****Stop by the NAMC Booth this week at MathFest for your NAMC Namebadge Sticker****

July 26-29, 2017

Location: Chicago, IL

Download your MathFest Guide for Math Circle related activities: **Click here!**

For additional information related to MathFest visit:

- SIGMAA-MCST Website: http://sigmaa.maa.org/mcst/
- MathFest Website: http://www.maa.org/mathfest/
- MathFest Program:
**Click Here!**

## Schedule at a Glance

**Wednesday, July 26**

- 6:00- 8:00pm. Grand Opening Exhibit Hall Reception – Visit the NAMC Booth
**for your NAMC Namebadge sticker**

**Thursday, July 27**

- 9:00 am – 5:00 pm. Exhibit Hall Open – Visit the NAMC Booth
- 1:00 pm – 3:15 pm. SIGMAA-MCST Contributed Paper Session: My Favorite Math Circle Problem, Part A. (Salon C-1 & C-2)
- 6:00 pm – 8:00 pm. National Association of Math Circles/SIGMAA-MCST/Math Teachers’ Circle Network Math Circles Social Gathering

**Location: Bar Louie, 47 W Polk Street.**Appetizers will be provided.

**Friday, July 28**

- 9:00am – 5:00 pm. Exhibit Hall Open – Visit the NAMC Booth
- 1:00 pm – 3:55 pm. SIGMAA-MCST Contributed Paper Session: My Favorite Math Circle Problem, Part B. (Salon C-1 & C-2)

**Saturday, July 29**

- 9:00am – 12:30 pm, Exhibit Hall Open – Visit the NAMC Booth
- 1:00pm – 1:50pm.
__Special Presentation for High School Students, Parents and Teachers:__(Continental Ballroom B)*Those Infamous Exploding Dots: A preview to Global Math Week* - 2:00 pm – 3:30 pm. SIGMAA-MCST Math Teachers’ Circle Demonstration (Salon C-1 & C-2)
- 4:00 pm – 5:30 pm. Math Wrangle (Salon C-1 & C-2)

## Wednesday, July 26

**6:00- 8:00pm, Grand Opening Exhibit Hall Reception – Visit the NAMC Booth for your NAMC Namebadge sticker.**

## Thursday, July 27

**9:00am – 5:00 pm, Exhibit Hall Open – Visit the NAMC Booth.**

**1:00 PM – 3:15 PM. SIGMAA-MCST Contributed Paper Session: My Favorite Math Circle Problem, Part A**

Location: Salon C-1 & C-2

Organizer: Bob Klein, Ohio University

A Math Circle is an enrichment experience that brings mathematics professionals in direct contact with pre-college students and/or their teachers. Circles foster passion and excitement for deep mathematics. Papers in this session highlight either a favorite problem from a Math Circle, or a favorite collection of problems used together for multiple sessions of a Math Circle.

### Talks include:

**1:00 PM – 1:15 PM. Superfactorials and Perfect Squares**

*Diana White, University of Colorado Denver and NAMC*Can you remove one of the terms of 100!*99!*98!*…*3!*2!*1!, so that what remains is a perfect square? Since first learning about this problem, it has been one of the author’s favorite problems to facilitate in Math Teachers’ Circles. In this talk, we provide an overview of how teachers commonly approach the problem, and the mathematics that often emerges along the way.

**1:20 PM – 1:35 PM. Mathematical Ciphers: A Math Teachers’ Circle Day Long Workshop**

*David Crombecque, University of Southern California*

The Los Angeles MTC offers a two day workshop for local math teachers. One day is devoted to Applied Mathematics (like Mathematical Modelization) and the other day to General Mathematics (like Geometry). The activities presented here constitutes an entire day of the workshop but can also be split and used for monthly meetings. The theme of Mathematical Ciphers was chosen as it introduces the beautiful mathematics of Modular Arithmetic while dealing with mathematical concepts familiar and essential to middle-school and high school math teachers. Encryption methods are very much a hot topic in our era so it will peak the curiosity of many teachers. And of course, this can lead to a lot of fun activities!**1:40 PM – 1:55 PM. Divide Your Cake (and Eat It, Too!)**

