Winter 2012 Math 46 Home Page

Green Sheet

The final exam is Tuesday, 4-6 PM.
During the exam I will do the final homework check of chapter 7.
During the next few days I will check your journals.
During the exam I will also check your portfolio - bring it to class!

Class 22, Th., Mar. 15, 2012
We went over the Barbie and modular arithmetic handouts, and went over some problems from the final exam study guide.
Note that the study guide is from a previous year; you won't have an essay question.
Here are some more problems from a more recent study guide:
Recent sample problem sheet.
Sample problems with some hints and solutions.

Class 21, Tue., Mar. 20, 2012
We went over exam 2 and did the Barbie activity.

Class 20, Th., Mar. 15, 2012
We went over material on decimals and converting fractions to decimals and repeating decimals to fractions.
Which fractions convert to terminating decimals? (Those in lowest terms with denominators that are products of powers of 2 and powers of 5.)

Class 19, Tue., Mar. 13, 2012
We played FracJack, a card game about fractions. We also learned a card trick based on parity, and heard the online story of George Vacarro, who questioned his Verizon bill, when Verizon misunderstood the difference between .01 dollars and .01 cents.

Class 18, Th., Mar. 8, 2012
We saw short videos about learning and teaching; you can find the links within Keith Devlin's recent online column.
We also watched two more sections of Vi Hart's Fibonacci number videos.

Here is the set of slides of fraction problems.
Here is the set of slides of decimal/ratio problems.
Ch. 5 homework will be due on Tuesday.

We finished material in chapter 6, and have started chapter 7.
Here are chapters 6 and 7 homework problems.
(if you are rusty on fractions also do many of the problems 1-10 in each section of chapter 6!)
Ch. 6.1: # 2,3,5,6,11,23,24,30,31,41
Ch. 6.2: # 1,2,9,13,21,22,23
Ch. 6.3: #1,2,10,13,14,16,17,18,20,34
Ch. 6.4: # 1,12,13,16,19,27,28,29,34

Ch. 7.1: # 1-7,9,10,18,19,20,21,22,25,34
Ch. 7.1: # 7,8,17,18,21,28,29
Ch. 7.1: # 1,3,7,8,12,18,19,29,36
Ch. 7.1: # 4,6,8,19,20,22,23,26,34

Class 17, Tue., Mar. 6, 2012
We worked on take-home problems.
Chapter 5 homework:
Ch. 5.1: # 1,4,7,8,17,18,22,23
Ch. 5.2: # 1,2,13,16,19,27,28,30,31
Ch. 5.3: # 5,6,11,13,14,18,20,21

Class 16, Thu., Mar. 1, 2012
We worked on fractions.

Class 15, Tue., Feb. 28, 2012
We worked on addition and subtraction of positive and negative numbers.

Class 14, Th., Feb. 23, 2012
We worked on the group problems

Class 13, Tue., Feb. 21, 2012
We went over group problems and some of the take-home problems.
You will present group problems on Thursday.
Bring Patterns and Modular Arithmetic to class on Thursday.

Class 12, Thu., Feb. 16, 2012
We heard reports based on the essays turned in today.
Many of you have stopped updating your journals. You need to have one entry per class, and I will be checking them in a couple of weeks!

Class 11, Tue., Feb. 14, 2012
We went over section 4.4 on codes, and also learned more about modular arithmetic.

Class 10, Thu., Feb. 9, 2012
We went over sections 4.2 and 4.3, worked on group problems, and learned about modular arithmetic.
We did the "Clap your name" activity.
Chapter 3 homework is due on Tuesday.
Your essay is due at Turnitin on Thursday.

Here is the Chapter 4 homework (everyone is responsible for knowing how to do group problems)
Ch 4.1 # 6,8,11,14,15,16, group: 22-24, 25, group: 31-32
Ch 4.2 # 1,2,6,9,10,12,14, group: 16 & 17, group: 20
Ch 4.3 # 1a,2a,3a,4a,5a,12,26,32,group:16,group:17&20, group:21
Ch 4.4 # 1,3,5,6a,7a,14,17,18

Here are some handouts relating to patterns and modular arithmetic:
(1) A handout describing the pattern game we played in class on the first day of class.
(2) A handout with problems on Patterns and Modular Arithmetic for you to work and hand in - please print this and bring to class, we'll work on it in class. It will be due a week from Tuesday.
(3) A handout, The Hidden Role of Modular Arithmetic, that reviews what we did in the first two classes and relates it to some other problems from chapter 1.

Here are some links about modular arithmetic, which we will learn more about throughout the quarter:
Here's a site on modular arithmetic.
Here's a site which will do modular arithmetic calculations for you.
Here's a site on modular arithmetic by Susan Addington.

