Don't forget to read the previous post if you haven't already!
What we did today:
• We discussed the student solutions to the "silly stories" #1 That's a Meanie Genie, #3 The Fountain of Knowledge, and #10 Dot of Fortune.
It turned out that The Fountain of Knowledge had two different ways it could be solved. There might be another... maybe.
• The Pigeonhole Principle:
If you have more pigeons than you have pigeonholes, and you put all the pigeons into pigeonholes, then at least one pigeonhole will have more than one pigeon in it.
That's all there is to it. Kind of obvious, but very useful. (Good examples of the power of the Pigeonhole Principle at that link!)
From the reading from Mind your decisions, fun applications of the Pigeonhole Principle, we discussed up to #8.
The Pigeonhole Principle is a theorem about the Natural Numbers. The Natural Numbers will be the subject of our investigations for the next few topics. Make sure you know what they are, because later on we will be talking about other sets of numbers!
Homework:
• Journal assignment: write up the solution or partial solution that your group arrived at for each of the problems we worked on in class, explaining your reasoning, and then describe the correct solution for that problem, explaining its reasoning and whatever you learned from that process. As an example of describing a reasoning process, I've created a sample journal entry (admittedly rather detaled!) to show the kind of thing I mean.
If you want to discuss the problems or any aspect of them while you are working on this, please feel free to post a question to the Piazza discussion board!
• Homework problems:
Make sure that you record your reasoning (including anything that didn't work out!) and not just your answer, and explain how you know your answer works. In each case, we are asking for the smallest number necessary to make sure you have what you want. [Explanation of that last part in case it's not clear.]
Suppose you own 15 black socks and 10 blue socks. The socks are all mixed together in your sock drawer, not paired. In the middle of the night with the light burnt out, you want to take enough socks so that you know for sure you have a pair of matching socks.
1) How many socks must you take so that you know that you have a matching pair?
2) How many socks must you take so that you know that you have a pair of black socks? This is not the same as the first question. Think it through. If you get stuck, here is a Nudge.
3) How many socks must you take so that you know that you have a pair of blue socks?
• Reading for tomorrow: We will continue with the Pigeonhole Principle a bit (to see its proof), and then begin with another topic from number theory:
Fibonacci numbers: from Math is Fun. This is where you will maybe need to compute square roots. You may want to look through the questions they provide at the end of that webpage: pay special attention to #10.
Next up will be prime numbers and prime factorization of the natural numbers.
30 August 2016
25 August 2016
Thursday 25 August class
This blog will contain documents and/or links for all the readings you have to do and handouts given out in class, as well as the daily homework assignments and (later) the projects. I'm still working on this blog (to put in labels and so on) so be patient!
For discussion, we will be using the Piazza discussion board which will be linked in the sidebar as well. You should have received an invite (their word, not mine) to join this discussion board from the Piazza team - if necessary, check your spam folder. Follow the instructions and join the discussion board! Tomorrow I will do a demo on how to use it effectively.
Today we worked on this problem:
1) The Wason selection task. [link is to PhilsophyExperiments.com, the source of the version I handed out in class - you can work through it again and read what they have to say about this problem]
Wikipedia gives some more information and references if you want to pursue the various explanations for this "paradox".
Homework: The Meanie Genie and two other "silly stories" from The Heart of Mathematics by Edward B. Burger and Michael Starbird. This book may be available in the BC Library as I formerly used it as a textbook. [The entire first chapter is a very good source of problems (you do have to get used to Starbird's sense of humor, of course) and indeed I think it is an excellent textbook, but pricey, as they all are these days, sigh.]
Here is the advice given in that textbook about working on these "silly story" problems:
Homework:
Note: all documents which are from the textbook The Heart of Mathematics are posted over on the Piazza discussion board. The reason for this is that I copied those parts of the copyrighted textbook under the "Fair Use" concept (copying limited portions of the material for educational use only), and that means that access to them should be limited to students in my class.
• Your first homework is to get your looseleaf binder to keep your journal organized! Also check into getting a simple calculator that can compute square roots, but which does not communicate with the outside world (that is, not a cell phone!)
