Monday I will assign a week long assignment, and then we will have the final assignment quick after that, and then we're done! You will have midterm responses back on Monday as well.
Homework 20. Assigned 12.07. Due 12.10.
Construct one of the objects from this website: http://korthalsaltes.com/
Tell me the number of edges, sides, vertices.
If you're feeling amazing, find the surface area and volume. If you're feeling only kind of amazing, come up with a plan that would allow you to find the surface area and volume.
Classwork 19. Assigned 12.04. Due 12.04.
It's below under the title "10 Questions". You should be working with other people. Let's do some math.
Final Assignment. Assigned 12.03. Due 12.12.
Below you will find the final assignment, entitled f2015.entry.to.math.final. It is due to me in electronic form by the time you leave campus, or by the 12th, whichever is later. Do not mess around with this one. There's a lot there. Lots of questions. Get it done. Do good work.
Homework 18. Assigned 11.16. Due: 11.19
Nothing new. just assignment 3, get your stuff ready for class (see assignment 17)
Assignment 3. Assigned 11.16. Due: before Thanksgiving.
1. Read this: http://mathwithbaddrawings.com/2015/10/21/the-best-way-to-kill-a-math-test-try-to-make-it-fair/#more-3722. This blog post really got me thinking--what IS a fair question when it comes to mathematics--and how do I test for thinking as opposed to testing to see what you can look up online? Some of the questions later in the assignment will certainly be of this latter type, but for now:
consider the things we've covered thus far this year. (look at the list in entry to mathematics over on the left hand side if you need a refresher).
pick two specific topics, and FOR EACH:
come up with a question that would allow a teacher the ability to search for 'understanding' of the information
give a possible outline of a solution or rubric that would allow you to see if someone truly had understanding of the information.
come up with a question that doesn't require understanding or nuance, but rather just rote memorization
solve that question.
2. Assignment 3 is below, and attached as well as the "Right Triangle Trig" sheet you'll need as well.
Homework 17: Assigned 11.12. Due 11.16
1. Make sure you get your sample of 15 people. Check homework 16 for this information if you are confused.
2. Again, make sure you've got your games to play for Monday. Yes, this means bring the materials needed, one with positive EV and one with negative EV.
3. READING: This is a classic in the non-traditional mathematical canon. We are going to talk about it in class to start Monday. You only need to read to the top of page 10, until the line "So how do we teach mathematics?" You can read further if you want to, but you are not required to.
http://www.maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf
Think about the following questions:
What experiences in math have you had that ring true with regards to Lockhart's Lament?
Are there any of the ideas presented that you specifically agree with?
What about disagree with?
Find a couple of quotes from the article that we can use to start conversation about this on Monday.
here's a response by the editor and Lockhart: https://www.maa.org/external_archive/devlin/devlin_05_08.html
...and bring your energy!
Homework 16. Assigned 11.09. Due 11.12.
1) Find the Expected Value of the MegaMillions ticket you were given in class. Here is a website that might help you: http://www.megamillions.com/how-to-play
2) A MegaMillions ticket costs $1. This amount should be higher than the current expected value (the thing you found in question one). That being said, the expected value of a ticket increases as the jackpot value rises. At what jackpot level does the expected value become $1?
3) In class we played the game that if you rolled a 12 you won $50 and cost $2 to play. I want you to 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 THURSDAY.
4) In class we discussed the odds for when we roll one die, and when we add up the dots on two dice. Figure out the odds for the sum of:
* 9 when rolling 2 dice
* 10 when rolling three dice
5) I flip a coin five times. What are the chances of me:
* flipping, in order: H, T, H, T, H
* flipping three heads and two tails in any order
* flipping five heads
6) I want you to sample 15 random students on campus and ask them how many credits they are taking this semester. Bring these values to class on Thursday for use.
Homework 15. Assigned 11.05. Due 11.09.
1. In class we made the square wave and the sawtooth wave. I'd like you, in desmos, to try to make the triangle wave. More info on what each of them are and look like can be found here: http://pages.uoregon.edu/emi/11.php
2. I'd like you to graph the following functions in desmos. Each one is special, and I'd ask you to consider why it is the way it is.
f(x) = sin^2(x)+cos^2(x)
g(x) = cos(x)tan(x)
h(x) = (1/sin(x))(tan(x))
3. Create the following summations:
add the first 500 natural numbers.
add the first 30 terms of the equation 3x+5
add the first 50 terms of 4(.6)^x
create a summation that adds to 436 after 30 terms.