By the way, here are some of the vocabulary words we used during past classes. Try to use each one in a sentence, to make sure you understand them:
multiple: 12 is a "multiple" of 3 and of 4. 3 and 4 are "factors" of 12. Is 13 a multiple of 1? Is 0 a multiple of 13?
horizontal (row): parallel to the horizon. Often means we are thinking about right and left.
vertical (column): up and down
odd numbers : 1,3,5,7,... These numbers are congruent to 1, mod 2. Is -1 and odd number?
even numbers : 0,2,4,6,8, .... Is 0 even? These numbers are congruent to 0, mod 2. Is -6 and even number?
alternate: a pattern in which two "sub-patterns" are each displayed in every other section of the pattern.
inductive thinking: arguing from specific cases to a general rule
deductive thinking: arguing from a general rule to a specific case

Here are the group problem assignments:

Class 9, Tue., Feb. 7, 2012
We went over sections 3.5, 3.6, and 4.1.
Do homework through 4.1.
Chapter 3 homework will be due next Tuesday.

Please create your own PEMDAS for Thursday. So far we have:
Alysse: Purple Elephants must dance and sing
Alysse: Peter’s extravagant moustache doesn’t allow soup
Asia: Pink emus make dinner at school
Felicite: Patrick eats Macdonald’s dinner at seven.

Class 8, Thu., Feb. 2, 2012
We went over the exam and sections 3.3 and 3.4, and part of 3.2.
Do homework through section 3.4.
Bring a scientific or graphing calculator to class on Tuesday.
Fibonacci number assignment due by midnight tonight.
Write your own "PEMDAS" memory mnemonic, and record it as part of your journal record.
Chapter 3 homework will be due next Thursday.
(Take home problems will be given out shortly.)
Article by Brian Hayes on the history of Gauss's Trick, published in 2006.
Here are articles on Nines Complement subtraction and the Gelosia mulitplication method.
Here are some other methods of addition, etc.

You have a short paper on a subject related to the course that catches your interest due Thu. Feb. 16 and worth 5% of your grade.
Here's the description of the essay:
Report on an article or chapter from a popular book about mathematics or math education. The report will be one to two pages long, typewritten, (it must be at least 600 words), and will cover the mathematics from one to several chapters of a book from the following list; other books or sources may also be used. You must use published material, not just web sites, unless you get permission from the instructor, and you MUST cite your sources. A short oral report to the class will also be required.
You should include in what you write and talk about:
(1) why you chose this topic,
(2) what you learned, and
(3) what you think about the subject in question.
(4) What you might like to find out about the subject in the future.

Examples of books with mathematical content:
The Mathematical Tourist and Islands of Truth, by Ivars Peterson.
Any of the books of Martin Gardner on mathematics (over 15 titles).
Game, Set, Math and Does God Play Dice by Ian Stewart, or other titles on math by Stewart.
The Mathematical Experience by Davis and Hersh.
A Number For Your Thoughts and Numbers At Work and At Play by Stephen P. Richards.
Tilings and Patterns by Grunbaum and Shepard.
Mathematical Snapshots by Steinhaus.
Mathematics: The New Golden Age by Keith Devlin, or other titles by Devlin.
The Emperor's New Mind by Roger Penrose.
The Mathematics of Games by John Beasley.
Archimedes' Revenge by Paul Hoffman
What is Happening in the Mathematical Sciences, ed. by Barry Cipra, Vols 1-5 (on reserve in campus library)

Examples of books with cultural content:
Ethnomathematics by Marcia Ascher.
You can also consult this Multicultural Mathematics Bibliography. Many of the references are in our library, and the bibliography contains call numbers for those that are in the library.
A number of Martin Gardner's books are in the De Anza library.

Class 7, Tue., Jan. 31, 2012
We had exam 1, but did not cover any new material.
The Fibonacci assignment is due on Thursday.

Class 6, Thu., Jan. 26, 2012
We went over sections 3.1 and part of 3.2.
We learned about Fibonacci's book Liber Abaci, and its relationship to the history of the Indo-Arabic number system and other number systems.
We saw this TED Dan Meyer video.
Here's a site on Base systems.

Site on number systems.
Number systems associated with languages.
Site with links to number system sites.

How things work on basketball players' numbers: "Each uniform must display one or two digits on the front and back of the jersey. The numbers on a jersey are used to identify a player when calling violations. In most cases, the digits can only be 0, 1, 2, 3, 4 or 5. While the NBA has allowed players to use numerals higher than 5, it is a rare allowance. This limitation on numerals allows referees to use their hands to signal player numbers to the game's official scorekeeper. Otherwise, a player wearing number 9 could be confused with a player wearing number 54."

