M46, Spring 2011, Home Page

Class 20, Mon., June 13, 2011
We went over take-home exams, and also material of ratio and proportion.
We went over material on linear versus exponential functions.
Please do homework through 8.1
On Wednesday we will do the "Barbie" activity. Please bring any Barbie or Ken dolls you can.

Class 19, Wed., June 8
We went over more material on decimals, and examined how fractions are converted to decimals, and decimals are converted to fractions. We also saw a proof that the square root of two is irrational. Complete section 7.3 homework.
Next Wednesday we will do an activity on proportion and Barbie - if you have access to a Barbie (or Ken) doll, plan to bring it next Wednesday!

Class 18, Mon., June 6, 2011
We went over and discussed the standards document and material from chapter 7.

Class 17, Wed., June 1, 2011
We worked on some pattern and modular arithmetic questions, and worked more on writing story versions of the fraction problem 1-1/4 divided by 1/2 (your journal entry should include your reflections on why this was a difficult problem), as well as on decimal questions.
Here is the set of slides of decimal/ratio problems.
Here is the link to the transcript of George Vaccaro's battle with Verizon about the misplaced decimal point.
Here's Vaccaro's blog entries about the whole thing.

Do homework through section 7.2. Chapter 6 will be due next Wednesday.
Here is a handout on Egyptian fractions. We will discuss on Monday, and it will be due Wednesday.

Please read this set of California "Mathematical Practice Standards" and fill in the blanks after each section as to how we might have applied these standards this quarter. Plan to turn this in Monday, June 6.

Class 16, Wed., May 25, 2011
We went over several of the take-home problems, played "fraction war," and worked on several fraction problems. Homework includes writing a word problem that involves the calculation 1-1/2 divided by 1/2. Turn in chapter 5 homework next Wednesday, and do problems through section 6.2.

Class 15, Mon., May 23, 2011
We worked on take-home exams (Due Wed.), also began chapter 6 work on fractions (here are fraction problems from class).
Chapter 5 homework is due Wed. June 1 (Monday, May 30 is Memorial Day - no classes.)

Class 14, Wed., May 18, 2011
Group problems presented plus work on take-home exams.

Class 13, Mon., May 16, 2011
We worked on chapter 5 material and group problems.

Class 12, Wed., May 11, 2011
We worked in problem groups, and you will present your problem on Monday to your "vertical group."
We also learned about the use of modular arithmetic in error-detecting codes like the ISBN code, and saw some ways to represent addition and subtraction with positive and negative numbers.

Do homework through 5.2, and turn in chapter 4 homework on Monday.
Your take-home exam has been emailed to you and is due in two weeks on Wed., May 25. There were two emails with a total of 4 attached files that you should have received.
Begin working on the handout with problems on Patterns and Modular Arithmetic that we went over today, it is due next Wednesday.

Class 11, Mon., May 9, 2011
We heard reports based on student papers, went over Russian Peasant multiplication, which is similar to ancient Egyptian multiplication, and saw its relationship to binary arithmetic. We also went over the Euclidean algorithm for finding the GCD of two numbers, and worked on group problems (see below). On Wednesday we will again meet with the problem groups, and if we have time, meet in the "letter groups" to present the problems.
Please also complete homework through chapter 4.3. We will finish chapter 4 and begin chapter 5 on Wednesday, and chapter 4 homework will be due next Monday.

Class 10, Wed., May 4, 2011
Your paper is due at Turnitin.com by Monday, May 9. You will give a short (2-3 min. oral presentation on your report on Monday). See details below.

We went over material from sections 4.1, 4.2, and we began 4.3. Work on homework for sections 4.1 and 4.2. We assigned group problems and did the Clap Your Name activity. Here are the group assignments. You are responsible for presenting the problem in your row to the group with the letter above your name. On Monday we will work on the problems, and present them next Wednesday.

Class 9, Mon., May 2, 2011
We worked on some review problems involving the take-away game, modular arithmetic, and the concept of closed operations.
We also went over how to change from base ten to other bases, and some alternative calculation methods, including:
Nines Complement subtraction.
Gelosia mulitplication method
We also went over calculator usage.
Please do section 3.6 homework and turn in chapter 3 homework on Wednesday.
We will begin chapter 4 on Wednesday.

Class 8, Wed., April 27, 2011
We went over the exam, and looked more closely at how we really do calculations.
We also went over material from section 3.5, do homework through 3.5 for Monday.
Last day to have your looseleaf notebook in order is next Monday, May 2.
Last day to have your journal together and up to date is the Friday, Apr. 29 (if I noted at your journal site that you received credit 10/10, then I won't recheck until later in the quarter.)
Monday, May 2: bring a calculator (graphing or scientific) to class, as we will go over their use.

