Spring 2012 Math 46 Home Page

Green Sheet

Class 22, Thu., June 21, 2012
We reviewed for the final.

Your portfolio and chapter 7 homework is due during the final exam.
I'll be checking journals one more time during the next few days.
Recent final exam study guide
Note that the study guide is from a previous year; you won't have an essay question.
Recent sample problem sheet.
Sample problems with some hints and solutions.

Class 21, Tue., June 19, 2012
We did the Barbie activity and went over chapter 7 and chapter 8.1 material.

Class 20, Thu., June 14, 2012
We went over chapter 7 material.
On Tuesday we'll do the Barbie activity. Please bring any Barbie or Ken dolls that you have access to.
Chapter 6 homework is due Tuesday.

Class 19, Tue., June 12, 2012
We went over chapter 6 material; also Egyptian fractions and reasons for multiplying and dividing fractions using the usual algorithms.
We also began chapter 7. Work on chapter 6 homework, due Tuesday (some of you still need to turn in chapter 5 HW, by this Thursday.)

Please do these Ch. 5.4 homework and turn in with the next assignment: 2,3,6,8,9,13,14,20

Class 18, Thu., June 7, 2012
We worked on fraction problems.
Please work on chapter 6 homework, which will be due next Thursday.

Class 17, Tue., June 5, 2012
We began going over material in chapter 6, and received the take-home exam back.

Class 16, Thu., May 31, 2012
We worked on group problems and finished in most groups. Chapter 4 homework is due on Tuesday. Please also complete your journal entries, as they will be given a final check #2 in next few days.

Class 15, Tue., May 29, 2012
We worked on group problems and take-home exams (exams due this Thursday!)

Class 14, Thu., May 24, 2012
We went over sections 5.1 and 5.2. Turn in chapter 4 homework on Tuesday.

Class 13, Tue., May 22, 2012
We went over sections 4.3 and 4.4 and assigned group problems.
Bring your take-home exams to class Thursday, we can spend some class time on them.

Class 12, Thu., May 17, 2012
We went over more material from chapter 4, including modular arithmetic, how divisibility rules work, and how the binary take-away game works.

Here is a handout showing how to explain your solution to a Ken Ken puzzle.

Class 11, Tue., May 15, 2012
We heard essay reports and started on section 4.2, divisibility tests.
Remember to keep your journals up to date!

Class 10, Thu., May 10, 2012
We went over sections 3.6, 4.1, and much of 4.2.
Essay 2 is due Tuesday. Remember: use a book as a source, not an online blog or Wikipedia. And cite your source(s).

Class 9, Tue., May 8, 2012
We went over more alternative algorithms, and estimation (sections 3.4 and 3.5).
Bring a scientific or graphing calculator this Thursday.
Chapter 3 homework will be due next Thursday.
Note that problem 24, on Egyptian Multiplication, is now included in the 3.4 homework.

Here's the wikipedia site on Nines Complement subtraction. Here's a link for the Gelosia mulitplication method.
But here's a wonderful article recounting the invention of the first mechanical pocket calculator, the "Curta," conceived and designed by Curt Hertzstark while a prisoner in a German concentration camp during World War II. He might have been one of the first to come up with this subtraction method.

Here's a site on Base systems.
Site on number systems.
Number systems associated with languages.
Site with links to number system sites.
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."

Info on Al Khwarizmi.

Class 8, Thu., May 3, 2012
We went over the exam, and also chapter 3.2 and part of 3.3.
If you did not have your portfolio during the exam, I will check again on Tuesday.

Second Essay Assignment.
You have a short paper on a subject related to the course that catches your interest due Tue., May 15, 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., May 1, 2012
We had exam 1, and went over more of chapter 3.1.
Chapter 2 and 1.6 homework problems are due Thursday.

By the way, should we even be giving "exams?" - see this article "Stop Tellng Students to Study for Exams, from the Chronicle of Higher Education!

Class 6, Thu., Apr. 26, 2012
We went over the rest of chapter 2, and some of chapter 3.1.
The first exam will be on Tuesday, and covers chapters 1 and 2, and anything we've done in class.

To help you, here are
Study guide for the first exam
Solutions to the study guide for the first exam problems

Please add the following problems from chapter 1.6, which will be due with your chapter 2 homework next Thursday:
Ch. 1.6: 1,4,9,10,12,15

Class 5, Tue., Apr. 24, 2012
We went over more chapter 1 homework, also chapter 2.1, 2.2, and 2.3.
The Fibonacci assignment is due Thursday.
Here is a handout on what I call the Sorting Junk game, which we played in class today.
We also discussed the difference between inductive and deductive thinking.
Work on chapter 2 homework.

