Table of Contents:
What
Would the Graph Look Like if…? A CBL Adventure
Robert
Ruzich
Fenton
High School, Bensenville, Illinois
As you travel through the streets of Chicagoland and admire the beauty of the mathematics around you, you are viewing the accomplishments of others. These architectural accomplishments are the culmination of designs inspired by a vision, a vision brought to life by creatively integrating the disciplines of mathematics and science. In science, and typically in life, these accomplishments start with an idea, followed by an experiment, and then developed into a form that we can admire. On Friday, February 8th, Robert Ruzich, mathematics instructor at Fenton High School in Bensenville, will take us on an adventure into the world of science and mathematics that starts with a phenomena and then develops a generalization, a mathematical rule, when he speaks at M.M.C. in a talk entitled, “What Would the Graph Look Like if?…A CBL Adventure.” Bob has been active in T3, Teachers Teaching with Technology, an affiliate of the Educational Division of Texas Instruments. He has been giving integrated presentations using the graphing calculator, along with various interfaces, to do data modeling activities in the classroom. Bob will use the CBL (Calculator Based Laboratory), taking on an inductive process, to find mathematical rules. When teaching mathematics we typically start with a generalized rule and then end a unit with specific data to fit the rule. Bob will take us on an adventure that will allow our students to use their ideas to gather data and then discover a mathematical rule. Hope to see you on Friday, February 8th, at Fountain Blue, as Bob Ruzich uses the data gathered from a CBL to visualize mathematics.
Pat Bowler Johnson
Board Meeting/ Elections
February 11th, your
board will be meeting. If you have
anything that you would like to have discussed, please feel free to e-mail Fern
Tribbey at: <ftribbey@d113.lake.k12.il.us>.
You may also call me at school (847)926-9223.
One of the things that the board will be discussing is the ballot.
If you are interested in running for a board position or for
president-elect, please e-mail Ron Vavrinek at: <rvav@imsa.edu>.
Pryjma's Pedagogical Pondering Points
If you can't attend Terry Phillips' New Teacher Workshop at New Trier on Saturday February 9 but you still have a question or concern as a new teacher, e-mail George Pryjma at: <gpryjma@aol.com>
Have you seen any vanity license plates that are math related? For example: "QT314" or "MR MATH"? E-mail your sightings to: <tribbeys@excite.com> and I'll include them in a future Points & Angles.
RESULTS
of MMC MATH CONTEST NO. 17
Five
Pentagons and a Constant Sum
In this
year's contest, in the December 2001 Points and Angles, 25 circles were placed
on the vertices of 5 pentagons, and 75 circles were placed on the sides between
the vertices. One pentagon had 2
other circles on each side, one pentagon had 3 other circles on each side, and
so on up to a pentagon with 5 other circles on each side. The task was to place 100 different positive integers in the
100 circles so that the sum of the numbers on each of the 25 sides of the
pentagons would be the same number.
If the sum is
a large number, such as 1,000,000, then the task is rather easy to do.
But if the sum is a small number, such as 150, then the task is
impossible because there are only so many ways to obtain the sum using different
numbers. I believe it can be proved
that 224 is the lowest possible sum, and two entries achieved that sum.
They will split the first and second place prizes and each receive $40.
A third entry achieved 226 and will get the third place prize of $20.
The prize winners are:
1.
Tom Edwalds 224
actuary
Munich-American Reassurance Co.
1.
Gary Genualdi 224
teacher
Schaumburg Christian School
3.
Daniel Choist 226
10th grader Walter Payton College
Prep, Chicago
Two
other entrants, with sums of 230, receive honorable mention:
James Labuz, a 12th grader at St. Patrick H.S. in Chicago, and Doug
O'Roark, a teacher at Walter Payton. There
were only six other entries. Three
of these had sums of 250 and three had sums of 300.
The total of 11 entries indicates that it took a considerable amount of
work even to enter this contest. We
congratulate all the entrants.
Tom
Edwalds entry uses the integers from 1 to 100.
The vertices of each pentagon are in boldface.
Sides
of smallest pentagon: 61, 100,
63, 96, 65, 97, 62, 98, 64, 99.
2nd
smallest pentagon: 20, 94, 87, 23,
89, 93, 19, 91, 92, 22, 88, 90, 24, 85, 95.
Middle
pentagon: 1, 86, 72, 55, 10, 81,
66, 54, 13, 83, 67, 56, 5, 82, 68, 53, 16, 84, 71, 52.
2nd
largest pentagon: 2, 80, 75, 30,
29, 8, 76, 70, 32, 26, 12, 79, 74, 37, 18, 4, 77, 69, 31, 28, 15, 78, 73, 35,
21.
