Questions from Mr. Fozi
Casino Night Project
How do casinos make money?
What is an expectation value?
How is it different from probability?
Casinos generally make money by charging the players more money than the expectation value. The expectation value of a game shows, on average, how much profit is gained or lost each time.
The casinos first find every possible event in a game. They then find the probability of each event happening. They then multiply the profit by each respective probability, giving them the expectation value of the game. This expectation value is different from the probability. The probability only tells the chance of something happening, while the expectation value factors in how much profit is gained or lost. To make money, casinos want to have players play games where they will generally lose money, and the casino profits.
Eden Architecture
What makes a livable house?
What are some patterns that you incorporated into your house to make it livable? How did you approach the problem of making a small house? What were the technical problems you had to overcome? What did you learn about three-dimensional thinking?
The main aspects that make a house "livable" is separate spaces for different purposes. For example, a space for sleeping, working, cooking, eating, etc. Another very important thing a house must have is ample living space. At the very minimum, a room's dimensions (length and width) should be be greater than that of a person's. Basically, a person should be able to lie on either side of a room and fit.
2 very important "patterns" that I used in my designed house were the rule of "Clustered Sleeping Spaces" and "Windows on 2 Sides". The former requires the sleeping quarters of a home to be close together in one general area, and the latter is self explanatory, requiring a room to have a window on 2 of its sides.
Making a small house was quite a challenge, especially when trying to implement these architectural patterns. One way to overcome this was to use as much space given, and be creative to find space for everything.
3 dimensional thinking as a very high hurdle to jump over. It was difficult to think in such a non-linear way, but after experimenting and constant trial and error, it became easier to gain the correct mindset.
Mole Project
Why do we need the concept of the mole?
What is a mole? Why do we use it in chemistry? How do we calculate the number of moles in a particular mass of atoms, or the mass of a number of atoms? What is stoichiometry?
The concept of the mole expresses the amount of molecules in a sample, rather than a sample's mass. This is useful to discover how much of a certain element is contained in a molecule.
The calculation of finding "the mole" of a molecule is very straightforward.
1 mole = 6.022 x 10^23
[insert picture of Mole Island]
The practice and study of these conversions is referred to as "stochiometry".
In General
How do you think your skills as a learner of math and science have improved? What have you done to prepare yourself for learning Math III and Biology next year?
Overall, I've noticed my understanding of Math and Science has increased significantly. Projects and labs have challenged me especially to encourage critical thinking and learning from experience.
To prepare myself for next year's courses, I hope to take more challenge options to broaden my knowledge overall. This will help me create better quality, well thought out work that will be up to my teacher's, and my own, standards.
Dear Mr.Fozi - tPOL Questions and Answers
Reactions and Collisions Lab Pt. 3
1) Is energy gained or lost by the molecules? Which molecules have more energy, the reactants or the products?
During the reaction, energy is gained by the products. Thus, the products (after) have more energy than the reactants (before).
2) Predict what will happen when 50 A’s are added to the box and 50 BC’s are added.
I predict that the BC's will create several collisions with the A's, changing the number of each periodically.
3) In the box labeled “current amounts,” enter 50 for A and 50 for BC.
4) Was your prediction correct? Describe and explain any differences.
Though there were reactions between the two, not all of them reacted the same; only a fraction created effective collisions.
5) Predict what will happen when the temperature is raised so it is NOT above the activation energy max but IS above the energy level of the products.
Due to the raised temperature, the molecules will move much quicker. The faster movement will possibly cause more reactions and effective collisions to occur.
6) Raise the temperature as described. Did your prediction come true? Describe and explain any differences.
Again, faster movement, more reactions, but only a fraction of them.
7) Predict what will happen when the temperature is raised so it is above the activation energy max.
The temperature will be even higher, meaning a potentially higher rate of reaction due to the faster movement.
8) Raise the temperature as described. Again, was your prediction correct? Describe and explain any differences.
The molecules did in fact move quicker, and there were more effective collisions.
9) What did you notice about the rate at which reactants/products fluctuated between the three different temperatures? If you didn’t notice anything, hit “reset all” and test it again.
The amounts of each varied by very little (mostly by 1) and change much more often when the temperature was increased.
10) Did temperature affect equilibrium position? Did it affect it in the way you expected? Explain.
Higher temperature caused a closer equilibrium, while a lower temperature offset the equilibrium slightly.
11) Did temperature affect reaction rate? Did it affect it in the way you expected? Explain.
As aforementioned, higher temperature causes faster molecule movement, and I predicted that the faster movement will cause more frequent reactions.
