Class 22, Thu., Mar. 17, 2011
We reviewed (see review problems below), and went over some problems on factorization, GCD, LCM, and modular arithmetic.
Class 21, Tue., Mar. 15, 2011
We went over the take-home exam, and also more on algebraic thinking. Keep working on the Prediction Card Trick handout. Also finish the "Painting the Pool" worksheet to turn in Thursday. A
You may skip chapter 8.3, it's very similar to material you've done in intermediate and elementary algebra.
Here is a recent final
exam study guide. Your exam will be very similar.
Here's a recent
sample problem sheet.
Here are the sample
problems with some hints and solutions.
Class 20, Thu., Mar. 10, 2011
We did the Barbie/Ken activity, and also looked at an algebraic "card trick." Please complete the problems in this Prediction Card Trick handout; we will discuss and turn it in on Tuesday. Also turn in chapter 6 homework on Tuesday. Chapter 7/8 will be due during the final exam the next week.
Class 19, Tue., Mar. 8, 2011
We went over some chapter 5 problems. Please bring a Barbie doll (or Ken!) to class on Thursday for an activity on proportion.
Chapter 6 Homework is due next Tuesday. Chapter 7/8 homework will be due the day of the final exam.
We went over some magic square problems, and learned about mathematics from Africa, including developments of magic squares.
We also learned about new ideas about how we may be confused about certain arithmetic facts.
We also began chapter 8 with a "test" on paper folding. See this on Britney Gallivan, who folded a "sheet" of paper 12 times.
Class 18, Th., Mar. 3, 2011
We did more on decimals, including examining types of real numbers: rational and irrational; terminating, repeating and non-repeating decimals.
Chapter 5 homework is due on Tuesday, March 9.
The modular arithmetic homework is due Tuesday, March 9.
Bring a Barbie or Ken doll next Thursday, March 11, for an activity on proportion.
Here is the set of slides of fraction problems with the correct link!
Here is the set of slides of decimal/ratio problems we also worked on.
Class 17, Tue., Mar. 1, 2011
We went over decimals. You were asked to write a "story problem" which requires you to divide 1-1/4 by 1/2 in order to find the answer. Be careful, dividing by 1/2 is not the same as multiplying by 1/2!!
Class 16, Th., Feb. 24, 2011
Most of class spent on the group problems, with substitute
Class 15, Tue., Feb. 22, 2011
We went over more fraction problems, so we have now covered most of the material from sections 6.2 and 6.3.
Take home exams are due this Thursday.
Also on Thursday, you will present the group problems.
I will be absent Thursday, but roll will be taken, and remember that some of you are very close to the limit for numbers of absences.
Here is the set of slides of fraction problems we've been doing the last two classes.
Here's some more on Farey Sequences (skip the advanced part and the cute animation at the beginning!)
Chapter 5 will not be due until a week from Thursday.
Class 14, Thu., Feb. 17, 2011
We covered sections 5.4 and 6.1.
Take-home exams are due on Thursday (NOT Tuesday, sorry, I did change that!)
Chapter 4 homework is due Tuesday, Feb. 22.
We will present the group problems on Thursday.
Class 13, Tue., Feb. 15, 2011
We played a new "number line" game that deals with adding and subtracting positive and negative numbers.
We also saw the TED Dan Meyer video.
Please be ready to present your group problem (see below) on Thursday.
Class 12, Thu., Feb. 10, 2011
We worked on group problems, and also chapter 5.1 and 5.2.
We also did some work on the take home exams.
Class 11, Tue., Feb. 8, 2011
We heard reports today. We also learned about the game Ken Ken - this site has 6 new puzzles every day.
Here, by the way, is a site on Nines Complement subtraction. Here's info on the Gelosia mulitplication method and some other methods.
Homework for chapter 3 is due this Thursday.Take home exam will be emailed to everyone later.
If you were not here last Thursday, I have placed your name in the table below. You will be responsible for learning how to solve the problem whose row you are in, and you will present it to the students whose column you are in!
The Turnitin site is open for revisions, additions, uploads till midnight tonight (Tues., Feb. 8).
Class 10, Thu., Feb. 3, 2011
We went over sections 4.3 and 4.4.
We also did the "Clap your name" activity.
Your papers (see below) are due by Tuesday. Please use Turnitin to turn it in! I will email you the login and password.
For a pretty good summary of the issues involved in the use of Turnitin, see the Wikipedia entry on Turnitin.
Homework for chapter 3 is due next Thursday.
A number of chapter 4 problems are to be done in groups. The groups so far are:
| Group-> | A | B | C | D | E |
| 4.1 #10,17 | Lindsay | Kwasi | Cynthia | Melinda P. | Ying |
| 4.1 #18,19 | Lauren |
Nicole | Thang | Iris | Mareh |
| 4.1 #25,30 | Cassie | Nolan | Duaa | Winnie | Maria |
| 4.2 #9,11 | Kelly | Lisa | Matthew | Melinda N. | Jennifer |
| 4.3 #19,20 | Michelle | Meagan | Diana | Anna | Melissa |
| 4.4 #13,15 | Orlena | Faith | Sonja | John | Valerie |
| 4.3 # 21 | Sarah | Latasha | Michelle | Sacha |
Class 9, Tue., Feb. 1, 2011
We went over sections 3.6 and 4.2, lots of base arithmetic problems, a little about modular arithmetic, and a magic trick that uses mod 9 (do you understand how?) Try to figure out why the conversion method from base ten to another base works.