Here is a Study guide for the first exam.
Solutions to the study guide for the first exam problems

Chapter 3 homework:
Ch. 3.1 # 1,4,5,10,11
Ch. 3.2 # 1,6,9a,10a,11a,13a,14,19
Ch. 3.3 # 1a,7a,16,17,20,24
Ch. 3.4 # 1a,7,13,17,21,23,25
Ch. 3.5 # 1,2,3,4,8a,18,22
Ch. 3.6 # 1,5,16

Class 5, Tue., Jan. 24, 2012
We went over chapter 2.3 and 2.4.
We played the 15-sum game, and saw it was really "Magic Square tic-tac-toe."
We also saw the connection to sudoku, and learned about Ken Ken.

Here's a handout about the Fido puzzle from last class: Where's Fido?

Here's the Fibonacci assignment which will be due a week from Thursday.
For more about Fibonacci numbers:
A great site about Fibonacci numbers.
Fibonacci site with lots of pictures and interactive applets.
Interactive site that helps explain phyllotaxis, which is the pattern of spirals in many plants.

We also learned about al Khwarizmi.

Here is a Study guide for the first exam.

Use the list just below for the chapter 2 homework problems. Ch. 2 will be due next Tuesday.

Class 4, Thu., Jan. 19, 2012
We went over more ch. 1 homework.
Ch. 1 homework will be turned in Tue., Jan. 24.
We also went over ch. 2.1 and 2.2.
Work on homework for ch. 2.1 and 2.2
Here is the list of homework problems for ch. 2:
Ch. 2.1: 3,7,10,12,14,17,18,23,24
Ch. 2.2: 4,9,11,13,17,22,23
Ch. 2.3: 2,7,13,18,20,29,33,34
Ch. 2.4: 1,2,3,5,9,16,25,31,32

The game Set that we played can be found here as a daily puzzle.
Here is a handout on what I call the Sorting Junk game.

Class 3, Tue., Jan. 17, 2012
We went over homework and material from chapter 1.5 and 1.6.
Homework for chapter 1 is due next Tuesday.
You must have emailed me the URL for your journal etherpad site by Thursday.
We also went over a number of important sequences: triangle numbers, squares, Fibonacci numbers.

Here's a complete list of the chapter 1 HW from the textbook. Other homework will be assigned periodically. Please work on all of chapter 1 homework for Thursday:
Ch. 1.1, # 4,5,9,10,11,12,14,15
Ch. 1.2, # 4,5,11,13,19,22
Ch. 1.3, # 1,3,6,7,10,13,17,22
Ch. 1.4: # 5,7,8,9,10,12,18,21
Ch. 1.5: # 4,7,9,11,13,14,15,19
Ch. 1.6: # 1,4,9,10,12,15

In the pigeonhole principle "magic trick," I asked you to choose seven numbers from the list 1,2,3,...,12. The properties each of your lists had were:
(1) A pair of your numbers had a sum of 13.
(2) A pair of your numbers had a difference of 6.
(3) A pair of your numbers had a difference of 3.
(4) A pair of your numbers had the property that their only common factor was 1.
(5) A pair of your numbers had the property that one divided the other equally.
We saw how the pigeonhole principle explained why properties 1,2, and 3 are true. For Thursday, can you use the pigeonhole principle to explain property 4? Remember, it's all in how you label to (six) pigeonholes!
Property 5 is more difficult to explain; in this case the six pigeonholes have different numbers of numbers assigned to them! For example, one would have 3,6, and 12.

We also worked on the "Frogs on a log" problem, which is a textbook homework problem, and found that with
1 frog per side it took a minimum of 3 moves to exchange places
2 frogs per side it took a minimum of 8 moves to exchange places
3 frogs per side it took a minimum of 15 moves to exchange places
You might have guessed that 4 frogs per side would require 24 moves, 5 frogs per side would require 35 moves.
Figure out how to do these exchanges also, in the minimum number of moves. (See below for more explanation.)

Class 2, Thu., Jan. 12, 2012
We went over some of the homework problems from sections 1.1 - 1.4.
Your math autobiography is due Tuesday on Turnitin.
You should be working on Chapter 1 homework, as we will finish chapter 1 on Tuesday, and I will collect Chapter 1 homework either Thursday or the following Tuesday.

If you have not gotten a piratpad site for your class journal, do so now.
The site is http://piratepad.net/front-page/
If you have not entered a journal entry for Thursday also, please do so now, as I am already checking journals. Your first journal check will be complete by next Thursday, and will count 1-1/2 points of the 10 points for the "Portfolio" portion of your grade.

