Math 46, Fall 2008 Home page

Green Sheet

Class 21, Th., Dec. 4

Here is a review sheet with much more detail!
Here are some hints and answers for the review sheet. But don't look till you've tried them!

Essay question. In an effort to make this class more about process than exact answer, we will have an essay question worth 15 percent of your final exam grade. (That means I will grade it closely!)
This course has focused on mathematical problem solving. John Van de Walle has defined a mathematical problem as any task or exploration:
    · for which the solution has not already been explained,
    · that begins where kids are (that is, begins with their ideas),
    · that is challenging mathematically, and
    · for which justification and explanations for answers, methods, and results are understood to be the responsibility of the students.
Read this interview with Van de Walle, and make your response to it in terms of what we have done - or not done - in this class the subject of your essay.

Have your experiences in this class challenged, changed, had no effect on, or reinforced
your ideas about teaching mathematics through problem-solving? Be specific, give
concrete examples to support your statements, write at least two good sized paragraphs (400  words - so you can get an idea about this, the red text here includes about 300 words!)
– you may insert what you write at home inside the exam, if you'd like to write it before the exam.

In your essay, mention which statements of Van de Walles' that you are commenting on.

Do not write in vague generalities, refer to specific topics and ideas we have studied this quarter. Each and every sentence should convey factual information that supports your point of view! Be specific, mention specific facts or ideas or problems we have studied, in supporting your argument. I don't care whether you liked or didn't like the class, just how well you support your point of view with details about the coursework and its relation to the ideas expressed by Van de Walle.

During the final I'll check your portfolios and check homework one more time, so be sure to bring them to class!

We reviewed, especially Poinsot stars, ratios, fractions, linear functions.
Watch this space for review sheet.

For more on the math/dance stuff I do:

Here's info on the performance we're doing Sunday.

Listen to the interview with of Sept. 12, 2008, on The Math Factor, the podcast by the Univ. of Arkansas' Chaim Goodman-Strauss.

Discoveries and Breakthroughs in Science May 2008 story + video clip on Erik Stern and my work integrating math and dance (click on "Do the Math Dance," under the mathematics heading).

Class 20, Tue., Dec. 2
We went over the exams, learned about Egyptian fractions, and also worked on arithmetical sequences (or linear functions) and geometric sequences (or exponential functions). New homework:
Ch. 8.1 # 7,8,11,20,23
Ch. 8.2 1-17,24,25,27,28
Thursday will be review.
Here's a study outline for the final exam, from a recent quarter (yours will be similar). Will be working on a more detailed guide shortly, stay tuned.
Here's an interesting story about a high school student, Britney Gallivan, who broke the record for folding a single sheet of paper, and worked out the mathematics involved as well.

Class 19, Tue., Nov. 25
We saw that all fractions give rise to either terminating or repeating decimals. The ones that terminate must have (in lowest terms) denominators with only the primes 2 and 5 as factors. On the other hand, repeating decimals may easily be converted to fractions by dividing the "repetend" by a string of 9's of the same length. We also saw Euclid's proof that square root of 2 is irrational.

Then we did the Barbie activity.

We will go over Egyptian Fractions, among other things, on Tuesday.

Homework:
Ch. 7.3 #1-3,10,14-16,26
Ch. 7.4 #1-4,5-13,16-18

Class 18, Thu., Nov. 20
We went over more about fraction division, also new material on percentages and decimals.
If you did not have all ch. 5 and 6 HW today, bring on Tuesday.

IMPORTANT NOTE: if your student ID has either of the first two digits equal to 0, then you MUST change that digit to 7. There was a typo in the exam. By the way, there will only be 7 problems on this take-home exam.

Tuesday: we'll do an activity using Barbie or other dolls and the concept of proportion. Bring such a doll if you have one (Ken or Gi Joe or Bratz are also good for this activity.) Also print out and bring the Barbie handout to class on Tuesday.

New homework, due after Thanksgiving:
Ch. 7.1 # 1-6 part a only,16-18
Ch. 7.2 # 1-7, part a only, 15-17,19,20,27

Class 17,  Tue., Nov. 18, 2008
We worked on the take-home problems and on fractions.
Homework:
Ch. 6.3 # 1-21, part a only, 29,34
I will check ch. 5 and 6 homeowork on Thursday.

Class 16, Th., Nov. 13, 2008
Oral reports.

Class 15, Tue., Nov. 11, 2008
We went over some homework and spent a lot of time on fractions.
Think about the baseball addition problem: why, if a player hits 4 out of 5 and then 1 out of 3 in the two games of a double-header, is the player's average for the two games (4+1) out of (5+3)?
Also, if Delia cuts a lawn 3/2 as much as Sophia, how should they divide the $25 income?
Papers due Thursday.

