Dear Mr.Fozi - tPOL Questions and Answers

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.