Embedded Files
Homework 21. Assigned 12.01. Due 12.05.
Construct an object from this site: http://korthalsaltes.com/ and bring it to class. Come prepared with the following information:
Number of faces, edges, and vertices
Surface area of your object ... and how you proceeded to find that surface area
Homework 20. Assigned 11.28. Due 12.01.
There is a sheet called 'exponential word problems' in the shared work folder. Complete these, showing your work.
Final. Assigned 11.28. Due 12.09
All pieces for the final are in the shared work folder. Please pay attention to the instructions, and put forth your best effort.
Assignment 3. Assigned 11.17. Due 11.28.
All pieces for assignment 3 are in the shared work folder. There is the assignment and then a sheet called right angle trig.
Homework 19.b. Assigned 11.17. Due 11.21.
1) Find the Expected Value of the Powerball ticket you were given in class. Here is a website that might help you: http://www.powerball.com/powerball/pb_prizes.asp
2) A Powerball ticket costs $2. 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 $2?
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 MONDAY.
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
Homework 19. Assigned 11.14. Due 11.17
OK, change of pace. We're going to change our plan for Thursday a bit, and instead, do a reading and spend the first part of class talking about it. I've tried to show you why I do what I do, but I think this helps push that narrative a bit further.
READING: This is a classic in the non-traditional mathematical canon. 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 18. Assigned 11.10. Due 11.14
1. This focuses on the Trigonometric movement. If you get stuck there are places online to help you, but don't jump there first. They may be using radians as well, so it may help you less than you think.
You are 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 diameter 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?
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.
Homework 17. Assigned 11.07. Due 11.10.
2. 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
https://www.desmos.com/calculator/2bwwjqz0xb <-- 30, 32, 33, 38, 40
3. In Class, we started the baseball problem.
To reiterate it: Baseball Player in Outfield. 300 feet to Home. Throws at 60 mph ... will the baseball player be able to make the throw all the way home? What's the farthest this person could throw? How long would it take?
Try to make two formulas:
One should find out how far the person throws it, given an angle (we did 20 degrees, but how can we abstract that?)
One should find out how long it takes for the ball to travel, given a distance travelled (this is a little trickier)
https://www.desmos.com/calculator/dr10fmtzwg
EXTRA BONUS HARD PROBLEM:
We showed the max distance a person can throw, and how long it takes to get there. But here's an extension. Say I have 2 players, each who can throw the ball at 60 mph. I want the ball to travel 300 feet as quickly as possible. In baseball, they often use a cut off person to achieve this (see video here). This is because they can often throw it faster this way -- more velocity in the x direction. Given this information, at what angle should each of the players throw to make the process as fast as possible. (assume the person in the middle takes no time to throw the ball again).
https://www.desmos.com/calculator/z40bngb5q5
Homework 16. Assigned 11.03. Due 11.07
1) Right angle Trig.
Here's some work on seeing the angle and the sides. You should do these. 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.
If you aren't getting these right away, no worries. Here's something to help you:
Angles to Sides Practice: https://www.khanacademy.org/math/geometry-home/right-triangles-topic/trig-solve-for-a-side-geo/e/trigonometry_2
Sides to Angles Practice: https://www.khanacademy.org/math/geometry-home/right-triangles-topic/trig-solve-for-an-angle-geo/e/solve-for-an-angle-in-a-right-triangle
2) In class we went over the Law of Sines, and a proof for why it works. I want you to try a new one -- Law of Cosines.
Check out the second page here: http://pages.pacificcoast.net/~cazelais/173/law-sines-cosines.pdf for a nice proof. I would like you to analyze the proof, go through the steps, and convince yourself that the Law is Legit. Do the math, draw the pics -- DO NOT PASSIVELY MATH. We will discuss the proof in class, and I'm curious as to your insights -- what was easy, what was difficult? What did you think would be easy in the proof but wasn't?
3) Try the law of cosines: given three sides of a triangle (10, 13, 17) what are the angles of the triangle? Show your work.
Homework 15. Assigned 10.31. Due 11.03
1) Here are some of the problems y'all sent me. Try these:
1. You dropped your phone in a very deep port-a-potty that is filled to the brim with the mysterious blue liquid. The abyss is 11m deep. Your phone is descending through the foul sludge at a constant rate of 1/3 m/s. When will the phone reach the bottom of its sewagey grave?
2. 18 frogs have appeared on your planet and they breeding rapidly enough to double their population every 2 days. How many frogs will there be in 20 days? When will there be more frogs then people upon the planet earth?
3. A liquid is cooling according to the function f(x)=90(0.9)^x where temperature is in degrees Celsius. According to the model, when will the liquid have a temperature of 21 degrees?
