Homework 20. Assigned 12.4. Due 12.7
1) Analyze the expected value of your powerball ticket. You can find the information at: http://www.powerball.com/powerball/pb_prizes.asp.
2) Design two games. One of them should have an Expected Value that is in favor of the house (the non-player). Another should have an Expected Value that is in favor of the player. These two should be presented in a way where it is difficult to tell the difference. If these games need any tokens, dice, cards, whatever, you should bring them to class for Thursday. If you need me to, let me know by Wednesday.
3) Choose one game of chance (there can be choices, but in the end it should be determined by something created by chance, otherwise we are entering a different territory here) from somewhere. Analyze it completely, finding a probability model as well as the expected value. Be prepared to discuss this game not just with your group but with me as well if I get to choose you.
Homework 19: Assigned 11.30. Due 12.4
http://korthalsaltes.com/ <-- go to this site and make a 3D object. Make one that's neat, and nice, and clean, and fits your overall mood. Don't forget to start on the final.
Homework 18: Assigned 11.27. Due 11.30
In our folder, I have placed three papers. You should read, analyze, think and justify your way through one of the three papers according to the outline below:
1. Easiest: "Tiling A Checkerboard". You should be able to make it through this one completely, including figuring out how the proofs shown work. How do the pictures and words come together? There's some fun stuff in here.
2. Medium: "Self Tiling Sets". The ideas here start out simple -- a set of object that can form into themselves. But it get some complicated from there -- what if those sets can also form other sets? What if that blossoms out? You should work your way through to at least the section labeled "Beyond Polyforms." You may stop there if you desire.
3. Hardest: "Kepler Tilings". This one is very rich, very deep, and very long. Also amazingly beautiful. Lays out many of the basic ideas for what a tiling problem is, how one might approach it, and some of the terminology that has been created in order to talk about such things.
Homework 17: Assigned 11.16. Due 11.20
In our google folder there is a trigonometry word problems sheet using the law of sines or the law of cosines. The .pdf is "trig.laws.pdf." Do problems:
p. 415: 28, 29 (look up any words you need to),
p. 422: 39 (it asks for bearings, but just give me the angles inside), 43, 44
p. 423: 47
Homework 16: Assigned 11.13. Due 11.16
In our google folder there is a trigonometry word problems sheet using the law of sines or the law of cosines. The .pdf is "trig.laws.pdf." Do problems:
p. 415: 30, 32, 33
p. 422: 38, 40
p. 423: 48
Homework 15: Assigned 11.09. Due 11.13
1. Do "Trig both directions with answers". If you got them all correct, you can stop here.
2. If not, there is more practice under "Solving Triangles".
Homework 14: Assigned 11.06. Due 11.09
1. Create three problems -- one linear, one quadratic, one exponential. Email these to me by Thursday morning so I can pull some of them together for another round of these. The questions should require building a model (an equation) or using an equation that fairly accurately describes a real life situation. You should provide answers with these when you turn them in. The answers should be clear, concise, and written in a way others can follow your work.
2. Do the problems in our shared folder -- exponent_word.pdf
3. If you're working towards understanding of logarithms, use https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions to deepen your understanding. Feel free to get back at me with any questions or areas of concern.
Homework 13: Assigned 10.30. Due 11.06
Finish "11 Questions Bennington"
Homework 12: Assigned 10.26. Due 10.30
Find the sheet in our folder called 'Exponential HW.' Do the sheet in our folder called 'Exponential HW.'
Midterm Assignment Assigned 10.16. Due 10.26:
In your assignment folder. Due 10.26.2017. Please make sure your work is clean, neat, and easy to read. Make sure I can follow your reasoning.
Homework 11: Assigned 10.16. Due 10.19
1. Glastonbury Mountain is just off to the east from here. There used to be a lot of people who lived there, but now it is mostly abandoned and part of the Bennington Triangle. Teenagers go up there, hang out and generally try to scare each other. But things are changing--people are moving in. Three families, in fact. They know each other well and are willing to share in some basic needs.