Reactions and Collisions Lab Pt. 2
a. Predict what will happen to the rate of the reaction for each variable: increased temperature, decreased temperature, increased concentration (number of particles), decreased concentration (number of particles). Explain your predictions in terms of effective collisions.
Increased temperature: Increasing the temperature will cause the Reactants to move quicker, which will allow more effective reactions.
Decreased temperature: Decreasing the temperature will make the Reactants move slower, causing less effective reactions.
Decreased concentration: Increasing the concentration (less reactants) will provide a lesser probability of collisions, causing less effective reactions.
b. Test your prediction with the simulation and record observations.
c. Explain your observations. Were all of your predictions correct? Which tests changed your thinking about reaction rates? How did the simulation change your prediction?
Our predictions were correct, though the high speed and movement on some tests proved difficult to determine.
Reactions and Collisions Lab Pt. 1
1. See if you can reproduce each of the scenarios from the pre-lab. What did you have to do to make each unsuccessful collision happen? What did you have to do to make an effective collision happen?
To create an unsuccessful reaction, we used the Angled Shooter to shoot away from the second reactant. This caused Reactant A to completely miss Reactant B, causing an unsuccessful reaction. To create an effective collision, we used the straight shooter, shooting Reactant A directly into Reactant B with the most force possible.
2. Use the “design your own reaction” tab to change the energy levels of the “before” and “after” molecules. You can create a huge potential energy hump to represent a particularly difficult reaction. Where do you need to move the “total energy” to create an effective collision?
The total energy can be anywhere, as long as you shoot the first reactant hard enough to cause an effective reaction.
3. What is the effect of raising or lowering the temperature? The effect of raising the temperature will become clearer as you make the “potential energy hump” bigger. The effect of lowering the temperature will become clear if you choose the fourth reaction from the list on the right.
When the temperature is lowered (colder), the reactants move slower.
When the temperature is raised (warmer), the reactants move faster.
Reactions and Collisions Pre-Lab
1. A reaction did not occur between Reactant A and B in scenario 1. For a reaction to occur, the atoms or molecules must collide and hit each other. In scenario 1, there was no contact between the two reactants.
2. In scenario 2, a reaction did occur between the two reactants. It was a minor reaction, for the two reactants did not hit each other, and didn't make much contact.
3. In scenario 3, a similar reaction to scenario 2 occurred. The two reactants did not collide with much force, but they did make contact.
4. In scenario 4, a large, effective reaction occurred. The two reactants collided with a great amount of force and created a larger reaction.
5. The term "effective collision" probably refers to a reaction between two reactants where the reactants collide with a great amount of force, creating a large reaction.
6. Collision theory states that a reaction is most likely to occur if the two reactants collide with each other with generally large amounts of force, hitting each other almost directly/head-on.
7. An infant cannibalistic vampire shark with a lazer on it's head is being catapulted over a crystal mountain at 130 miles per hour. On the other side a Peter was being catapulted at exactly the same speed.They meet at the peek of the mountain and morphed into an infant cannibalistic vampire Peter shark with lazers on his head, *giggle*
Student Led Comments - Science/Humanities
Dear Mr. Fozi and Miss Fisk,
This year has been amazing.
-John Torres
The Presentation of Learning Series: 2008-09
"Pieces of Me: Rose Colored Glasses"
"Short Film: The Chocolate Man"
Find more videos like this on High Tech High
"The Walter Filter"
"The Molecule Project: Capsaicin"
Ratios! (from Personal Space Assistance Review)
Mr. Fozi assigned us a series of questions to answer based on the surface area, volumes, and ratios between the two of cubes and spheres, from Mr Fozi's DP.
MC Escher Project: Reflection Time
M.C. Escher (Maurits Cornelis) was born on June 17, 1898 in the Dutch province of Friesland. Later, Escher moved to Haarlem, studying architecture and decorative arts. After a short time in the city, he later acquainted with Jessurun de Mesquita, an artists that encouraged Escher's art. M.C. Escher is most famous for his intricately detailed tessellations, in addition to his numerous paintings, many of them physically impossible. For example, the Impossible Triangle, which he popularized, not created, or the Inifinite Staircase/
To create my own rendition of M.C. Escher's tessellations, my initial shape to begin with was a SQUARE. I was out of ideas, and the shape suggested to me was a giraffe. After several trials and errors, I ended up wit the shape as shown. The cuts made are shown in the diagram.
As my medium for this project, I decided to use a computer, creating my tessellation digitally, as opposed to using paper in the analog fashion. I chose to use Sketchup and Photoshop to create it. The reason I went Computer over paper is because Sketchup/Photoshop objects can be much more easily manipulated and created, without any waste in materials. If I were to use paper, cutting would be a permanent choice, and could not be undone. If I were to make a mistake, or wish to change my design, I would need several pieces of paper, wasting many resources.
