Online MTC Sessions this Summer

Hi everyone!

We hope you are all healthy during these strange times! We have good news and are excited to announce that AIM is organizing a weekly Math Teachers’ Circle Network Online Series that is open to all MTC members across the country! 

We will meet Tuesdays from 5 to 6 p.m. Pacific, beginning next Tuesday, May 19, when James Tanton will kick off the series with a session on “How to Fold Into Thirds”:
It is pretty easy to accurately fold a tie or a strip of paper or length of chord in half, or quarters, or even eighths. But how do you fold a strip into accurate thirds? Or how about sevenths? (Does this issue actually come up in everyday life?) Let’s play with some fun folding math and figure out how to become masters in folding lengths into most any fraction you like! Wild math to behold! 
To participate, please register at Future events will be posted on that page and will also be announced on the Joyful Math Online events calendar at
P.S. More details will be coming soon on a Nationwide Virtual MTC Workshop to take place this summer in July. Thanks to Chris Bolognese (Columbus MTC), Sloan Despeaux (Smoky Mountain MTC and NC Network of MTCs), Anne Ho (Tennessee Eastern & Appalachian MTC), and Lizi Metts (Middle Tennessee MTC) for organizing this workshop in conjunction with AIM.

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January Meeting Recap

In this month’s Math Teachers’ Circle session, run by Dr. Christina Jamroz of the University of St. Francis and Dr. Rita Patel of College of DuPage, we investigated Magic Squares.  We began the session by examining a magic square of order five to infer some of its defining properties.  Participants concluded that a magic square of order n must contain each of the numbers 1 through n^2 exactly once.  Furthermore, every row, column, and main diagonal in the square must add to the same number, called the magic sum.


The session continued with groups working to construct magic squares of order two, three, and four.   We observed that we could not construct a 2 x 2 magic square, but found eight magic squares of order three.  We also realized that all of these magic squares were related by a rotation or reflection.    During this discussion, we made conjectures related to patterns we noticed.  One of these conjecture concerned the middle number of an odd order magic square.  Is this middle number always going to be the median of the list of numbers used to fill the square?  After considering more examples, participants found that this is not always true.

The construction of a magic square of order four led to a discussion about strategies we could use to create magic squares.  Participants noted that knowing the magic sum would aid them while working on this problem.  We observed that all of the magic squares of order three had the same magic sum.  Does this generalize to all magic squares of a fixed order?  This led to the discovery that the magic sum of a magic square of order four was always 34.  Then, we deduced that the magic sum of a magic square of order n was n(n^2+1)/2.

At the conclusion of this session, we reflected on how we can use this topic in our classrooms.  Furthermore, we realized that we have seen magic squares before, with participants mentioning Sudoku puzzles, art, and math history.



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November Meeting Recap

In this Math Teacher’s Circle session, run by Dr. Amanda Harsy of Lewis University, we explored the world of prime numbers by playing Prime Climb. First, we made observations about the game board, specifically reflecting upon the coloring of the board. We played a simplified round of the game, and considered the mathematical operations behind the game.


Through group discovery and discussion, we noted effective strategies for moving along the game board. For example, we found that a player can land on any number up to twenty using addition on their first turn. Furthermore, you can land on any number that can be written as a product of two numbers that is less than, or equal to ten.

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Upon reflection, we realized the game of Prime Climb is relevant to our classrooms in many ways. First, the game can provide our students with practice finding factors and multiples. Prime Climb could be particularly helpful for struggling learners who need to practice their fact fluency. We also discussed that the color coordination of the dice and the game board spaces would be helpful for students who have difficulties with fact fluency. Colors can be a useful tool in helping students to make connections while studying difficult concepts, such as prime numbers. Furthermore, this game can help students discover that there is not a pattern of primes. Finally, we discussed the relevance of playing this game to explore the commutative property with various operations.

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The following link provides lessons to try after playing Prime Climb with your students:

These lessons especially target Common Core Math Standards 3.OA.C.7, 3.OA.D.8, 3.OA.D.9, 4.OA.A.3, and especially 4.OA.B.4 & 6.NS.4, as well as Math Practices 1 and 7.

mtc 2

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September Meeting Recap

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:


Join us for our next Math Teachers’ Circle Meeting at Saint Xavier University!

RSVP Here:

Math Circle Flyer Oct 21 2019 Xavier.jpg

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May 6, 2019 Meeting – Carpet Fractals

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.


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Professional Development Opportunity

Hi everyone,

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

2019 Chicago PCMI TLP Flyer

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January Meeting Canceled due to Weather

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:


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Thanks for a Great Fall!


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.

IMG_7409.JPGDuring 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!Math Circle Flyer Jan 28 2019 Xavier


RSVP here:

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RSVP for November 5 Meeting at University of St. Francis

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::

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: You can also use the following address in your GPS: 500 Wilcox Dr. Joliet, IL 60586. A campus map can be found here: 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!


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RSVP for our first Meeting of the 2018-19 School Year!

Math Circle Flyer Sept 17 2018 Lewis

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:!

If you cannot make this meeting but would like to be informed of
future events, please fill out this google form: 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



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