Class 4, Thu., Apr. 19, 2012
We went over homework, and learned how to find the Fibonacci numbers on a pinecone.

We played the 15-sum game, and saw how it is really "Magic Square tic-tac-toe." (The link has some history of magic squares. )

Here is the Fibonacci assignment, which is due this coming Thursday.
Here are Vi Hart's Fibonacci number videos.
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.
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.

Article by Brian Hayes on the history of Gauss's Trick, published in 2006.

Chapter 1 homework is due this Tuesday, Apr. 24.

Class 3, Tue., Apr. 17, 2012
We learned about the game Ken Ken. See their web site for daily puzzles.
We went over more homework from Chapter 1, which is now due next Tues., Apr. 24.
We also learned about the Pigeonhole Principle: placing n+1 pigeons in n pigeonholes guarantees that at least one pigeonhole has at least two pigeons!
Turn in the Ken Ken problems I gave out this Thursday, Apr. 19.

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 a difference of 1.
We saw how labeling six pigeonholes with the pairs of numbers {1,12}, {2,11}, {3,10}, {4,9}, {5,8}, and {6,7} explained property 1. Can you do a similar labeling to explain properties 2, 3, and 4?
Here's a fifth property that is very tricky to explain (hint: the best explanation uses doubling and some pigeonholes with only one number assigned!)
(5) A pair of your numbers have the property that one divided the other equally.
We saw how the pigeonhole principle explained why properties 1,2, and 3 are true. 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 pigeonhole would have 3,6, and 12.

The "Frogs on a log" problem, which is a textbook homework problem, and in which we will find 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.

Class 2, Thu., Apr. 12, 2012
We will go over some of the homework problems from sections 1.1 - 1.4.
Your math autobiography is due Tuesday, Apr. 17, on Turnitin at the start of class.
You should be working on Chapter 1 homework, as we will finish chapter 1 on Tuesday, and I will collect Chapter 1 homework next Thursday.

If you have not gotten an etherpad site for your class journal, do so now.
The site is either http://typewith.me/ or http://piratepad.net/front-page/.
If you have not entered a journal entry for Tuesday also, please do so now, as I am already checking journals. Your first journal check will be complete by Tuesday, April 24, and will count 2 points of the 10 points for the "Portfolio" portion of your grade.

Here are some of the vocabulary words we have used during 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

Class 1, Tue., Apr. 10, 2012
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.
Are you clear about the winning strategy in this game?

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. (See directions below or on the green sheet.)
(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 at which you will be uploading your essays.

Portfolio. Put together your portfolio, a loose leaf notebook with these sections:
Homework
Handouts or articles provided to you at this site (for example the pattern game handout.)
Exams
Class notes
Articles
Your papers or essays

Write a journal entry for each class. It should be one long (6 or more sentences) 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/ or http://typewith.me/.

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

Th. Jan. 12 (most recent entry)
Blah, blah, blah (at least 1 long - 6 or more sentences - or 3 medium size paragraphs).

Tue. Jan. 10 (older entry)
Blah, blah, blah (at least 1 long or 3 medium size paragraphs).

If you have trouble using an etherpad site, 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:

Study guide for the first exam
Solutions to the study guide for the first exam problems

Final Exam study guides:
Recent final exam study guide
Note that the study guide is from a previous year; you won't have an essay question.
Recent sample problem sheet.
Sample problems with some hints and solutions.

We will see several short videos about learning and teaching; you can find the links within Keith Devlin's recent online column.
Here is the set of slides of fraction problems.
Here is the set of slides of decimal/ratio problems

"PEMDAS" memory mnemonic

Prediction Card Trick handout
Painting the Pool
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.

Nines Complement subtraction.
Gelosia mulitplication method
"Clap your name" activity.
Wikipedia entry on Turnitin.
Common Core Standards,
National Council of Teachers of Mathematics.

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."

Voting methods and their history.
Where's Fido?

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.
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."

Al Khwarizmi.

History of the Magic Square.

Triangle numbers, squares, Fibonacci numbers.

The game Ken Ken - this site has 6 new puzzles every day.

Fibonacci assignment
Vi Hart's Fibonacci number videos.
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.
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.

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.

The pattern game we played in class
Handout with problems on Patterns and Modular Arithmetic
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.

The 15-sum game, and how it is really "Magic Square tic-tac-toe."

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

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

In the pigeonhole principle "magic trick," I will ask 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. 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 pigeonhole would have 3,6, and 12.

The "Frogs on a log" problem, which is a textbook homework problem, and in which we will find 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.