Math 46, Spring 2008
Home Page
Green Sheet
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!
Here's the list of fraction solutions
from the take-home exam.
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.
I'll try to update this information shortly with something a little
more specific, and will email the class at that time.
During the final I'll check your portfolios
and check homework one more time, so be sure to bring them to class!
Class 22, Thu., June 12
We went over a variety of problems similar to final exam problems.
Stay tuned for more info on the final.
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 essay
that I'd like you to read and write about for the final. I'll post
an essay question about it shortly.
Here's another
article by the same author, John Van de Walle, in case you want more
background on his thinking.
Class
21, Thu., June 12
We went over a bit more material on decimals, also looked
at the difference between exponential and linear functions. In the process,
we discovered a lucky dime that came up heads 8 times in a row. I'm keeping
it.
Class 20,
Thu., June 12
We did the Barbie activity.
We also spent time looking briefly at algebraic representation. Please
do the pool handout and bring to class
on Tuesday.
We also worked some on a few percentage/decimal place problems.
Ch. 8.1 # 7,8,11,20,23
Here's one additional problem to work on: A shipment of watermelons weighing
10,000 pounds is allowed to sit in the sun for several days. Before sitting
in the sun the watermelons are found to be 99% water. Afterwards they are
98% water. How much do they weigh now?
Class 19, Tue., June 10
Thursday: 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 Thursday.
We spent nearly all of class listening to reports. They were excellent!
Class 18,
Th., June 5
Your paper on a
chapter or two from a book related to this class is due next class, Tuesday,
June 10. The paper should be a 600 word summary of what you learned, how
it is related to the class, and what about it intrigued you. Was there a
particular reason you chose your topic - explain. I may ask you to give a
brief (2 minute) oral summary on Tuesday.
We went over fraction material, as well
as new material on percents, ratios, and proportion.
We also had a discussion about pi.
A bill was once
introduced in the Indiana Legislature that would have established the
value of pi as 3.2.
Here's a link to pi day.
Here are the first
million digits of pi.
New homework:
Ch. 7.3 #1-3,10,14-16,26
Ch. 7.4 #1-4,5-13,16-18
If you can read Spanish, here's an article in the
Costa Rican national newspaper about
the conference I attended last week (some work I did with students
there is mentioned in the article).
Here's that link to a recent online
story about the math/dance work I do (under "math and computers, click
on "Do the Math Dance," it has a short video clip).
Class 16, Tue., June 3, 2008
We went over fraction homework problems, and
started on 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
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
Tue., June 10. 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.
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)
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 15, Thu., May 29, 2008
Sub Renuka Kapur had you do the musical scales
handout, and went over fraction material.
Class 14, Thu.,
May 22, 2008
We worked in class on the take-home
problems, and went over material from chapter 6 on fractions.
Here's the new homework from chapter 6:
Ch. 6.1 # 1-21 odd and part a only, 26,27, 29,30,31
Ch. 6.2 #1-20, part a only.
Here's the Homework that will be due next Tuesday:
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
Your take-home exams are due in class Thursday, May 29.
Class 13, Tue., May 20, 2008
We
worked in the problem groups, and also saw a bit about "amicable numbers."
We briefly went over sections 5.1 and 5.3, which material we've covered
already.
New homework:
Ch. 5.3 # 10-13
Ch. 5.4 # 1-15 part a only, 20,21
By the way, here is a video story on some
of our math/dance work.
Bring your take-home exams on Thursday, we'll work on them some in class.
Class 12, Thu.,
May 15, 2008
Sorry this is so late getting out. We worked
on the group problems, which will be due on Tuesday.
We also went over sections 5.10 and 5.2.
Here is your take-home exam,
due a week from Thursday.
Here is the fraction list that goes
with the exam.
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.,
May 13, 2008
We went over some HW problems, collected exam
corrections, and did the "Clap your name" activity. We also went over least
common multiple, greatest common divisor, and the use of modular arithmetic
in check digit codes.
I forgot to place the PEMDAS assignment here. Come up with a replacement
for "Please Excuse Dear Aunt Sally" as a memory device for order of operations.
By the way, here is a main site
for doing distributed computing such as SETI on your home computer.