You have a short paper on a subject related to the course that catches your interest due Monday, May 9 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, Mon., April 25, 2011
We had exam 1 and went over sections 3.2 and 3.3. Do homework through 3.3, but turn in chapter 2 homework (only) on Wednesday, Apr. 27.

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."

Class 6, Wed., April 20, 2011
We learned about the use of attribute blocks and played the Sorting Junk game (print out this handout and place in portfolio!)
We also went over a few problems and learned about several ancient numeration systems. Please complete homework through section 3.1. Exam on Monday is open book/open notes, and will go through end of chapter 3.1. It is mostly multiple choice, with some non-multiple choice. Bring a scantron (the half page brown or green type). Also bring your portfolio, as I will check them during the exam. See below for description of what should be there.

We also reviewed the Pascal/Khayyim triangle, prime numbers and other patters, and saw a video by Vi Hart about such patterns. See Vi Hart's math doodle site.

Class 5, Mon., April 18, 2011
We reviewed the pigeonhole principle, and also patterns involving square numbers and odd numbers.
We went over some homework problems and new material from chapter 2 involving set theory notation and concepts, and basic ideas about how to model calculations using counters or measurement (number line).
We also did the Where's Fido? puzzle, and played the game Ken Ken - this site has 6 new puzzles every day. Please work the additional puzzles in the Where's Fido? handout, and go to the Ken Ken site and try several of their puzzles too.

Melissa Aguilar will run two help sessions in the math tutoring center for this class, Tuesday (tomorrow, Apr. 19) from 1-2 PM, and Wednesday Apr. 20 from 2:15 to 3:15, hope you can make use of them!

Also, work on homework for the rest of chapter 2 - that will not be due to be handed in till next Monday.

Class 4, Wed., April 13, 2011
We played the game Set, see their daily puzzle.

We went over homework form chapter 1. ALL of chapter 1 homework (including 1.4 and 1.5) is due Monday, Apr. 18. I do not accept late work.
We also went over a number of important sequences: triangle numbers, squares, Fibonacci numbers, primes.
We learned how to count the spirals on a pine cone.
Do the Fibonacci assignment, (to be turned in next Wednesday, April 20.)

Class 3, Monday, April 11, 2011
We went over problems from chapters 1.1-1.3, and material from chapter 1.4, including the pigeonhole principle.
Homework for chapter 1 will be due next Monday, April 18. We will finish chapter 1 on Wed., and go on to chapter 2.
Here are the two powerpoints I showed in class today: Modular Arithmetic. "Pascal's" Triangle. For more on Pingala, see
Rachel Hall's site. She credits this Indian mathematician/musician with the Fibonacci numbers - see her article "Math for Poets and Drummers" listed at her site.

Please upload your math autobiography by 11:59 PM tonight!
Please send me your journal page if you have not done so yet.

Class 2, April 6, 2011
On Monday your Math Autobio is due on turnitin.com, and you should have worked on problems from sections 1.1 to 1.5 (see the green sheet for the problem list and the math autobio outline). No need to copy the problems, but you should not just write down the answers, show your work. I will not collect chapter 1 homework at least until Monday, Apr. 18, we need to leave time for class members to have gotten their books. I grade homework for completion and attempts, not correctness.
You should also have two journal entries, and you should have emailed me your etherpad journal site by Monday.

In today's class we went over the take-away game and the pattern game and saw how multiples of 3 appear in the same way in both. We also introduced modular arithmetic notation, and examined the 3 by 3 magic square, and its use in a "Sum to 15" game, which may be reconfigured to become the game tic-tac-toe. The 3 by 3 magic square also has mod 3 patterning in its structure.

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.
(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.

By the way, here are some of the vocabulary words we used during the past two 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

We went over more details about use of software and web sites:
The class web site will be (until further notice) this site.
The Course Studio site started behaving badly already, and I did not want to wrestle with it!!

At the bottom of this page you'll find all the textbook homework assignments, as well as lots of links and handouts.

For the Math Autobiography, use turnitin.com.
You should have received an invitation to join if you are not a member.
The class ID number for Math 46 is: 3953105
The password is: WriteMath
We will also use Turnitin.com for the other paper.

For the journal let's use etherpad. This is a service that gives you an immediated web site that you can freely write and edit at. A number of companies provide free etherpad sites. I suggest either
Piratepad.net
or
ietherpad.com
The latter lets you rename your URL anything you like (for example ietherpad.com/MyMath46Journal. However that might be a poor choice since someone else might guess that name. Better to use the weird code they assign you. Once you have the site, copy and paste your journal entry already at Turnitin.com to the eitherpad site and just use that. I'll close down the turnitin.com journal assignment. Or just start entering your journal entries at your etherpad site.