Homework 14. Assigned 11.02. Due 11.05.
1. Here is a website that gives average temperatures for different cities, one for each month. http://www.usclimatedata.com/climate/united-states/us
Our goal is to pick a city and make a function that can tell us an expected temperature give a specific month. Let's work on Bennington, VT together.
Here is a desmos I made, with 24 months of data for Bennington, VT on it. I started with the January point. https://www.desmos.com/calculator/mys0jmjftl
Click on the function below it: it should fit the data pretty well.
A. Explain how I came up with the formula that I used to explain this data. As a hint, consider each of the different numbers that are in the function, how I came about them, and how they might change the function.
B. Find a city you are interested in finding the average temperatures for. Put down 24 months of them, and then find an accompanying function to describe it.
2. You get into a ferris wheel, and are the last person to enter. The ferris wheel is three feet above the ground, completes a circle every 40 seconds, and has a radius of 30 feet.
create an equation. You may want to use the desmos thing I made to help you. Link is http://www.desmos.com/calculator/qr9kz9lf2r
For how long in each rotation are you above 45 feet?
The ferris wheel stops after 4 minutes. where am I on the ferris wheel?
Extra: How fast is the ferris wheel going?
Homework 13. Assigned 10.29. Due 11.02.
1. Here is a proof from the law of cosines that I particularly like: http://pages.pacificcoast.net/~cazelais/173/law-sines-cosines.pdf (second page). Your goal is to walk through it, and see if you can understand all the parts. What are they doing? When? Why? Break apart each piece, and see if you could recreate what they were doing. What questions are you left with? This will inform our Monday discussion.
2. Below are some trigonometry word problems either 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
https://www.desmos.com/calculator/m1n76jskoo
Homework 12. Assigned 10.23. Due 10.26.
1. Try some of these Khan Academy questions. If you need help with them, there's videos before them. This is a nice way to relearn/look at some new trig information:
https://www.khanacademy.org/math/geometry/right_triangles_topic/cc-geometry-trig/e/trigonometry_0.5
https://www.khanacademy.org/math/geometry/right_triangles_topic/cc-geometry-trig/e/trigonometry_1
https://www.khanacademy.org/math/geometry/right_triangles_topic/cc-geometry-trig/e/trigonometry_1.5
2. Here's some work on seeing the angle and the sides. You should try the odds 1 - 15. Answers are attached. If you run into trouble, try some more. Additionally, you should feel free to find other resources to help you with this work.
Homework 11. Assigned 10.12. Due 10.15
1) In class, we found some pythagorean triples using the following numbers:
12 and 7 gave: 95^2+168^2=193^2
8 and 11 gave: 57^2+176^2 = 185^2
1 and 2 gave: 3^2+ 4^2 = 5^2
15 and 27 gave: 504^2 + 810^2 = 954^2
Your job is to figure out how I used the first two numbers to get to the pythagorean triple.
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.
Midterm Assignment. Assigned 10.12. Due 10.22.
(as a note, I will also be adding a homework for over long weekend, so be prepared)
Below is a .pdf entitled 'F2015 Midterm.' Answer all questions fully and completely.
They get harder as the midterm goes on. Give yourself plenty of time.
These are due Thursday, October 22, scanned or otherwise digitized, by midnight.
As usual, let me see your thinking and reasoning. I want to know not just the answer, but how you got there and why you did what you did. For some, there are multiple possible answers. The clearer you make how you got to yours, the better it is for me (and your grade).
Homework 10. Assigned 10.08. Due 10.12.
1. 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?
2. 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)
3. Speaking of checkerboards a while back reminded me of a great 'math' problem I want you to tackle. The page is below called "Tiling Problems" outlines the problem, taken from: https://people.math.osu.edu/shapiro.6/tiling.pdf. (we're only doing the first page). Read through the problem, make sure you understand it ("Can we tile an 8x8 checkerboard if we remove the top right and bottom left spaces?") and see how to tackle. In class we're going to talk about justification.