*Mike Janssen, Dordt College*

Many people are familiar with a fair way of dividing a resource (such as a cookie) between two people; we often learn it as children. In this talk, I’ll describe a math teachers’ circle session I ran on the notion of fair division, which included an inquiry component exploring means of dividing a resource between more than two players. This was a particularly fun session, and illuminating for teachers, as it involves the use of mathematical thinking applied to a problem which does not fall within a traditional subject in school mathematics.**2:00 PM – 2:15 PM. Islamic Geometric Pattern**

*R**ebin Muhammad, Ohio University*

An Islamic geometric pattern (IGP) is a 2D wallpaper that is created by using only a compass and a ruler. The history of IGPs date back to the 8th century and IGPs have been seen in most Islamic countries, where they have been used to decorate building walls and mosques. For the Math Circle session, we reconstruct one of these patterns, the “Seal of Solomon,” from scratch. Each student creates a tile and at the end of the session, we tile all of them into a single, decorated wall. Can we have different tilings? And why does the tiling work? What kind of symmetries do the tiles exhibit? Can you use the same construction line to create a different tile and are you sure that the lines between tiles are such that your design will tile the wall? In the second pattern, “Ten Chain,” students use modular arithmetic to construct the tile and to learn about Z_{10}. We ask questions like: Can you generalize this example? Can you create “5 Chain, 6 Chain, etc.”? What kind of chain cannot be constructed? This is followed by investigations of “interlacing” including when the strategy of interlacing works and the relationship between two neighboring chains.**2:20 PM – 2:35 PM. The Dissemination of Gossip**

*Parth Sarin, A&M Consolidated High School*

Philip B. Yasskin, Texas A&M UniversityWe will discuss a Math Circle on the dissemination of gossip. Each student in a group of

*n*students (perhaps 4, 5 or 6) has a different pet. Everyone wants to know who has which pet. They communicate by gossiping. Initially each student only knows their own pet. When two students gossip, they exchange all the information they have with one another. In a group of n students, what is the minimum number of conversations it takes until everyone knows everything? This activity is based on the Gossip Protocol for computing as discussed at https://en.wikipedia.org/wiki/Gossip_protocol**2:40 PM – 2:55 PM. Bulgarian Solitaire**

*Douglas O’Roark, Math Circles of Chicago*Bulgarian Solitaire is a math circle activity that is accessible and hands-on, with a low floor and a high ceiling. It allows for children to engage in important mathematics: deciding on appropriate representations, extending problems and developing an inquiry mindset, employing problem solving heuristics, and making mathematical connections. It can adapted to work with a range of age groups, and is an excellent activity for the first meeting of a math circle group in order to build buy in and set the stage for collaboration and expectations of engagement.

**3:00 PM – 3:15 PM. Frogs and Toads**

*Peter Tingley, Loyola University Chicago*

I will discuss the frogs and toads problem from the summer 2013 MTCircular magazine (in the “Problem Circle” by Joshua Zucker): Frogs and Toads sit in 5 by 5 grid, with the middle square empty, in the configuration

They want to switch places. Animals can move one step, or hop over one other animal, but only in the two directions they want to go. Is it possible?

**FFFTT**

FFFTT

FF_TT

FFTTT

FFTTT

I love this as an exercise in pure, creative problem solving. It emphasizes what I think is one of the most important strategies: do a simpler problem first. The obvious simpler problem is the 3 by 3 case, and this is a good thing to do, but the nicest solutions don’t stop there: They find an even simpler problem! The 3 by 1 case! (Well, the simplest is the 1 by 1 case, but that is a bit too trivial). Then there is 5 by 1 case and the 7 by 1 case, and if you do these you really understand some things. Then, if you just squint right, you suddenly see the solution! And not just the solution, but also the solution to generalizations, such as the 9 by 9 case or even the 7 by 9 case. It isn’t so clear what to do with e.g. the 4 by 5 case, but that just means there are still things to talk about.

