Math 46, Winter 2009 Home page
Green Sheet
Class 21, Mar. 17,. 2009
We went over some of the take-home problems, also finished group
problems.
Ch. 7.3 #1-3,10,14-16,26
Ch. 7.4 #1-4,5-13,16-18
Here's the musical
scales handout.
Classes 19,20, Mar. 3,10
Sub went over materials from chapter 7, also facilitated group work.
Please be working on the chapter 7 HW:
Ch. 7.1 # 1-6 part a only,16-18
Ch. 7.2 # 1-7, part a only, 15-17,19,20,27
Class 18, Th., Mar. 5, 2009
We went over more of chapter 6.
Class 17, Tue., Mar. 3, 2009
We went over sections 6.2 and 6.3, also a variety of fraction
problems.
New homework:
Ch. 6.2 #1-20, part a only.
Also
do 28,29,31,33,34
Ch. 6.3 # 1-21, part a only, 29,34
Here is the take-home exam,
and
here is the "list."
Class 16, Th., Feb. 26, 2009
We did most of the group problems, we'll finish them on Tuesday.
We went over some of the problems in the Poinsot
Stars handout (they are also known as star polygons),
please work on this for Tuesday.
We also began the new chapter on fractions.
New homework:
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
Class 15, Tues., Feb. 24, 2009
We spent a lot of time on the group problems. You will present
your problem on Thursday. We have also covered 5.2 and 5.3, and most of
5.4.
Ch. 5.2: # 1-3 a,b,c, 13,17-22,27,31
Ch. 5.3 # 10-13
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 Thursday also.
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A
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B
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C
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D
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E
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3.4 #21
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Rebecca
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Crystal |
Jade
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Alissa
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Hsueh Er
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4.1 #10,17
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Tracey
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Marie
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Bethany
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Yi
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Damen
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4.1 #18,19
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Gina |
Chi |
Rachael
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Natialie |
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4.1 #25,30
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Richard
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Zoe
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James
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Danielle |
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4.2 #9,11
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Marika |
Luis |
Julianna |
Praveena |
Ashley
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4.3 #19,20
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Leisa
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Jared
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Joana
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Wendelyn
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Katherine
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4.4 #13,15
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David
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Kathy N. |
My
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Vicky
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Dwiharini
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Blue
= absent Tuesday
Class 14,
Feb. 19, 2009
We went over sections 4.4 and 5.1, and finished 4.3.
New homework:
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
You were all assigned problems for group work, but the chart was
inadvertently erased. If you know the people in your group, please
email
me their names, and the problem you were assigned. If you were not
there
you will be assigned a problem later, when I have the chart redone!
By the way, why does the math geek confuse Halloween and Christmas?
(Hint: "Octal" refers to base 8...)
Class 13, Feb. 17, 2009
We heard reports and went over a few homework problems, then
started "Clap your name."
We'll continue with that on Thursday. We have also started section 4.3
on greatest common divisor and least common multiple.
Some links arising from today's discussion:
Tom Noddy, the Bubble Guy
Brookings
Report on misplaced algebra students
Who was Sonya
Kovalesky?
Article
on gender and mathematics
There's a short version of what we did with the name-clapping here.
Class 12, Feb. 12, 2009
We spent time on the new puzzle, KenKen - at the site you can find
some more puzzles!
Please read this short interview
with Will Shortz about it.
Your paper is due Tuesday, see description below; please READ the
description and use as a guide to what you write about!
I will collect handout
on language and mathematical properties next week also.
For Tuesday, find the largest sum 3- and 4-letter words, where A counts
as 1, B as 2, C as 3, ..., Z as 26.
We went over sections 4.1 and 4.2, do the HW from those sections.
If you are interested in mathematics and the arts, here's an
announcement about mathematical
plays about one-sidedness. to be performed in Berkeley this coming
Monday.
Class 11, Feb. 10, 2009
We did the Fibonacci number
activity. Can you, as part of your journal entry for this class, give
an explanation as to why this game produces the Fibonacci numbers?
(That is, an explanation that others not in the class might read and be
able to understand.)
We also went over sections 3.5 and 3.6, do the HW for those sections.
Can you think of a film in which someone was filmed walking backwards,
the film was reversed to show them walking forwards? This would be an
example of a negative of a negative is a positive.
Class 10, Feb. 5, 2009
We went over homework from chapter 3, and also sections 3.3 and
3.4.
Bring a scientific or graphing calculator to class on Tuesday.