In terms of Geometry, I learned much from this project. It taught me how different shapes, based on their angles/measurements, tessellate, and why others don't.
To a new Geometry student, I would first and foremost tell them to go Digital over Analog. The reasons why digital is better are previously mentioned. I would also tell them how important saving your work is, because it only takes one crash to lose a lifetime's worth of work.
Emulating Escher: Project overview
The Emulating Escher project project is a project based on creating tesselations, in the manner of M.C. Escher. By learning about geometry and the different shape transformations, we were able to replicate what M.C. Escher is most known for.
M.C. Escher (Maurits Cornelis) was born on June 17, 1898 in the Dutch province of Friesland. Later, Escher moved to Haarlem, studying architecture and decorative arts. After a short time in the city, he later acquainted with Jessurun de Mesquita, an artists that encouraged Escher's art. M.C. Escher is most famous for his intricately detailed tessellations, in addition to his numerous paintings, many of them physically impossible. For example, the Impossible Triangle, which he popularized, not created, or the Inifinite Staircase/
To create my own rendition of M.C. Escher's tessellations, my initial shape to begin with was a SQUARE. I was out of ideas, and the shape suggested to me was a giraffe. After several trials and errors, I ended up wit the shape as shown. The cuts made are shown in the diagram.
As my medium for this project, I decided to use a computer, creating my tessellation digitally, as opposed to using paper in the analog fashion. I chose to use Sketchup and Photoshop to create it. The reason I went Computer over paper is because Sketchup/Photoshop objects can be much more easily manipulated and created, without any waste in materials. If I were to use paper, cutting would be a permanent choice, and could not be undone. If I were to make a mistake, or wish to change my design, I would need several pieces of paper, wasting many resources.
In terms of Geometry, I learned much from this project. It taught me how different shapes, based on their angles/measurements, tessellate, and why others don't.
To a new Geometry student, I would first and foremost tell them to go Digital over Analog. The reasons why digital is better are previously mentioned. I would also tell them how important saving your work is, because it only takes one crash to lose a lifetime's worth of work.
Barbie Bungie Jump REVIEW
On the 3rd day of the Barbie Bungie Jump activity, we were to review a partner's DP and its contents. We are to critique it, and fulfill Mr. Fozi's checklist:http://wp.nc.hightechhigh.org/vfozi/2008/10/22/barbie-bungee-jump-day-3/
I decided to review Gabby's DP: http://wp.nc.hightechhigh.org/golivas/2008/10/21/barbie-bungee-jumpday2/
I was able to clearly understand the information provided on Gabby's digital portfolio.
Checklist:
-All the points are on the same graph
-The rubber bands are correctly represented on the x-axis
-The distance traveled is on the y-axis
-I was able to clearly understand the purpose of the x ad y axes.
-The slope IS between 10-40cm. [21.17 to be exact]
-And finally, you were able to solve the linear equation using the 400cm rubber bands problem.
What I learned
In this project, I was able to learn how to use equations to figure out situations on a bigger scale. Let me reiterate; we were to find the equation for our data. It was at a small scale - the barbie was dropped only a few feet up. But using the equation, we were able to find out how many rubber bands are needed to safely launch Barbie from 400 cm. It is a very handy skill to learn, and this project really helped in the learning process.
Overall, this was a very good project that helped me learn things I've never known before. Woo! Enlightenment!
The Barbie Bungee Jump
Explanation of the experimental procedure
1. The first step of this activity is to attach different amounts of rubber bands to the Barbie (or Ken doll) in bungee-jump fashion. First, attach 2 rubber bands, then 4, 6, 8, and 10.
2. The doll was dropped from a certain marked point.
3. Once the doll is dropped, the group was to find the lowest point the doll reaches when dropped.
This scatter plot shows the results of the experiment.
In this diagram, the y-axis represents the distance the doll traveled from its initial point (in centimeters).
The r-value shown (.99) is a representation of how close the line-of-best-fit is to the actual points. The line of best fit is a straight line that is as close to all the plots on a graph as possible. The closer the r-value is to 1, the closer the line of best fit is to the plotted points.
The slope of this equation is as follows: y=21.17x + 33.27
Predict the number of rubber bands needed for Barbie to jump from a height of 400 cm.
To answer this question, simply input 400 cm into the y of the equation, because the y value represents how high the drop is.
Once completed, the answer I've come with is about 17 rubber bands.
This means that Barbie can safely bungie jump with 17 rubber bands from a height of 400 cm.