Homework 09. Assigned 10.05. Due 10.08
1. Below is a .pdf "ThreeQuestions.pdf". Work through these. Remember, if you can't solve something, you should be working towards an answer. Talk to a friend, a person in the class, someone who likes problems like this. Try to figure out a pattern, a reasoning, a goal for what a model might do for you.
2. This is you: http://abstrusegoose.com/353
Homework 08. Assigned 10.01. Due 10.05
1. Finish the 'Quadratic Questions' sheet started in class.
...that's it.
Homework 07. Assigned 09.28. Due 10.01
1. Below you will find a sheet called 'Domain and Range'. Complete the first page, giving the domain, range, and saying whether or not it is a function.
2. Complete the sheet 'inverse_functions', also below.
Homework 06. Assigned 09.24. Due 09.28
Work on the sheets we were given on class on linear programming. Finish the two that we did not yet do.
Assignment 01. Assigned 09.21. Due 09.28
Find the .pdf "F.2015.Assignment.1" below. This is due by midnight on Monday, September28. Be sure to show work where indicated, as well as make it easy for me to follow work and where you are in the Assignment. These must be turned in electronically--mail them to me.
Extra points for clarity and neatness--remember, I'm trying to walk with you on the mathematical journey, so make it easy on me.
Homework 05. Assigned 09.18. Due 09.21
1. Complete the systems of equations worksheet below. You may need to look up methods for solving. Please, no decimal answers unless there were decimals in the problem. Otherwise, please give answers as improper fractions.
2. A printer needs to make a poster that will have a total area (margin and printed) of 200 square inched and will have 1 in margins on the sides, a 2 in margin on the top and a 1.5 in margin on the bottom. What dimensions of the poster will give the largest printed area?
3. A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12 m of framing materials what must the dimensions of the window be to let in the most light?
Homework 04. Assigned 09.14. Due 09.17
1. Below is the data for "cat years" to go along with the dog years.
create a line you think best fits the data where x is years and y is "cat years".
how old does your line say a cat should be after 3 years? Is this different than the actual point?
how old does your line say a cat should be after 12 years?
if a cat is 67 in "cat years", how many years does your line say have passed?
the oldest cat ever lived to be 38 years old in human years. According to your line, how old was the cat in "cat years"?
2. Read this wonderful little piece: http://v.cx/2010/04/feynman-brazil-education. Note that this should not be taken as a hit on Brazil, but rather should be a piece to think about how you've learned mathematics over the course of your time on this Earth. Are there similarities to what you have witnessed? In class I will ask the following questions:
What is mathematics to you?
What does a formula do?
What have you seen mathematics do well?
3. Complete the .pdf found here. you can skip the last question: http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/ExpLin-AS-Weights.pdf
Homework 03. Assigned 09.10. Due 09.14
1. Complete the attached sheet called "Practice Solving Literal Equations".
2. Complete the sheet called "Fractional Operations".
3. There is an adage that 'dog years' are 7:1 for human years. In other words, that dogs age 7 years for every year that a human ages. Below is a chart for us to look at to help assess this claim. Use whatever tools you would like to help look at this claim, and see if it appears to be true. Be prepared to discuss how you went about this, and the facts, terms, and information you used to help make that happen.
Homework 02. Assigned 09.07. Due 09.10
1. Do the attached sheet called "Due Class 3".
2. Do the work on the attached 'kitties' sheet.
3. Check out these resources on Fermi Estimation. (note, two of these talk about estimating the number of piano tuners in Chicago and use very different numbers (and give different answers!) . One is talking about JUST the city, and the other is giving the values for the metro area).
There are some differences in how the estimations are done, but seems like an interesting way for us to estimate these different numbers. Towards that end, try to come up with the following estimations:
number of cars registered in Vermont
Pieces of mail delivered to Bennington College weekly
Weight of all mammals on Bennington College Property on a Wednesday at like 2:30 PM.
number of earrings on campus (both worn and sitting somewhere like a dresser drawer) on a Friday night
A question of your own choosing. We will discuss these to start class Thursday.
Homework 01. Assigned 09.03. Due 09.07
1. Complete the Quick Survey here.
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.
As a hint--it's not as simple as breaking the fencing into two subsections of 60 ft and going from there.
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. Identify ways to best estimate this information. You may use the internet, your common sense, measurements, etc. etc. Detail your process, and we still start class with this question on Monday.