It's run out of UC Berkeley.
Ch. 4.3 # 1-5 part a only, 6-13,19
Ch. 4.4 # 10, 13,16
Here are the problem groups:
Group->
|
A
|
B
|
C
|
D
|
Ch. 4.1, #10 and 17
|
Ashley
|
Carrie
|
Amanda O.
|
Bryan
|
| Ch. 4.1, #18 and 19 |
Pam |
Jessica
|
Grace
|
Crystal
|
Ch. 4.1, #25 and 30
|
Nancy
|
Carmen
|
Courtney
|
|
| Ch. 4.2, #9 and 11 |
Pearline
|
Amanda S.
|
Katelyn
|
Jose
|
Ch. 4.3, #19 and 20
|
Xiong
|
Samuel
|
Jayson
|
Amanda G.
|
| Ch. 4.4, #13-15 |
|
|
|
|
We'll work on the problems on Thursday, and present next
Tuesday.
Class 10, Thu.,
May 8, 2008
We went over sections 3.6, 4.1 and 4.2.
Your corrections to the exam are due on Tuesday.
I've set up a class yahoo web group at
http://groups.yahoo.com/group/math_46/
You should have received an email invitation to join the group. Let me
know if you did not. Please use the discussion group to work on the exam
corrections - or anything else associated with the class.
New homework:
Ch. 4.1 # 5-9 part a only, 10,13,15,17-19,21,30
Ch. 4.2 # 1-4,8,9
Class 9, Tue.,
May 6, 2008
Important: Your corrections to
exam 1 are due next Tuesday. In order to receive 1/2 the points missed, you
must:
(a) Correct all incorrect answers on the exam itself near the incorrect
answer - do not use extra sheets. (Write small!)
(b) Make a short statement explaining what your error was, if it was
a problem that did not originally require an explanation.
(c) Cross out the incorrect answers with a single line (do not erase)
so that I can see what the original error was.
(d) Use a different color ink or pencil for your corrections, and circle
the correct answer.
(e) If all corrections are correct, you will receive 1/2 of missed points
on the exam.
(f) Turn in at start of class on Tuesday.
(g) You may work together outside of class,
but your work may not look exactly like someone elses!
(h) We won't take any more class time. Be prepared to stay after class,
or work with other students before class, if you want to work together.
We went over the Brazilian street math
study (also see Keith Devlin's other article
about this here. See other
references, here.) and also the "How
we calculate" handout. Finish that handout to turn in on Thursday.
We discussed several methods of mental calculation and estimation, also.
New homework:
Ch. 3.5 # 1-3,8-10,15,16,18,19,20,32
Ch. 3.6 # 1-4 (a) only, 9,18
Class 8, Thu., May 1, 2008
We went over sections 3.3 and 3.4, and also the
pentomino
sequence problem. Turn that in on Tuesday. Also went over the Poinsot
Stars handout, turn that in on Tuesday also. See
the hint at the diagram
of the 12 pentominoes that I suggested you use to solve the problem.
Don't look if you are still working on
it yourself!
New homework:
Ch 3.3 # 1,3,5,9a,d,17,21,25
Ch. 3.4 # 3,17,19-24
Class 7, Tue., April 29, 2008
We had the first exam. We also went over chapter 3.2 on
base systems.
HW Ch. 3.2 # 1,5,10,15,16,20
You might like to read the discussion of possible
sources for the Babylonian base 60 at this site.
Class 6, Thu., April 24, 2008
We went over mateial from chapter 3.1, also homework from
chapter 2. We also did the Where's
Fido puzzle.
Here's a few hints
for the sample test for the first exam.
New homework:
Ch. 2.4 # 1-5,7,9,11,15,17,26,32
Ch. 3.1: # 1-5,9-10,25
Bring Homework to class on Tuesday.
Class 5, Tue.,
April 22, 2008
We played
the game Set and also the "Sorting
Junk" game. We also went over a number of
homework problems and introduced sections 2.2, 2.3, and 2.4.
Homework: choose an everyday object, and write a list of all the
attributes of that object that you can think of. We will collect the lists
on Thursday, and read out the list of attributes for some of the objects,
and see whether the other students can determine what the object described
is.