Class 1, Tue., Jan. 10
We played the pattern game (print out this handout and include in your portfolio!
We also played the take-away game, in which each player removes 1 or 2 counters on each move, the last player to move winning.
Homework:
(1) Get a looseleaf notebook and set up sections as described on the third page of the green sheet or below
(2) Write a journal entry for this class today and store it at an etherpad site. Email me the URL of your site.
(3) Read and work on homework from sections 1.1 and 1.2.
(4) Register or login to Turnitin.com to make sure you can access the class site.

First week assignment: Put together your portfolio, a loose leaf notebook with these sections:
Homework
Handouts
Exams
Journal
Class notes
Articles
Your papers

Write a journal entry for each class. It should be one long or several short paragraphs detailing your reflections on each day’s class. What struck you as interesting, useful, helpful, unhelpful, puzzling, etc.? How are you feeling about the class? What are your expectations of the class and your own participation? Imagine you are writing to your future self (as in a popular South Park episode?!) and mention those things most memorable! Keep your journal entries at a page you get at an etherpad site, for example, http://piratepad.net/.

Use this format:
Stanley Student (keep your name at the top)

Th. Jan. 12 (most recent entry)
Blah, blah, blah (at least 2 long or 3 medium size paragraphs).

Tue. Jan. 10
Blah, blah, blah (at least 2 long or 3 medium size paragraphs).

If you have trouble using piratepad, try opening it with a different browser. I have no trouble using the (free) Google Chrome browser.

Join Turnitin.com for the following class. I have added everyone to the class list already.
Class: Math 46, Winter 2012
Password: Math46W2012

Many links and handouts:

Prediction Card Trick handout
Painting the Pool
Recent final exam study guide
Recent sample problem sheet.
Sample problems with some hints and solutions.
Britney Gallivan, who folded a "sheet" of paper 12 times.
Here is the set of slides of fraction problems.
Here is the set of slides of decimal/ratio problems.
Farey Sequences (skip the advanced part and the cute animation at the beginning!)
TED Dan Meyer video.
game Ken Ken - this site has 6 new puzzles every day.
Nines Complement subtraction.
Gelosia mulitplication method
"Clap your name" activity.
Wikipedia entry on Turnitin.
Common Core Standards,
National Council of Teachers of Mathematics.

Solutions to the study guide for the first exam problems
Site on number systems.
Number systems associated with languages.
Site with links to number system sites.
The triangle numbers,
Base systems
How things work on basketball players' numbers: "Each uniform must display one or two digits on the front and back of the jersey. The numbers on a jersey are used to identify a player when calling violations. In most cases, the digits can only be 0, 1, 2, 3, 4 or 5. While the NBA has allowed players to use numerals higher than 5, it is a rare allowance. This limitation on numerals allows referees to use their hands to signal player numbers to the game's official scorekeeper. Otherwise, a player wearing number 9 could be confused with a player wearing number 54."
Keith Devlin's articles on multiplication as repeated addition.
Brief history of the New Math.
The game Set, see their daily puzzle.
Sorting Junk game.

Here's a quote from Lewis Carroll's Through the Looking Glass. Alice is talking with the White Knight, who many commentators believe to be a stand-in for Carroll himself. We'll see it's relevance later in the course!
"The name of the song is called 'Haddock's Eyes'."
"Oh, that's the name of the song, is it?" Alice said, trying to feel interested.
"No, you don't understand," the Knight said, looking a little vexed. "That's what the name is called. The name really is 'The Aged Aged Man'."
"Then I ought to have said 'That's what the song is called?'" Alice corrected herself.
"No, you oughtn't: that's quite another thing! The song is called 'Ways and Means': but that's only what it's called, you know!"
"Well, what is the song, then?" said Alice, who was by this time completely bewildered.
"I was coming to that," the Knight said. "The song really is 'A-sitting on a Gate': and the tune's my own invention."
Fibonacci assignment
Study guide for the first exam
Voting methods and their history.
Where's Fido?
Pingala's possible use of the Fibonacci Numbers
Rachel Hall who credits Indian mathematician/musician with the Fibonacci numbers - see her article "Math for Poets and Drummers" listed at her site.
History of the Magic Square.
Patterns and Modular Arithmetic
A great site about Fibonacci numbers.
Fibonacci site with lots of pictures and interactive applets.
Interactive site that helps explain phyllotaxis, which is the pattern of spirals in many plants.
Article by Brian Hayes on the history of Gauss's Trick, published in 2006.
The pattern game we played in class