Here is the Fibonacci
number assignment, turn in Tuesday as a "quiz."
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.
Do the Chapter 3.3 and 3.4 homework.
Class 9, Tue., Feb. 3, 2009
We went over the exam, also the Modular
arithmetic intro and Patterns
and Modular Arithmetic handouts. They are both due Thursday.
We also went over sections 3.1 and 3.2, do the HW through section 3.2.
You should have printed out and be working on the questions in this handout
on language and mathematical properties.
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
Tuesday, Feb. 27. 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.
Class 8, Thu., Jan. 29, 2009
We had first exam, but also went over parts of chapter 2.1, and also
some new material on modular arithmetic.
Here is the article I mentioned by Keith Devlin on
teaching math by counting or by measuring.
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.
(1) Do HW from chapter 3.1.
(2) Also, do the problems in these handouts, and be prepared to
turn them in Tuesday:
Modular arithmetic intro
Patterns and Modular Arithmetic
(3) Please print out and answer the questions in this handout
on language and mathematical properties.
(4) Please remember to write one journal entry per class.
Class 7, Tue., Jan. 27, 2009
We did the Calculation Activity and saw slides about the Brazilian Street
Math study (this is a link to an article on the study.)
We also went over some homework from 2.3 and 2.4.
Turn in the Calculation Activity worsheet on Thursday - complete ALL
questions!
First exam on Thursday.
Here are
solutions to the study guide for the first exam problems.
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., Jan 22, 2009
We went over many homework problems, also did the "Where's Fido?" activity.
Please read the problems in this handout for next time.
Here's a study
guide for the first exam from last quarter. So far, we've covered
most of these topics.
Do homework for sections 2.3 and 2.4.
Class 5, Tue., Jan. 20, 2009
We went over homework, including some pigeonhole principle
problems, also sets and Venn diagrams, the game Set, and played the Sorting
Junk game! Look at the Set site and try to
play the game again before class.
Please print out these handouts, and bring them to class on Tuesday:
Modular
arithmetic intro
Patterns
and Modular Arithmetic
You should be writing several paragraph journal entry for each class!
Do homework for sections 2.1 and 2.2
Class 3, Thu., Jan. 15, 2009
We went over the take-away games we played last class, and saw how they
were related to the concept of remainder.
We also went over some homework problems from sections 1.1, 1.2, and
1.3, and then went over material from 1.4 and 1.5, especially the
pigeonhole principle and inductive versus deductive reasoning.
Please print out these handouts, and bring them to class on Tuesday:
Modular
arithmetic intro
Patterns
and 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.
Do homework for text sections 1.4 and 1.5.
Class 2, Tue., Jan. 13, 2009
We went over some HW, especially magic squares,
and
their relationship to
Latin squares.
Also went over Polya's
problem solving
techniques.
We worked on the perimeter problem, and also played a take-away game:
(1) Two players begin with 11 counters. Each may remove either 1 or 2
counters on a move. The player who removes the last counter wins.
What is the winning strategy, and which player, first or second, has
that winning strategy?
(2) What if the players start with 50 counters. Who has the winning
strategy, first or second player, and what is that strategy?
(3) Given any starting number of counters, how do you determine who has
the winning strategy?
(4) Suppose that instead each player may remove either 1,2, or 3
counters on a move. Which player has the winning strategy, and what is
it?
(5) In this new version, given any starting number of counters, how do
you determine the winning strategy, and which player has it?
Do the homework at the bottom of this page for sections 1.2 and 1.3.
Class 1, Thu., Jan. 8, 2009
We went over the pattern game, and also worked on the jumping frog
problem.
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 Tuesday though, since some of you don't yet have the text.)
(3) Here is a handout describing the
pattern game we played in class, and showing the pattern we used.
Figure out what will be in box (100,100), and write an explanation of
why you think your pattern extends in the way you say.
(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
Figure out how to do these exchanges also, in the minimum number of
moves. (See below for more explanation.)
(5) Get a looseleaf notebook, create sections for the
following, and bring to class on Tuesday. Write two paragraphs giving
your thoughts, feelings, response to today's class, as your first
journal entry. Bring this to class
Tuesday!!
- Homework
- Handouts
- Exams
- Journal
- Class notes
- Articles
- Your papers
(7) Paper due next
Tuesday: Mathematical Autobiography, description on page two of
the Green Sheet
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 many of you discovered how it can be done in 15 moves.
Two frogs on a three space log can take each other's places in three
moves:
Four frogs on a five space log can change places in 8
moves, as we also discovered in class.
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