• Journal assignment: write up the solution or partial solution that your group arrived at for the problem (Wason card selection) we worked on in class, explaining your reasoning, and then describe the correct solution for that problem, explaining its reasoning and whatever you learned from that process. As an example of describing a reasoning process, I've created a sample journal entry (admittedly rather detaled!) to show the kind of thing I mean.
If you want to discuss the problems or any aspect of them while you are working on this, please feel free to post a question to the Piazza discussion board!
• Homework problems: work on solutions for the "silly stories" #1 The Meanie Genie, #3 The Fountain of Knowledge, and #10 Dot of Fortune. #10 is available on the Piazza discussion board as indicated above.
• Reading for tomorrow: We will begin with some topics from number theory: The Pigeonhole Principle and then Fibonacci numbers.
The Pigeonhole Principle: from Mind your decisions, fun applications of the Pigeonhole Principle (read down through #8)
There are literally scads (joke!) of sources on the internet which refer to this principle, but most of them get very deep very quickly. We just want to see how such a simple idea can be powerful.
Fibonacci numbers: from Math is Fun. This is where you will maybe need to compute square roots.
For discussion, we will be using the Piazza discussion board which will be linked in the sidebar as well. You should have received an invite (their word, not mine) to join this discussion board from the Piazza team - if necessary, check your spam folder. Follow the instructions and join the discussion board! Tomorrow I will do a demo on how to use it effectively.
Today we worked on this problem:
1) The Wason selection task. [link is to PhilsophyExperiments.com, the source of the version I handed out in class - you can work through it again and read what they have to say about this problem]
Wikipedia gives some more information and references if you want to pursue the various explanations for this "paradox".
Homework: The Meanie Genie and two other "silly stories" from The Heart of Mathematics by Edward B. Burger and Michael Starbird. This book may be available in the BC Library as I formerly used it as a textbook. [The entire first chapter is a very good source of problems (you do have to get used to Starbird's sense of humor, of course) and indeed I think it is an excellent textbook, but pricey, as they all are these days, sigh.]
Here is the advice given in that textbook about working on these "silly story" problems:
1. Make an earnest attempt to solve each puzzle.
2. Be creative.
3. Don't give up: If you get stuck, look at the story in a different way.
4. If you become frustrated, stop working, move on, and then return to the story later.
5. Share these stories with your family and friends.
6. HAVE FUN!
Homework:
Note: all documents which are from the textbook The Heart of Mathematics are posted over on the Piazza discussion board. The reason for this is that I copied those parts of the copyrighted textbook under the "Fair Use" concept (copying limited portions of the material for educational use only), and that means that access to them should be limited to students in my class.
• Your first homework is to get your looseleaf binder to keep your journal organized! Also check into getting a simple calculator that can compute square roots, but which does not communicate with the outside world (that is, not a cell phone!)
• Journal assignment: write up the solution or partial solution that your group arrived at for the problem (Wason card selection) we worked on in class, explaining your reasoning, and then describe the correct solution for that problem, explaining its reasoning and whatever you learned from that process. As an example of describing a reasoning process, I've created a sample journal entry (admittedly rather detaled!) to show the kind of thing I mean.
If you want to discuss the problems or any aspect of them while you are working on this, please feel free to post a question to the Piazza discussion board!
• Homework problems: work on solutions for the "silly stories" #1 The Meanie Genie, #3 The Fountain of Knowledge, and #10 Dot of Fortune. #10 is available on the Piazza discussion board as indicated above.
• Reading for tomorrow: We will begin with some topics from number theory: The Pigeonhole Principle and then Fibonacci numbers.
The Pigeonhole Principle: from Mind your decisions, fun applications of the Pigeonhole Principle (read down through #8)
There are literally scads (joke!) of sources on the internet which refer to this principle, but most of them get very deep very quickly. We just want to see how such a simple idea can be powerful.
Fibonacci numbers: from Math is Fun. This is where you will maybe need to compute square roots.