Spring 2014 Math 46 Home Page

Green Sheet

Thu., June 5, Class 22
Last day of class. Some of you wanted a potluck, which is fine!
We'll also review for the final exam.

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.

Tue., June 3, Class 21
This is the day we'll do the Barbie (and Ken) proportion activity
Please bring any Barbie or Ken dolls that you have access to.
Chapter 6 homework is due Tuesday. .

Thu., June 12, Class 20
We went over more of chapter 7.

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!)

Tue., June 10, Class 19
We went over more of chapter 7, turned in the exams, and went over some of the problems.

Thu., June 5, Class 18
We went over more about fractions, including Egyptian fractions and Farey sequences.

Tue., June 3, Class 17
We went through some of the powerpoint fraction questions.
We learned how to justify the algorithm for fraction multiplication with a rectangular diagram.

Thu., May 29, Class 16
We began chapter 6, working on alternative approaches to fraction calculations. We also discussed how the calendar works, noticing, for example that the months of April and July have the same dates on the same day of the week, because they are separated by 30 + 31 + 30 = 91 days, a multiple of 7.

We worked on this handout with problems on Patterns and Modular Arithmetic.
Please turn it in this comingTuesday. Please turn in chapter 5 homework this comingThursday.

Tue., May 27, Class 15
We learned about sutraction of negative numbers using counters and also using patterns of walking forwards and backwards. We also discussed ways of understanding why a negative times a negative is positive.

Thu., May 22, Class 14
We heard reports and finished work on group problems.

Tue, May 20, Class 13

Below is the set of group problems we did on Tuesday:

Thu., May 15, Class 12
We went over more material from chapter 4 and worked on group problems:
(If you were not present for the past class or two, your assignment is below!)

Second Essay Assignment.
You have a short paper on a subject related to the course that catches your interest due Thu., May 22, and worth 5% of your grade. You will turn the paper in via Turnitin.com. If you reported on the math/dance concert last time, you may do your math autobiography this time.

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.

Tue., May 13, Class 11
We went over exam, also chapters 3.5 and 4. We also did the name/rhythm activity.

Th. May 8, Class 10
We had exam 1, and also went over material from chapter 4.1 and 4.2.

Tue., May 6, Class 9
We went over material in chapter 4.1 and 4.2.
Bring calculators on Thursday and we will go over sections 3.5 and 3.6.
First exam is also on Thursday.
We saw the TED Dan Meyer video.

Thu., May 1, 2014, Class 8
We went over chapter 3.4.
We also did the "How we calculate" activity, and saw slides on the Brazilian Street Math Study.

Here are articles on Nines Complement subtraction and the Gelosia mulitplication method.
Here are some other methods of addition, etc. Here's another such web site.

Please bring calculators (graphing or scientific) to class on Tuesday, as we'll go over use of calculators.

Chapter 3 homework is due next Thursday, May 8, after the first exam.

Tue., April 29, 2014, Class 7
We went over chapter 3.2 and 3.3, including base systems other than base ten.
We also learned about nines complement subtraction.

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.

Thu., April 24, 2014, Class 6
We went over some homework questions from chapter 2, also started chapter 3 and went over section 3.1 on various number systems.
Do homework through section 3.1.

We did the Fido puzzle - please print out this Where's Fido handout and include in your portfolio. Include the extra problems in the handout as part of homework!

On Tuesday of next week turn in your Fibonacci assignment.
On Thursday of next week turn in chapter 2 homework.
I will also check journals next week.

Study guide for the first exam
Solutions to the study guide for the first exam problems
Here's another old exam 1.

Tue., April 22, 2014, Class 5
We went over chapters 2.3 and 2.4, also some homework problems.
We also had an introduction by Melissa Aguilar to the Smartthinking online tutoring system, avaialble to all De Anza students.
We also learned how to count the Fibonacci numbers on pine cones.
Here is the Fibonacci assignment, which is due next Tuesday, April 29. Read it CAREFULLY and do everything it asks!!

We went over the "Frogs on a log" problem, which is a textbook homework problem, and in which we 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.

