In this Math Teacher’s Circle session, run by Dr. Angela Antonou of the University of St. Francis and Dr. Brittany Stephenson of Lewis University, we explored the world of continued fractions. This activity put complex fractions in their place. We began with a visual exploration of continued fractions through a jigsaw puzzle activity. Participants were provided with one large rectangle with integer dimensions and several squares of various sizes (also with integer dimensions). The first task was to try to fill the rectangle using the least number of squares.
After group discovery and discussion about the least number of squares needed to fill the rectangle, participants kept track of how many of each size of the squares they used to fill the rectangle. We observed that we were able to create a fraction using the number of squares of each size used to fill the rectangle and then successively taking the sum and the reciprocal in a particular way. For example, if we used 5 of the largest squares, 4 of the next largest, and 2 of the smallest, we would obtain the continued fraction 5 + 1/(4+1/2).
After completing the jigsaw activity process, participants discovered that writing a continued fraction in this way based on the number of squares needed to fill the original rectangle was equivalent to writing a fraction for the length divided by the width of the original rectangle. In particular, each group began with a 16 by 13 rectangle and found that we could fill the rectangle with one square of size 13 by 13, four squares of size 3 by 3, and three squares of size 1 by 1. This created the continued fraction 1 + 1/(4+1/3)), which equals 16/13 (the size of the original rectangle).
After observing this relationship between continued fractions and the original rectangle, we continued to play around with continued fractions. We observed how continued fractions relate to Fibonacci numbers and can be used to create the Fibonacci spiral!
Another cool application of continued fractions that we explored is how certain irrational numbers, such as square roots, can be written in terms of continued fractions with a periodic pattern that repeats forever. We can also use continued fraction forms to compare two fractions to determine which is larger. Throughout this session, we had many interesting discussions about the uses of continued fractions. For more information, here is a helpful website we used as resource that details many more applications of continued fractions: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html#section6.4
Join us for our next Math Teachers’ Circle Meeting at Saint Xavier University!
RSVP Here: http://bit.ly/MTCOct2019
We had a great meeting on May 6 at Lewis University – led by Kristen Schreck from Saint Xavier University. We discussed the Sierpinski Triangle and Carpet Fractals. Some people even won some beautiful constructions done on a 3-D printer. Here are some images from the fun and creative event.
A teacher professional development workshop coming up in Chicago on 23 March. You are listed as part of the leadership of the Southwest Chicago Math Circle; we have seen a strong affinity between these programs and the Math Teachers’ Circles in both philosophy and content.
This program is open to both in-service mathematics teachers and pre-service student-teachers with classroom experience. Let me explain that there is funding for hotel rooms for participants who live beyond easy commuting distance.
This outreach comes from the Teacher Leadership Program of the Park City Mathematics Institute, a program of the Institute for Advanced Study in Princeton NJ. PCMI is a 3 week summer program which includes rich mathematics content and also applied pedagogy, “reflecting on practice.” We are in our fourth year of weekend outreaches, spreading the PCMI teacher program beyond the small number who can attend the summer session.
If you have questions please contact Matt Roseberg at firstname.lastname@example.org
We are canceling our January Meeting due to weather… stay safe and stay warm and we hope to see you at our February 25th meeting at Trinity Christian College. RSVP now: http://bit.ly/MTCFeb2019
We had 3 great sessions this fall!
Our Septemeber session was run by Dr. Angela Antonou and Dr. Rita Patel.
During this Math Teachers’ Circle event, we explored new visual representations of functions and discover properties of numbers and functions using these new representations.
Our October Meeting was run by a guest leader from our Sister Circle, Brian Seguin.
During this session, we explored patterns and a Number Machine which takes in two numbers and produces a new number.
Our November Meeting was run by Dr. Amanda Harsy.
The session titled, “Voting Fairly,” was well timed with election day. During this event, we explored various voting systems. We applied and analyzed several established methods for determining the “voice” of the majority.
Participants also created and analyzed their own voting methods!
We look forward to more events this spring! Remember to RSVP for our January event!
Don’t forget to RSVP for the November 5 Meeting to be held at University of St. Francis in Tower Hall (N307 and N309). You can register here:: http://bit.ly/MTCNov2018
Topic: “Voting Fairly” by Dr. Harsy.
Description: In this Math Teachers’ Circle Session, participants will explore voting systems. Specifically, this session will facilitate discovery and inquiry-based experiences in order for participants to apply and analyze several established methods for determining the “voice” of the majority. Finally, participants will be asked to create and analyze their own voting methods and decide which methods seem better suited to reflect the preferences of the voters.
Campus and parking information: Directions to USF can be found here: https://www.stfrancis.edu/visitors/campusmaps/main/. You can also use the following address in your GPS: 500 Wilcox Dr. Joliet, IL 60586. A campus map can be found here: https://www.stfrancis.edu/visitors/campusmaps/main/. You may park in the Wilcox Street Lot which is near Tower Hall (the room for the event is N307 and N309, both located on the North side of the third floor of tower hall, which is the building numbered 11 and 12 on the campus map). Additional parking is available in the Recreation Center Lot.
If parking in Wilcox Street Lot, the building is directly across the street. Enter the nearest doors and walk toward the center (south side) of the building. You’ll reach a large set of stairs near the center of the building which you can take to the 3rd floor (exit to your right to travel north on the 3rd floor and you will reach N307/309; you’ll know you’re going the right direction if the rooms start with “N” instead of “S”). If you prefer an elevator, it is located just south of the stairs near a water fountain on the first floor; if you reach the cafeteria, you traveled too far.
We hope to see you there!
Please consider joining us for an evening of collaboration
and hands-on problem-solving guided by college faculty members and
fellow practicing mathematics teachers. Math Circle Meetings are
designed to meet the requirements for Professional Development Hours
and dinner is provided so please RSVP here: http://bit.ly/MTCSept2018!
If you cannot make this meeting but would like to be informed of
future events, please fill out this google form:
http://bit.ly/SWChicagoMathCircle in order to be put on our email
Also Save the Dates for our future meetings
- October 15th at St. Xavier University
- November 5th at University of St. Francis
- January 28th at St. Xavier University
- February 25th at Trinity Christian College
- May 6th at Lewis University