There are three houses. Call them A, B, and C.
These houses each need water coming from the well (W).
These houses each need electricity from the generator (G)
These houses each need propane from the shared Propane Tank (P)
You have plenty of piping for all of these different needs (W, G, and P), but there are some issues:
because you are on rocky ground, you cannot bury the pipes
none of the pipes can overlap
each person needs their own pipes from each utility directly to their house
This means that there are three different pipes from the Well that cannot overlap. These pipes also cannot overlap the three separate pipes from Propane, or the generator.
This family is depending on YOU to design the system for their utility needs. Design it in the best fashion--you may place the six objects wherever you want and make the pipes as convoluted as needed.
If, for some reason, you are not capable of accomplishing this task, dig into the reasons why. Attempt to come up with a reason that you are unsuccessful. A good, rational, clear reason.
Homework 10: Assigned 10.12. Due 10.16
0. Relook at the three questions you did on Homework 9. Try our process:
use specific numbers
create a general formula
what's our input/what's our output?
find an answer to at least one more question than you had previously.
1. We started on four questions in class (on the sheet "Class 10.12.2017"). Do as many as you can, in a way that you could explain them to other people. Question 4 is optional, but fun.
2. One person at Bennington came back from long weekend with a terrible cold. They share it with two people. Those people each share it with two other people. Each of these 'Shares' we will consider a generation.
At what generation will everyone have had the terrible cold?
How many generations until all of Vermont has had the cold?
How about the entire WORLD?
3. If we take an integer and square it, what are all possible results for the ones place? Can you convince me of that fact?
(for example, we square 11 ... 11^2 = 121 ... so the ones digit is 1)
(if we square 14 ... 14^2 = 196 ... so the ones digit is 6)
Homework 9: Assigned 10.09. Due 10.12
0. Finish any problems we didn't get to on the Quadratics Questions Page.
1. In the shared documents folder, there is a sheet labeled 'three questions'. Do those -- and for each one you have trouble with, document your process, what you tried and where you went with the problems. What model can you use? What pictures can you draw? What examples can you try? Do not passively look at the problem; attack it from myriad angles. You got this.
2. This is you: http://abstrusegoose.com/353
Homework 8: Assigned 10.02. Due 10.05
0. Type up and send me the linear programming question you made up.
1. The page we started in class was called domain.range.pdf. On the first page of that, complete questions 4 - 9.
2. Functions_Relations.pdf. Starting on page 3, do questions 1 - 16.
Assignment 1. Assigned 09.28. Due 10.05
note -- don't forget about the other homework, below.
In our folder, there is a .pdf entitled 2017 Assignment One. All of these questions should be answered and turned in to me by no later than MIDNIGHT, OCTOBER 05. You may work with others, but please be sure that whatever you turn is is something you can call your own.
You must turn them in via email. All pieces need to be legible (and the easier they are to read, the better).
Any questions? email me and let me know.
Homework 7: Assigned 09.28. Due 10.02
1. Do the linear programming questions 3, 6, and 7 from the packet we started in class.
2. Come up with a linear programming question of your own. This question should have several constraints and a 'best solution'. Try to make it applicable to an actual situation in your life. If you are still stuck on this, email me on Sunday, and I can help you come up with a scenario.
3. Check out this Khan work on Inequalities. It's pretty awesome and should point out any places you're having issues. Do the work you need to do in order to feel like you've 'got it' with inequalities.
Homework 6: Assigned 09.25. Due 09.28
1. There is a sheet called 'systems of equations' in our google folder. These are old school problems, with just the equations, and I ask you to find the solution that works for both. This may be easy, this may be difficult -- I'm trying to dredge up old memories of how we tackle these, and what we can do.
2. there's also a sheet called 'extra parametrics'. Tackle those as well.