Take-home exam - here are 7 of the 8 problems.
Here is the list that goes with the exam.
Bring to class on Thursday, you will have time to work together on the problems.

New Homework:
Ch. 6.1 # 1-21 odd and part a only, 26,27, 29,30,31
Ch. 6.2 #1-20, part a only.

Class 14, Thu., Nov. 6, 2008
We went over earlier handouts, the voting problem, and I took up the Fibonacci handout. The Poinsot Stars handout is due on Tuesday. We also went over sections 5.3, 5.4, and 6.1.  Your papers are due on Thursday of next week.
Homework from text:
Ch. 5.3 # 10-13
Ch. 5.4 # 1-15 part a only, 20,21
Sections 6.1 and 6.2 HW will be assigned for  next Thursday.
I will either hand out on Tuesday or post here the take-home exam, along with due date updated to give you two weeks to work on it.

Class 13, Tue., Nov. 4, 2008
We went over electoral mathematics, in honor of today being election day!
Here are the homework problems on voting; we did number 1 in class, please work out the problem on the 1980 New York Senate race for Thursday. The site I referred you to is FiveThirtyEight. Here is a site that explains the various voting methods we talked about today. Especially look at the 3rd section of the site.

We also went over the group problems, and will finish on Thursday. Also bring your Fibonacci number assignment on Thursday, the Poinsot Stars handout, and the magic square homework problems, to turn in.

Class 12, Thu., Oct. 30, 2008
We went over the group problems. You will present your problem on Tuesday, please be prepared! (You'll have a few minutes to meet with your problem group before we split up into presentation groups A through F.)

Here is the  Fibonacci number assignment.  I'll let you turn it in on Thursday, since I was late getting it up here.

Here are some links to Fibonacci sites, please take a look at them:
A great site about Fibonacci numbers.
Here's another Fibonacci site with lots of pictures and interactive applets.
Here's an interactive site that helps explain phyllotaxis, which is the pattern of spirals in many plants.

Print out and bring the Poinsot Stars handout, and try the problems. We went over this briefly in class. We'll do some work on it in class Tuesday also.

Here are the magic square slides that I showed on Thursday, and here are the magic square homework problems, please complete them also as part of your homework.

You have a short paper on a subject related to the course that catches your interest due in several weeks, and worth 5% of your grade. Due date Thursday, Nov. 13. 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.

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 library.

I will check homework for chapters 3 and 4 while you do your problem presentations.

New Homework:
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

Class 11, Tue., Oct. 28, 2008
We went over homework problems and set up problem groups - will post them here shortly. We also went over sections 4.3 and 4.4. We also did the least common multiple "Clap your name" activity.
Homework:
Ch. 4.3 # 1-5 part a only, 6-13,19
Ch. 4.4 # 10, 13,16

Class 10, Th. Oc.t 23, 2008
We went over exam 1, also briefly, calculators, divisibility tests and GCD and LCM.
Homework:
Ch. 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
I'll add something later this weekend about the next writing assignment.

By the way, here's how the site "How things work" describe basketball player's 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 9, Tue., Oct. 21, 2008
We went over the Fibonacci numbers, learned how to find the Fibonacci numbers on pine cones, looked at mental arithmetic methods, and began to look at number theory by investigating prime factorization and divisors.

For Thursday, find the largest sum 3- and 4-letter words, where A counts as 1, B as 2, C as 3, ..., Z as 26.
Also for Thursday, write your own "mnemonic" for PEMDAS, the order of operations.

Please bring a scientific or graphing calculator to class on Thursday.
Homework:
Ch. 3.4 # 3,17,19-24
Ch. 3.5 # 1-3,8-10,15,16,18,19,20,32

Class 8, Thu., Oct. 16, 2008
We went over sections 3.2 and much of 3.3 and some of 3.4.
Here's a site on number systems. (Note that this site talks about a more standard base 20 system that the Mayans also used.) Here's a site showing number systems associated with languages. Here's another site with links to number system sites.
Please remember to write one journal entry per class.
Do the homework for 3.2 and 3.3:
Ch. 3.2 # 1,5,10,15,16,20
Ch 3.3 # 1,3,5,9a,d,17,21,25

Here are solutions to the study guide for the first exam problems. We did not get to some of the problems in this guide that we usually get to, so I'll replace them with problems that more similar to those we did work on.

Class 7, Tue., Oct. 14, 2008
We went over homework from chapter 2 and also some of chapter 3.1. Your exam will cover chapters 1 and 2, and there might be a question on the part of 3.1 that we covered.
Homework:
Ch. 3.1: # 1-5,9-10,25

Here are solution to the patterns and modular arithmetic handout.