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
Go to the site for the
game set, which we played during class, and do the daily puzzle (Click
under "Set and Triology").
Here is a sample test for the
first exam. There are 16 problems on the sample test, but the exam
will probably have about ten to twelve, chosen to be similar to problems
from the sample test. We will cover some of the material on the sample test
in Thursday's class! Watch this site for any updates!
Class 4, Thu., April
17, 2008
We went over some homework, and also explored the Fibonacci numbers.
We also looked briefly at sets and Venn diagrams.
Due on Tues., April 22: Fibonacci
number assignment. This will count as a "quiz."
Print and bring to class on Tues: Poinsot
Stars - we'll talk about this in class.
New homework (I will check homework on Tuesday):
Ch. 1.5: # 1,3,5,6,7,9,10,12,15
Ch. 2.1 #8,9,11,14.15,16-20,25,26
Class 3, Tue., April
15, 2008
We introduced the pigeonhole principle.
We also tried to find all the pentominoes. Print
out the pentomino
sequence problem. You might want to start working on these problems
(they'll be due later next week). You might want to cut out small squares
for the pentomino chain problem, or cut out actual pentominoes for the second
set of problems.
We spent a little time trying to make a 4 by 4 magic square, using the
numbers 0,1,2,..., 15. See what you can do!
Here's a reference
for magic squares.
Here's another site
with some historical references (Wikipedia).
Work on
problems from section 1.3 and 1.4:
Ch. 1.3, # 4,7-11,14
Ch. 1.3: # 20,21,24
Ch. 1.4: # 1,9,13-15,19
Here are some links for polyominoes and pentominoes. There's
lots more!
Class 2, Th., April 10, 2008
We worked more on the Frogs on a Log problem,
and noticed some new things: if there are N frogs on each side, then the
minimum number of moves seems to be N(N+2) = (N+1)2
- 1. Also, we noticed that it will take 2N+1 more moves
than the previous problem in which there were 1 fewer frogs on each side.
But we have not yet figured out why? See if you can come to some conclusions.
We also worked on more of the problems from the first chapter. For example,
we established that in the take-away game, described in chapter 1, in which
each player removes 1,2,or 3 counters, the first player has a winning strategy
when the initial number of counters is congruent to 1,2, or 3, mod 4, and
the second player has a winning strategy otherwise.
We also worked on the pattern handout. Complete and turn in Tuesday.
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:
symmety: we'll define this more carefully later, but for now, think of
it as a design in which parts are repeated in some fashion.
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
odds: 1,3,5,7,... Is -1 and odd number?
evens: 0,2,4,6,8, .... Is -6 and even number? Is 0 even?
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
Due on Tuesday:
(1) Math autobiography
(2) Pattern handout
(3) Problems from chapter 1, sections 1.1 and 1.2
Class 1, Tue., April 7, 2008
We played the pattern game, and worked on the
"frogs on a log" problem.
Your tasks for the next two classes are numbered (1) through (6) below:
(1) Here's a description of the Pattern
game that we played. Please print out and include in your portfolio.
(2) Please print out the handout Patterns
and Modular Arithmetic, work the problems, and bring to class on Thursday.
Here are some links about modular arithmetic, which we will
examine in more depth soon:
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.
(3) HW due next Tuesday: problems in sections 1.1,
and 1.2 (See the list below at end of site of all the HW from the text
for the quarter.)
Read through end of chapter 1.
Ch. 1.1, # 2,4,9,10,11,12,14,15
Ch. 1.2, # 5,8,10,20,24
Here's a list of final
exam review problems from a previous quarter.
(4) By Thursday: Get a loose-leaf notebook,
make separate sections for
- Homework
- Handouts
- Exams
- Journal
- Class notes
- Articles
- Your papers
(5) Paper due next Tuesday:
Mathematical Autobiography, description on page two of the Green Sheet
(6) We also worked on the "Frog Crossing" problem.
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. Show how it can be done in 15 moves.
Two frogs on a three space log can take each other's places in three
moves:
Can you explain how? Four frogs on a five space log can change
places in 8 moves, as we discovered in class.
Use what you discovered to decide in how few moves eight frogs can change
places:
Can you generalize what you have discovered?
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