I’ve done this with several different groups of teachers and students, and it has always been fun and led to interesting discussions. It is approachable by everyone, and most people leave feeling they’ve gained some insight. All of which is to say, it is one of my favorite math circle problems!**6:00pm – 8:00 Math Teachers’ Circle Network/SIGMAA-MCST/NAMC Math Circles hosted Social Gathering**

Location: TBD

## Friday, July 28

**9:00am – 5:00 pm, Exhibit Hall Open – Visit the NAMC Booth.****1:00 PM – 3:55 PM. SIGMAA-MCST Contributed Paper Session: My Favorite Math Circle Problem, Part B**

Location: Salon C-1 & C-2

Organizer: Bob Klein, Ohio UniversityA Math Circle is an enrichment experience that brings mathematics professionals in direct contact with pre-college students and/or their teachers. Circles foster passion and excitement for deep mathematics. Papers in this session highlight either a favorite problem from a Math Circle, or a favorite collection of problems used together for multiple sessions of a Math Circle.

### Talks include:

**1:00 PM – 1:15 PM. Great Problems, Great Sessions, Great Circles**

*Brianna Donaldson, American Institute of Mathematics*The foundation of every great Math Circle community is inspiring mathematics problems, facilitated in an inspiring way. So, what makes a great Math Circle problem? Once you have a great problem to work with, how can you build a great session around it? Drawing on workshop surveys, discussions, a little bit of research, and plenty of examples and anecdotes, we explore some characteristics of good problems and good sessions in the context of Math Teachers’ Circles. We then consider the art and science of transforming great problems into great sessions, by examining the evolution of a few perennial favorites, including a session based on the card game SET.

**1:20 PM – 1:35 PM. Exploring Patterns with Technology**

*Jonas Meyer, Loras College*

Amanda Matson, Clarke University

In this talk we will present some of our favorite pattern finding problems in which online and offline computing tools provide ways to better experiment and visualize the problems. Our teacher participants enjoy learning new technology to bring to the classroom, and the technology offers more entry points for challenging problems where patterns are hard to find from limited “by hand” experimentation.**1:40 PM – 1:55 PM. Problems with a Twist**

*Gabriella Pinter, University of Wisconsin-Milwaukee*

At the UWM Math Circle we strive to engage middle and high school students in open-ended, collaborative problem solving activities. The problems presented here are some of our favorite start- or end-of-session problems that have a little twist, and are surprising or entertaining in some way. We find that these problems grab students’ attention and motivate lively discussions.**2:00 PM – 2:15 PM. Recognizing Group Structure in Shapes and Images**

*Angela Antonou, University of St. Francis*

Mallory Johnson, University of St. Francis

In middle and high school mathematics, students have often been exposed to systems of numbers which satisfy certain properties. These properties generally satisfy the definition of a group. In addition, students study symmetries within geometry. In this talk, we present a math circle activity which relates geometry with the abstract concept of a group, resulting in artistic images which are derived from the mathematics.**2:20 PM – 2:35 PM. Middle School Math Circle Problems**

*Monika Kiss, Saint Leo University*

Rachel Cunio, Saint Leo UniversityMath Circle at Saint Leo University draws middle school students. We will discuss three different topics that are the most popular with students at our circle. The first activity involves M&M’s and statistics. The second involves building Platonic as well as Archimedean solids using Magformers and discovering Euler’s formula. Last, we will discuss Graph Theory problems that students of all ages enjoy. We will provide instructions and directions on how the activities are run as well as how we guide the students’ discovery of the theories.

**2:40 PM – 2:55 PM. Roman Numeral Poker: Hilarity Did Ensue**

*J. Lyn Miller, Slippery Rock University*This talk describes an activity adapted by our undergraduate Math Club for hosting an on-campus visit by local gifted middle school students. The setting is that of playing a variation on the classic card game poker, with a deck featuring multiple occurrences of the individual Roman digits. Each player’s goal is to create a legitimate Roman numeral of highest – or lowest – possible value, sometimes subject to constraints. Detailed rules of the game, implementation, selected feedback from the undergraduate hosts and the middle school participants, variations, and follow-up exercises will be presented.