I will check your homework for chapters 1 and 2 during the exam, as well as whether you have the portfolio in order, and also look at your journals (have one entry per class).

Class 6, Thu., Oct. 9, 2008
We went over the modular arithmetic homework. We played the Sorting Junk game!
We also went over material from sections 2.3 and 2.4.

Here's a study guide for the first exam. We'll look at the game Set, mentioned in one of the problems, on Tuesday. But you should look at the Set site and try to play the game before class.

Homework:
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
Check this site in the next couple of days for more info on the first exam, which is next Thursday, Oct. 16.

Class 5, Tue., Oct. 7, 2008
We did the "How do we calculate" activity during the first hour, and the "Where's Fido?" activity during the second hour, also introduced sections 2.1 and 2.2.
Read the Where's Fido? handout and try to work the problems in it.
Homework:
Ch. 2.1 #8,9,11,14.15,16-20,25,26
Ch. 2.2 #1,9,12,13,17,22,28,31,34
On Thursday, have homework completed for chapter 1, also the handouts
Modular arithmetic intro
Patterns and Modular Arithmetic

Class 4, Thu., Oct. 2, 2008
We went over more chapter 1 problems, also the pigeonhole principle, a bit about the prime numbers, the triangle numbers, and several base systems, an intro to the Fibonacci numbers, and more about modular arithmetic.

Here are some links to Fibonacci sites, please take a look at them:
A great site about Fibonacci numbers.
Here's another Fibonacci site with lots of pictures and interactive applets.
Here's an interactive site that helps explain phyllotaxis, which is the pattern of spirals in many plants.

Finsh HW from 1.1-1.4, work HW problems for section1.5:
Ch. 1.5: # 1,3,5,6,7,9,10,12,15
Also work the problems on these two handouts:
Modular arithmetic intro
Patterns and Modular Arithmetic

Here's that modular arithmetic powerpoint: Modular Arithmetic Powerpoint slides
Be prepared to turn in the handouts on Tuesday.

Class 3, Tue., Sep. 30, 2008
We went over some chapter 1 problems and some voting math "mental arithmetic" problems.
Homework:
Ch. 1.3, # 4,7-11,14, 20,21,24
Ch. 1.4: # 1,9,13-15,19

Class 2, Tue., Sep. 25, 2008
We went over the pattern problems, also the "Frog on a Log" problem, and the Take-Away game, and did the Electoral College quiz.
Homework: Turn in your math autobiography on Tuesday (see Green Sheet). Also begin work on the problems at the end of chapter 1, but Iin chapters 1.1 and 1.2, but I won't collect them on Tuesday.
I'll place more background here shortly on voting math, check in again in a day or two.

Class 1, Tue., Sep. 23, 2008

We played the "pattern game." We also worked on the "Frogs on a log" problem. And we played the "Take Away" game with 15 counters.

I will ask you to write a journal entry for each class. For the 1st class, please write a description of what your expectations for the class were, and how they were met or not during the first class. I'll talk more about the journal on Thursday.

By Thursday: Get a loose-leaf notebook, make separate sections for
Paper due next Tuesday: Mathematical Autobiography, description on page two of the Green Sheet

Homework:
(1) Get your textbook! (See green sheet.)
(2) Begin reading Ch. 1. At the bottom of this page, see the complete list of HW problems. Start working on those from section 1.1 (I won't collect them on Thursday though, since some of you don't yet have the text.)
(3) During class I had you create a 6 by 6 pattern, with columns numbered 0,1,2,3,4,5, and rows numbered 0,1,2,3,4,5. Figure out what will be in boxes (75,0), (75.75), (200,0), and (200,200), and write an explanation of why you think your pattern extends in the way you say. I plan to collect these.
(4) We also worked on the "Frogs on a log" 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
We 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.)
(5) We played the "Take Away" game: starting with 15 counters, two players alternate removing 1, 2, or 3 counters. Whoever takes the last counter wins. Figure out a winning strategy for one of the players (that's a plan or strategy that allows that player to always win, no matter what the opponent plays.) Is there a guaranteed win for the 1st or for the 2nd player? Play the game with someone not in the class. Write a description of what you think the winning strategy is, and which player has it.

Three round frogs (O's) and three crossed frogs (X's)  are sitting on a log with seven spaces, and want to take each other's places. A frog can move one step to a vacant square, or jump over one neighbor to a vacant square. In class we showed how it can be done in 15 moves.
O
 O
 O
  
X
 X
 X

Two frogs on a three space log can take each other's places in three moves:
O
   
X

Four frogs on a five space log can change places in 8 moves, as we also discovered in class.

O
 O
  
X
X

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 # 1-3,8-10,15,16,18,19,20,32
Ch. 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

Review problems chapter 1 on page 68-71, do #2,9,14,17,22