There is a flaw in this model ... if time goes far enough, what does the temperature of the liquid tend towards? Why is this not realistic? Try to create a model where the temperature starts at 90 and then rests at a more realistic final temperature.
4. A ball was thrown up into the air, with a starting height of 5 m. After seven seconds it hits the ground again. What was the starting velocity of the ball? What was hte maximum height the ball reached?
5. The annual Bennington Bake Sale sold banana cream pies for $5 and cake pops for $1. The total amount of money brought in was $4168, while there were 2,072 items sold. How many pies were sold?
6. There is a water reservoir that is leaking water at the rate of 5% per hour. If it started filled to max capacity, how much will be left after 9 hours? When will there be 20% of the water left?
7. It's Friday night and Ingrid is out having a nice time. She just finished roller skating at the Rollerama Skating Rink, Schenectady, NY (It's a real place! Also, Rollerama is happening in Greenwall, this week, 4 November!) The total cost of her session was $14.30. She had to pay a $9 entrance fee and $1.50 for every half hour she was on the skating rink. Find out for how many minutes was Ingrid roller skating.
8.
Homework 14. Assigned 10.24. Due 10.31
In class, we did 11 problems. They broke down in that:
some were linear
some were quadratic
some were exponential
1. Make sure all problems are finished; I will ask for explanations on all questions in class next week. Refresh your brain on ones we did in class, specifically how you decided on a model, and what you did to get your actual answer after the model.
2. Create three problems -- one linear, one quadratic, one exponential. Email these to me by Saturday evening (before I wake up on Sunday) 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.
Homework 13. Assigned 10.20. Due 10.24
In the shared folder is a .pdf named "Exponential HW".
Midterm Assignment. This is Due at 11:59 pm on October 20, 2016.
Please find the assignment in our shared documents folder. As you run across questions, please let me know. I'm here for you! Also -- the other people in the class are here for you!
Homework 11. Assigned 10.07. Due 10.10
In class, we found some pythagorean triples using the following numbers:
10 and 7 gave: 51, 140, 149
2 and 1 gave: 3, 4, 5
3 and 2 gave: 5, 12, 13
5 and 6 gave: 11, 60, 61
Your job is to figure out how I used the first two numbers to get to the pythagorean triples.
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 10.03. Due 10.07
0. There are several questions to try in the document labeled for our 10.3 class. Do those.
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 09.29. Due 10.03
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 08. Assigned 09.26. Due 09.29.
note: I understand there is no homework 07. Just trying to keep it aligned to our class number.
1. Finish the problems on the Quadratic Questions sheet.
2. Work on the Inverse Functions Sheet.
Both sheets can be found in the shared documents folder.
No new hw due 09.26. Just the Assignment. Enjoy family weekend.
Assignment 01. Assigned 09.19. Due (e-mailed to me) by 09.26.
The assignment can be found here: https://drive.google.com/open?id=0Bxt5G5LUOcMKSFRjbFczaTc1ejA
Please make sure you work is neat, easy to read, and well thought out. I'm looking for thought process and reasoning on these, so clearly explain how you came to your conclusions. You are welcome to work together, but make sure that whatever you turn in your feel comfortable in calling your own.
Homework 06. Assigned 09.19. Due 09.22.
1. Work on the remaining linear programming questions (which specific ones are outlined in class)
2. Finish the last page of the domain and range worksheet. It can be found here: https://drive.google.com/open?id=0Bxt5G5LUOcMKSFRjbFczaTc1ejA
Homework 05. Assigned 09.15. Due 09.19
note: your first assignment will be assigned on Monday, along with another homework as well.
1. Below is a worksheet on System of Equations (no word problems). Try these, and think back to previous times in your life you had to solve these. What worked best for you? What systems did well for you?
2. Create a word problem based upon the idea of using a system of equations. Bring it for us to work on in class on Monday.
3. Finish the problem about the car we started. In particular, think about how we can turn that into a system of equations that might help us make appropriate decisions?
Homework 04. Assigned 09.12. Due 09.15
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. Complete the sheet here: http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/ExpLin-AS-Weights.pdf .
4. Test your ability to graph lines in these forms:
Standard Form <-- this you may need to look things up.
Homework 03. Assigned 09.08. Due 09.12
0. Take the question you created for homework 2, question three, email it to me with your answer. We discussed doing this in class, this is just a reminder.
1. Work on the sheet we started in class: Practice with literal equations.
2. Want fraction practice in the comfort of your own home?
http://www.thegreatmartinicompany.com/fractions/fraction-problems-home.html
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 09.05. Due 09.08
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 09.01. Due 09.05
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 (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. Detail your process, and we still start class with this question on Monday.
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