You must email me your etherpad site URL.

Again, for info on past Math 46 classes, go to
Karl Schaffer's Home Page

Class 1, Mon., Apr. 4, 2011
We played the pattern game and the "take-away" game.
Try to figure out a winning strategy for the take-away game.
A winning strategy for this game is a set of rules that will determine whether the first or second player has a guaranteed win if that player plays the best game possible, and what steps that player must take to guarantee a win. In this game the player with the winning strategy is determined by the number of tokens at the start of the game. For example, if there are 14 tokens, as in class, there is a winning strategy for the first player. What is it?

Please work on homework problems from sections 1.1, 1.2, and 1.3 for Wednesday.
Homework is collected at the end of each chapter.
Begin writing your journal. You should place journal entries at the turnitin.com site.A
You should have received an email from turnitin.com notifiying you of your inclusion in the turnitin class.
The Turnitin ID# for this class is 3953105, and the password is WriteMath.
The site with info on past Math 46 classes is
http://nebula2.deanza.edu/~karl/
Click on Math Classes at the top of the page.
The login name is damath
The password is kmath

(1) Get your textbook! (See green sheet.)
(2) Assignment: Ch. 1.1, 1.2, and 1.3 (see problems below).
(3) We worked on the pattern game and associated problems.
(4) We worked on the the take-away game.
(5) Put together your portfolio, a looseleaf notebook with these sections:

(6) Write a journal entry for each class Again, should be one long or several short paragraphs detailing your reflections on today'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

Here's a complete list of the HW from the textbook:
Ch. 1.1, # 2,4,9,10,11,12,14,15
Ch. 1.2, # 5,8,10,20,24
Ch. 1.3, # 4,7-11,14
Ch. 1.3: # 20,21,24
Ch. 1.4: # 1,9,13-15,19
Ch. 1.5: # 1,3,5,6,7,9,10,12,15
Ch. 2.1 #8,9,11,14.15,16-20,25,26
Ch. 2.2 #1,9,12,13,17,22,28,31,34
Ch. 2.3 # 5,6,7,10,14,18,19,26,27,31
Ch. 2.4 # 1-5,7,9,11,15,17,26,32
Ch. 3.1: # 1-5,9-10,25
Ch. 3.2 # 1,5,10,15,16,20
Ch 3.3 # 1,3,5,9a,d,17,21,25
Ch. 3.4 # 3,17,19-24
Ch. 3.5 # 1-3,8-10,15,16,18,19,20,32Ch. 3.6 # 1-4 (a) only, 9,18
Ch. 4.1 # 5-9 part a only, 10,13,15,17-19,21,30
Ch. 4.2 # 1-4,8,9
Ch. 4.3 # 1-5 part a only, 6-13,19
Ch. 4.4 # 10, 13,16
Ch. 5.1 # 1-3,7,8,13-16,19,20,22,24
Ch. 5.2: # 1-3 a,b,c, 13,17-22,27,31
Ch. 5.3 # 10-13
Ch. 5.4 # 1-15 part a only, 20,21
Ch. 6.1 # 1-21 odd and part a only, 26,27, 29,30,31
Ch. 6.2 #1-20, part a only.
Ch. 6.1 Also do 26,27,29-31
Ch. 6.2 Also do 28,29,31,33,34
Ch. 6.3 # 1-21, part a only, 29,34
Ch. 7.1 # 1-6 part a only,16-18
Ch. 7.2 # 1-7, part a only, 15-17,19,20,27
Ch. 7.3 #1-3,10,14-16,26
Ch. 7.4 #1-4,5-13,16-18
Ch. 8.1 # 7,8,11,20,23
Ch. 8.2 1-17,24,25,27,28
Ch. 8.3 #24-27, 31,32,34,35

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

Group->	A	B	C	D	E
4.1 #10,17	John	Adrianna	Jacqui	Michelle	Brian
4.1 #18,19	Sarah	Valerie	Araceli	Emily	Maria M
4.1 #25,30	Veronica	Rabia	JuliaRose	Winnie
4.2 #9,11	Nicole	Blair	Ida	Christian	Allegra
4.3 #19,20	Ramin	Fatima	Laura	Sukamrit	Maria C.
4.4 #13,15	Amanda	Kathryn	Aimee	Sonia	Romulo
4.3 # 21	Kendell	Gurjeet	Shannon	Delaram	Shilpa

Math 46, Spring 2011, Home Page Green Sheet Return to Karl Schaffer's Home Page

Math 46, Spring 2011, Home Page
Green Sheet
Return to Karl Schaffer's Home Page