Homework for chapter 2 is due Thursday, May 1.

Here are Vi Hart's Fibonacci number videos.
Here is a great site about Fibonacci numbers.
Here is a Fibonacci site with lots of pictures and interactive applets.
Here is an interactive site that helps explain phyllotaxis, which is the pattern of spirals in many plants.
Here is a site about Pingala's possible use of the Fibonacci Numbers in ancient India.
Look up Rachel Hall who credits Indian mathematician/musician with the Fibonacci numbers - see her article "Math for Poets and Drummers" listed at her site.

Work on problems from chapter 2, which will be due next Thursday.

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

Thu., Apr. 17, 2014, Class 4
We went over homework problems, also material from chapters 2.1 and 2.2 on set theory and logic, and learned about the New Math, the space race, and Sputnik! Please turn in chapter 1 homework on Tuesday of next week.
Homework: chapter 2.1 and 2.2. We'll finish chapter 2 on Tuesday.

We also played what I call the Sorting Junk game and also the online game Set.
The game Set can be found here as a daily puzzle.
Here is a handout on the Sorting Junk game. Print out such handouts to include in your portfolio for the class.

I talked about the New Math and how it grew out of the launch of Sputnik - see this article.
I also talked about how the symbolism of set theory and logic was developed during the late 1800s and later to try to make all mathematics into an algebraic activity, and how that failed totally due to the work of Kurt Godel.

We played the game Ken Ken. Please go to the Ken Ken site and practive playing the game!

Tue., Apr. 15, 2014, Class 3
We went over some homework problems from chapter 1. We also learned about the Pascal-Khayyim number triangle and the Pigeonhole Principle.

Your first essay paper is due this Thursday on Turnitin.

Thu., Apr. 10, 2014, Class 2
We worked more on the {1,2}-Take Away Game (in which each player may remove either 1 or 2 counters on a turn, and the player taking the last counter wins. We developed a winning strategy involving leaving your opponent with a multiple of 3 on each turn, if possible.We also learned about a connection between the patterns in this game and the 3 by 3 magic square. Here's a handout on magic squares and modular arithmetic. We haven't covered all of the material in this handout yet, but will soon.

You should print out such handouts as the one above and include in your portfolio.

We learned about several number sequences which are important, including
The odds: 1,3,5,7,...
The evens: 0,2,4,6,...
The squares: 1,4,9,16,...
The triangular numbers: 1,3,6,10,15,...
The cubes: 1,8, 27, 64, 125, 216,...
The primes: 2,3,5,7,11,13,...
The Fibonacci numbers: 1,1,2,3,5,8,13,21,24,...
We also learned about the Online Encyclopedia of Integer Sequences (OEIS), started by mathematician Neil Sloane, at which you can find just about any number sequence you can imagine!

Tue., Apr. 8, 2014, Class 1
We played the pattern game. Here's a handout about the pattern game, please print and include in your portfolio.
We played the take-away game, in which each player removes 1 or 2 counters on each move, the last player to move winning.
Try to figure out the winning strategy in this game. Try to figure out the connection between this game and the pattern game we played at the beginning of class.

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, at the Mozilla etherpad site (at Mozilla click on "Create new public pad.")

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 if you have not already. I have added everyone to the class list already.

Many Links and Handouts from previous quarters:

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.

Here is the set of slides of fraction problems.
Here's a related handout on star polygons. Here are some materials on "modular arithmetic," which explains some of the properties we observed when looking at the rhythm patterns within circles:
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.

By the way, how is Halloween like Christmas?
Because Oct 31 = Dec 25 (do you know what this refers to? Hint: base systems...)
Here's a handout with a Ken Ken example, with solution explained, which will help you with one of the take home problems.

Here are articles on Nines Complement subtraction and the Gelosia mulitplication method.
Here are some other methods of addition, etc. Here's another such web site.

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.

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 the Fibonacci assignment, which is due next Tuesday, Feb. 4. Read it CAREFULLY and do everything it asks!!

If you have not gotten an etherpad site for your class journal, do so now.
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.

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.