was my group. My group was tasked with explaining the equations y=kx, y=k/x, and y=k/x^2. However, instead of all of the wonderful things that the first group did we did the exact opposite. We moved fast and almost the whole conversation was ran by three people. We did however use white boards and tried to explain why did what we did (even though later we would discover that was wrong). Our findings was that the first equation would start at the origin and be linear, the second equation would be doubling, and the last equation would be decreasing by a factor of 4. It was a very confusing time for the whole class. We ended the day by explaining what directly proportional, inverse, direct, and indirect. These would be further explained the next day.

Day 3
On this day we would go even further into the parent equations of direct, indirect, inverse, and proportional functions along with there qualities. We decided that in order for a function to be proportional it would need to go through the origin and go up at a constant rate. We also discovered that this equation can also go under the category as a direct variation, however, this can not be reversed. In addition to those findings we also discovered that direct variation means that an equation goes up on both axis or down on both axis, this can be compared an indirect equation where each axis varies in which way it goes. We also discovered that direct/ indirect equations don't have to be just linear, they can inverse, quadratic, and exponential too. This was a huge change from what I originally thought.  Then with inverse we discovered that they will never touch an axis but each axis will be the inverse of the other, so instead of being divided by 3 the other would be times 3. However, these findings were after much debate and a lot of being off topic. We finally ended this day with creating white boards for the rest of the labs in the lab-o-rama. We however did not get to talk about them.


Final Thoughts
To begin with, I liked the fact that we did go so much into detail about these issues because for me it did clear up some of my questions. I also liked how it was run by the class and we ultimately created a set list of criteria for each of the graphs. Then, some of the things that could be improved upon is the having us stay on task more so. I also believe that the texting portion of the second day needs to either be really reformed or gotten rid of completely. Finally, I believe we could have had some more background information on the first day about the packet or maybe filled it in as we went through the week instead of having us try to do it before hand.