**3:00 PM – 3:15 PM. Mathematical Explorations of Musical Scales**

*Cory Johnson, California State University, San Bernardino*

Jeremy Aikin, California State University, San Bernardino

This spring, the Inland Empire Math Teachers’ Circle explored the connections between musical scales and mathematics. In this session, participants constructed a mathematical model of a piano by utilizing the periodicity of the keyboard. Participants were then able to explore different types of musical scales by analyzing the symmetries that were highlighted by the model. Natural questions arose such as “What makes two musical scales the same or different?” “How many scales of a particular type exist?” “Can you find a musical scale in which there are a prescribed number of different scales?” This talk will describe the setup of the model and the discussions that transpired during the MTC session.**3:20 PM – 3:35 PM. Quilting Squares in a Math Circle**

*Katie Haymaker, Villanova University*This math circle problem deals with designing quilt-passing patterns for a quilting circle so that all participants can visit with each other in the process. The problem translates into a question about constructing row complete Latin squares. Small cases yield a rich exploration for math circle activities, and there are also several natural extensions.

**3:40 PM – 3:55 PM. Math Unbounded: Math Circles without Borders**

*Bob Klein, Ohio University*

Math Unbounded is a global effort to work with communities to create sustainable math circles. Premised on the Navajo Math Circles Project model for remotely-supported circle mentorship, Math Unbounded works with local stakeholders to recruit and train circle leaders and participants to sustain math circles for students and teachers. Furthermore, Math Unbounded opens the spaces for mathematician collaborators to visit and contribute to the development of circles around the globe. Great and joyful mathematics belongs to all, and engaging communities in collaborative problem solving helps contribute to a more peaceful and just world. Focus areas for development have included Mexico, Panama, Guatemala, Nepal, and the Navajo Nation.

## Saturday, July 29

**9:00am – 12:30 pm, Exhibit Hall Open – Visit the NAMC Booth.****1:00pm – 1:50 pm, Special Presentation for High School Students, Parents, and Teachers**

*Those Infamous Exploding Dots: A Preview to Global Math Week.*

Location: Continental Ballroom B

Here is a story that isn’t true.

When I was a young child I invented a machine (not true) that was nothing more than a series of boxes that could hold dots. And these dots would, upon certain actions, explode. And with this machine (in this non-true story) I realized that I could explain true things! I could explain all the mathematics of arithmetic I learnt in grade school (true), all the polynomial algebra I was to learn in high-school (true), pre-calculus series formulas (true), elements of calculus and number theory I was to learn in university (true), and explore unanswered research questions mathematicians are studying today (also true)!

Come see an astounding mathematical story that unites element of the K-12 curriculum, and beyond, in one accessible fell swoop. Bring pencil and paper, and possibly an extra pair of socks – this session will knock your first pair right off!

**Leader: James Tanton**,*Mathematical Association of America***Organizer: Elgin Johnston**,*Iowa State University***Sponsored by the MAA Council on Outreach****2:00pm – 3:30 pm, Math Teacher’s Circle Demonstration. Location: Salon C-1 & C-2**

A math circle is an enrichment experience that brings mathematics professionals in direct contact with pre-college students and/or their teachers. Circles foster passion and excitement for deep mathematics. This demonstration session offers the opportunity for conference attendees to observe and then discuss a math circle experience. While participants are engaged in a mathematical investigation, mathematicians will have a discussion focused on appreciating and better understanding the organic and creative process of learning that circles offer, and on the logistics and dynamics of running an effective circle.*Organizer: Paul Zeitz, University of San Francisco*

*Sponsored by SIGMAA MCST***4:00pm – 5:30 pm, Math Wrangle, Location: Salon C-1 & C-2**

Math Wrangle will pit teams of students against each other, the clock, and a slate of great math problems. The format of a Math Wrangle is designed to engage students in mathematical problem solving, promote effective teamwork, provide a venue for oral presentations, and develop critical listening skills. A Math Wrangle incorporates elements of team sports and debate, with a dose of strategy tossed in for good measure. The intention of the Math Wrangle demonstration at the Joint Math Meetings is to show how teachers, schools, circles, and clubs can get students started in this exciting combination of mathematical problem solving with careful argumentation via public speaking, strategy and rebuttal.Organizers: Doug Ensley, Mathematical Association of America

Ed Keppelmann, University of Nevada, Reno

Philip B. Yasskin, Texas A&M

Paul Zeitz, University of San FranciscoSponsored by SIGMAA on Math Circles for Students and Teachers (SIGMAA-MCST) and American Mathematics Competitions