Do homework through section 4.2.
Chapter 3 is due Th. Feb. 10, your paper is due Tu. Feb. 8.
Class 8, Thu., Jan. 27, 2011
We went over the exam. We also went over section 3.5 and 4.1. Bring a calculator to class on Tuesday so we can go over section 3.6.
We also discussed the use of estimation, mental arithmetic, and various methods of calculation.
Here's the web site for the Common Core Standards, published by the U.S. Governors' Association last June, and adopted by California in August.
The most important math education organization in the U.S. is the National Council of Teachers of Mathematics. Their site has many resources.
You have a short paper on a subject related to the course that catches
your interest due Tuesday, Feb. 8 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 library.
Class 7, Tue., Jan. 25, 2011
We had exam 1 and went over sections 3.4.
Do homework through section 3.4.
Class 6, Th., Jan. 20, 2011
We went over homework and sections 3.2 and 3.3. Exam 1 on Tuesday will go through section 3.1. Bring a scantron form (the half page green or brown form), though some questions will not be scantron questions. Turn in chapter 2 homework following the exam. During the exam I will check your portfolio/notebook. Work on homework up to section 3.3.
Here are solutions to the study guide for the first exam problems (it's also available in a previous class's web log!) 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. And some of the problems the answer sheet says we didn't get to, we did get to this quarter!
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.
Here's a site on the triangle numbers,
and another on several base systems
By the way, here's how the site "How things work" describes 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 5, Tue., Jan. 18, 2011
We went over material from sections 2.4 and 3.1 and talked about controversies about multiplication and set theory.
See Keith Devlin's articles on multiplication as repeated addition.
See this brief history of the New Math.
We also played the game Set, see their daily puzzle.
And we played the "Sorting Junk" game.
Work on homework through section 3.1
Homework for chapter 2 will be due Tuesday, Jan. 25.
Here's that 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:
"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."
Class 4, Thu., Jan. 13, 2011
We went over lots of chapter 1 homework problems, and also sections 2.2 and 2.3.
Turn in the Fibonacci assignment next Tuesday, Jan. 18.
Chapter 2 homework will be due Tuesday, Jan. 25.
Here's a study
guide
for
the
first
exam from a previous quarter.
Here's a decent (Wikipedia) site with lots of voting methods and their history.
We did the "Where's
Fido?" activity - work the other problems in this handout as part
of your homework.
We talked about Pingala's possible use of the Fibonacci Numbers (prior to Fibonacci!) for counting syllables in music and poetry.
Rachel Hall (who I mentioned) credits Indian mathematician/musician with the Fibonacci numbers (also prior to Fibonacci) - see her article "Math for Poets and Drummers" listed at her site.
By the way, here's some history of the Magic Square.
On Tuesday we'll do two new activities about sets, and go over chapters 2.4 and 3.1.
Class 3, Tue., Jan. 11, 2011
We went over the 20 friends problem, the nine-square perimeter problem, counted the Fibonacci numbers on pine cones, and briefly went over section 2.1. Do homework through 2.1. Turn in chapter 1 homework on Thursday. Turn in the Fibonacci assignment next Tuesday, Jan. 18.
Math/Science Tutorial Center in S-43
Melissa Aguilar spoke to us about what kind of support is available.
Irina and Svetlana are two of the tutors familiar with this class.
Thur., Jan. 20, 3-4 PM review session for exam 1, which is Tue., Jan. 25
Friday, Jan. 21, 8:30AM -12:30 PM
review session for exam, which is Tue., Jan. 25
Other times for group sessions:
Tu/Th 12-1PM or 3-4 PM
Fri. 8:30AM-12:30 PM
Last week, in the pigeonhole principle "magic trick," I asked 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. For Thursday, 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!
Here's a study guide for the first exam from a previous quarter.
Print out the handout Patterns and Modular Arithmetic, begin working on the problems, and bring to class Thursday.
Here are some links to Fibonacci sites, take a look at them. The second and third have lots of pictures!
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. Within the site is a
short film clip that is part of the explanation as to why the Fibonacci
numbers appear in plants.
Here's a wonderful article by Brian Hayes on the history of Gauss's Trick, published in 2006.
Class 2, Thu., Jan. 6, 2011
We went over sections 1.3, 1.4, and 1.5.
Do homework through 1.5.
Turn in your mathematical autobiography on Tuesday, Jan. 11.
Turn in chapter 1 homework on Thursday, Jan. 13.
We played the Toe-Tac-Tic magic square game.
We also saw connections between several sequences of numbers: Fibonacci numbers, triangular numbers, primes, and the elements of the "Pascal" triangle, and learned about the history of these concepts.
We saw how the pigeonhole principle explains a "mind-reading" magic trick.
Print out the handout Patterns
and Modular Arithmetic, begin working on the problems, and bring to class Thursday.
Class 1, Tue., Jan. 4, 2011
Here is a handout describing the
pattern game we played in class, and showing the pattern we used.
(1) Get your textbook! (See green sheet.)
(2) Assignment: Ch. 1.1 and 1.2 (see problems below).
(3) We worked on the pattern game and associated problems.
(4) We worked on the "frogs on a log" puzzle and 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
Skip Ch. 8.3 #24-27, 31,32,34,35