Largest
pentagon: 3, 60, 48, 39, 34, 33, 7,
58, 50, 45, 44, 9, 11, 59, 46, 43, 42, 17, 6, 51, 49, 41, 36, 27, 14, 57, 47,
40, 38, 25.
Gary
Genualdi's entry uses the integers from 1 to 101 but not 91.
Sides
of smallest pentagon: 61, 101,
62, 99, 63, 97, 64, 95, 65, 98.
2nd
smallest pentagon: 20, 100, 81, 23,
90, 89, 22, 87, 94, 21, 96, 88, 19, 93, 92.
Middle
pentagon: 11, 71, 57, 73, 12, 74,
75, 50, 13, 40, 78, 79, 14, 80, 33, 82, 15, 8963, 30, 85
2nd
largest pentagon: 6, 51, 52, 53,
55, 7, 68, 56, 27, 58, 8, 59, 35, 76, 37, 9, 70, 24, 25, 86, 10, 67, 54, 69, 18.
Largest
pentagon: 1, 26, 49, 16, 46, 84, 2,
31, 28, 66, 34, 60, 3, 36, 17, 48, 39, 77, 4, 41, 42, 43 44, 45, 5, 29, 47, 38,
72, 32.
We hope that all of you who worked on this contest or used it in your classes found it to be a worthwhile activity. Please address any comments to Zalman Usiskin, University of Chicago, 5835 S. Kimbark, Chicago, IL 60637.
The Metropolitan Mathematics Club of Chicago is offering $1,000 in scholarships for high school students who plan a career in the teaching of mathematics. Contact Conrad Wayne at Rich South High School, 708-679-3150
The Metropolitan Mathematics Club of Chicago is offering $1,000 in scholarships for high school students who plan a career in the teaching of mathematics. The selected students, their parents, and their sponsoring teachers will also be invited to the May meeting of the MMC at which time the recipients will be honored.
The guidelines used for selection shall
be:
I. A. Demonstration of overall academic scholarship with inclusion of at
least eight semesters of college preparatory mathematics. (A minimum
cumulative grade point average of 3.0, with A = 4.)
B. A statement of
the intention to pursue a career in mathematics teaching.
C.
Indication of participation in extra curricular activities, especially those
which may have a positive influence on a teaching career.
II. Applicants must have a letter of recommendation from a member of the Metropolitan Mathematics Club who is familiar with the applicant’s academic performance and his or her potential as a mathematics teacher.
III. Applicants must submit an essay of at most 400 words explaining why they would like to be a mathematics teacher.
The scholarship award or
awards will be determined by a selection committee of MMC members appointed by
the Executive Board. To be eligible, an applicant must submit the
application, have an official transcript sent, and request a letter of
recommendation from a member of the MMC such that all of the materials are
received by the date on the application.
The committee will establish
its own guidelines for evaluating applications, and will make a recommendation
to the Executive Board as to the awarding of the scholarship. No member of
the selection committee may nominate nor recommend a candidate.
APPLICATION FOR THE METROPOLITAN MATHEMATICS CLUB SCHOLARSHIP
Application Deadline: March 18, 2002
Name:__________________________________________ Date:_________________
Address:______________________________________________________________
_______________________________________________________________
School:_______________________________________________________________
School Address:________________________________________________________
________________________________________________________
Home Phone:(____)___________________ School Phone:(____)________________
Sponsoring Teacher (Must be MMC member):_________________________________
Please complete the following:
Overall Grade Point Average:_________ (A = 4, B = 3, C = 2, D = 1, F = 0)
Mathematics Courses Grade Mathematics Courses Grade
___________________ _____ __________________ _____
___________________ _____ __________________ _____
___________________ _____ __________________ _____
___________________ _____ __________________ _____
Extracurricular Activities:____________________________________________
_____________________________________________________________________
_____________________________________________________________________
In addition applicants must also send:
1. A letter of recommendation from the sponsoring teacher, who is a
member
of the Metropolitan Mathematics Club of
Chicago: **
2. A current transcript for seven semesters of high school.**
3. An essay not to exceed 400 words on: “Why I would like to
teach
mathematics.”
Please send all information to: Conrad Wayne
Mathematics Department
Rich South High School
5000 Sauk Trail
Richton Park, IL 60471
phone: 708-679-3150; fax: 708-679-3168
**(Letters of recommendation and transcripts may be sent by separate mail.)
(Photocopy as needed)
The Chicago Area
All-Star Math Team will be holding tryouts for the 2002 team on Thursday,
February 28, from 4 to 9:30 p.m. in room S112 at Evanston Township High School.