Homework 5: Assigned 09.21. Due 09.25
1. Finish the questions on 'Problems for Class 4". Be sure to talk to others.
2. Can you figure out a way to win at the game we learned at the end of class? Play with people in the class, out of the class, whatever. Come up with strategies. See if you can come to class and beat me on Monday. In addition, think about (and try) writing down what strategic facts, ideas, thoughts you have about how to play this game.
Homework 4: Assigned 09.18. Due 09.21
1. Find someone else in the class to do the rest of the HW questions with. They are in our folder, aptly labeled Class 4 HW.
Homework 3: Assigned 09.14. Due 09.18
1. Is it possible for a positive numbers to exceed its reciprocal by exactly 1? For example -- one that comes close is 8/5. 8/5 - 5/8 is 39/40. That's pretty close to 1 ... but are there any fractions that come closer?
2. Keep working on the literal equations sheet that we started in class. The answers are attached; do as many or as few as you feel appropriate to your need and situation in life, knowing that you will have some of these on your take home assignment next week. If you need more, please let me know.
3. Make sure you are comfortable with fractions in their various forms and what to do with them. A good source for that material is here:
https://www.khanacademy.org/math/arithmetic-home/arith-review-fractions . Do the practice, or watch the video, or get yourself in a place where you can do these do these do these. Many of you have asked for the repeated iteration of work, and here it is. You can do these ... forever if you want, though that's probably not the best use of your time. Instead, make sure you are competent in the idea of fractions.
Homework 2: Assigned 09.11. Due 09.14
1. In the shared google folder (link here), you'll find a sheet entitled "kitties.pdf". Complete your assessment of the statement, according to your own reasoning. Be able to defend your answer in class, given the constraints on the paper.
2. In class we discussed the plight of Farmer John. At this point, it’s gotten worse. You see, Farmer John decided to buy two alpacas (Alphonse and Albert). These alpacas DO NOT get along. Farmer John has bought 120 ft of fence to fence in these alpacas, but now he realizes he actually needs to create two different pens for the alpacas.
a. The two pens should be the same area.
b. The pens should be made with only right angle turns.
DESCRIBE how you came to your conclusions about the pen, and any formulas you may have used. Expect to explain your reasoning in class. A picture would do wonders. You may break apart the fence, if needed.
3. In the shared folder, you will find problem 584. IGNORE PROBLEM 585. As you solve, think about process. Think about how you are going about solving it. Don't forget to talk to others.
Homework 1: Assigned 09.07. Due 09.11
1. Fill out this brief survey.
2. Hanging out at the local watering hole, you strike up a conversation with a small man in a white hat who calls himself 'Farmer John'. Farmer John has a problem. You see, he recently acquired a loving, wonderful alpaca named Alphonse.
The problem is that Alphonse likes to wander, and so our intrepid farmer wants to make a fenced in area for Alphonse. He goes out and buys 400 ft of fencing. There are a few constraints upon the building of this fenced in area, however:
He wants Alphonse to have as much space as possible to run around, to frolic, to commune with nature and experience life (within the confines of the pen, of course)
Farmer John, while into new ideas, still believes that fences should have only right angles. So there's that.
What is the maximum amount of area that the fence can contain, given the constraints?
How do you KNOW that's the right answer?
You've convinced yourself, and hopefully your group of the right answer.
What if you had to convince someone else, outside the group?
What if you had to convince your mortal enemy?
What evidence could you use to show that you were right and that your enemy cannot stand up to your logical rigor?
Finally, what if instead of 400 ft of fencing, you were given an unspecified amount of fencing (say, x ft of fencing). How much area would you be able to contain?
3. How many blades of grass are there on commons lawn? (define commons lawn as from the path in front of the dining hall, between the four lawn houses, straight through to the wall at the end of the world).
Obviously, you won't get the exact right answer (or, perhaps more specifically, you might, but we would have no way to verify). Identify ways to best estimate this information. You may use the internet, your common sense, measurements, etc. etc. Be sure to think about how and why you are choosing the numbers, values, reasons you are choosing. Detail your process and be prepared to share both your number and the process used to get there.