The All-Star Team will practice in the Spring and will travel to Iowa to compete
in the ARML (American Regions Math
League) competition on June 2, 2002. Any high school student is eligible to
tryout for the team. About 35 students will be selected the night of the tryout
and about 30 more will be selected a few days later. Please contact Mary Lappan
(lappanm@newtrier.k12.il.us, 847.784.6608) with any questions.
POINTS FROM THE INTERIOR
Our organization is sponsoring a new teachers’
workshop on Saturday, February 9th at New Trier High School.
Terry Phillips is doing a great job in making this event for our new
(within the first two years) teachers an exciting and informative one.
Can you remember your first year of teaching?
Even though I am in my twenty-seventh year, I still can remember my first
year as if it was yesterday! I
remember being so excited before the school year began and thinking about how I
was going to set up my classroom. I
was to share my room with another teacher for one of the periods of the day.
One day before the year began I was stopped by school personnel while
walking in with a box of supplies, mistaken for a student.
I was told to come back the first day when students are to report.
I proudly stated that I am one of the new teachers and then I was able to
proceed to my classroom. I remember
the first day of classes that year and how excited I was to finally begin my
lifelong dream of being a mathematics teacher, I could hardly sleep.
I realized that using humor got me further with my students.
Then I can remember one day in November of that year, walking out of the
building at the end of a very long day questioning whether I chose the correct
profession. The principal had asked
me how things were going. After I
shed a few tears, he told me that the first year is the hardest and that the
following years will be better. He
also encouraged me to continue with my dream because I was enabling my students
to learn. Looking back on that day
in November, I realized that he was quite right in what he told me. I am glad that I continued with my dream.
I still have a lot to learn and am not afraid to ask for assistance and
am not afraid to share my thoughts with the new teachers in my department. I am
asking you to share your memories with a new teacher that you know.
They might not feel so alone in what and how they are feeling about the
job that they are doing in such a rewarding profession such as ours. Be a mentor.
February 11th, your board will be meeting. If you have anything that you would like to have discussed, please feel free to e-mail me at: ftribbey@d113.lake.k12.il.us. You may also call me at school (847)926-9223. One of the things that the board will be discussing is the ballot. If you are interested in running for a board position or for president-elect, please e-mail Ron Vavrinek at: rvav@imsa.edu.
I am looking forward to seeing everyone at the Fountain Blue on February 8th to hear what Bob Ruzich of Fenton High School has to say.
"The Mathematics of Frank Lloyd Wright's Architecture"
Mary Wiltjer
Addison Trail High
School
At the largest dinner-meeting this year, and our first at the Fountain Blue, Mary Wiltjer treated a very enthusiast crowd to a delightful virtual tour of many of Frank Lloyd Wright's houses. Each house was designed to relate to the person who was to live in it.
The Robie House is Wright's
most famous "prairie house" and an excellent example of Wright's use
of the straight line to make the house part of its natural setting.
The courtyard is enclosed with a brick wall and is covered by overhanging
eaves, which parallel the wall. The
eaves extend around to the front of the house, keeping the same horizontal line,
where it is accentuated by a series of casement windows.
In designing his own home,
Frank Lloyd Wright used the circle to create open space.
Always emphasizing the human scale, he scaled the playroom to a child's
size. In some homes, he went beyond
the architecture of the home and designed furniture, china, and even dresses.
He was insistent that everything should fit together.
Frank Lloyd Wright's architecture reflects his concern that a house provides shelter with warmth. He would put something "light" where the building is heaviest, placing windows immediately under the roof or around corners. He used pigment in the concrete used to separate the bricks vertically so that the lines would flow only in a horizontal direction.
In designing the Guggenheim Museum, Wright used circles and spirals and an elegant skylight to connect to nature. Visitors take an elevator to the top and spiral back down, with each spiral smaller than the one above. In other homes, he played with hexagons, pentagons, octagons and even half circles.
Within his homes, Frank Lloyd Wright was concerned about the flow of space. He wanted to define space without confining it. Unlike other houses of his time, he took small spaces and made them larger, at times creating a room within a room. Seeing out, but not seeing in, and being in touch with nature were important. There is an emphasis on beautiful, geometric shapes, not orientation.
Mary's talk, an excellent start for 2002 and for our stay at the Fountain Blue, left us all fascinated with the architecture of Frank Lloyd Wright and his incorporation of mathematics into each house. Those who are going (or should we say, "have gone") on the tours are looking forward to an additional treat.
-Ron Vavrinek
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