National Association of Math Circles Wiki

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

August 3-6, 2016

Location: Columbus, OH

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!

**Wednesday, Aug 3**

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

**Thursday, Aug 4**

- 9:00 am - 5:00 pm. Exhibit Hall Open - Visit the NAMC Booth.
- 10:00 am - Noon. Quick Outreach Ideas, presented by NAMC
**Stomp Rockets**. At the NAMC Exhibit Booth. - 1:00 pm - 5:45 pm. SIGMAA-MCST Contributed Paper Session: My Favorite Math Circle Problem. (Franklin C)
- 6:00 pm - 8:00 pm. NAMC MathCircle hosted Happy Hour.

Location: Dick's Last Resort, 343 N. Front Street, #100, Columbus, OH

**Friday, Aug 5**

- 9:00am - 5:00 pm. Exhibit Hall Open - Visit the NAMC Booth.
- 10:00 am - Noon. Quick Outreach Ideas, presented by NAMC
**Four Square**. At the NAMC Exhibit Booth. - 2:00 pm - 4:00pm. Quick Outreach Ideas, presented by NAMC
**Mathematical Tiling**. At the NAMC Exhibit Booth.

**Saturday, Aug 6**

- 9:00am - 12:00 pm, Exhibit Hall Open - Visit the NAMC Booth.
- 10:00 am - Noon. Quick Outreach Ideas, presented by NAMC
**Criss-Cross**. At the NAMC Exhibit Booth. - 1:00pm - 1:50pm. Special Presentation for High School Students, Parents, and Teachers:

The Astounding Mathematics of Bicycle Tracks. (Hayes) - 1:00 pm - 4:55 pm. General Paper Session on Outreach. (Union D)
- 2:00 pm - 3:30 pm. SIGMAA-MCST Math Teachers' Circle Demonstration. (Morrow)
- 4:00 pm - 5:30 pm. Math Wrangle. (Morrow)

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

**1:00 PM - 5:20 PM. SIGMAA-MCST Contributed Paper Session: My Favorite Math Circle Problem**

Location: Franklin C

Organizers: Katherine Morrison, University of Northern Colorado & Philip Yasskin, Texas A&M University

A math circle is an enrichment activity for K-12 students or their teachers, which brings them into direct contact with mathematically sophisticated leaders, fostering a passion and excitement for deep mathematics in the participants. Math circles combine significant discovery and excitement about mathematics through problem solving and exploration. Talks in this session will address a favorite problem or topic that was successful with a math circle audience.

Judith Covington, LSU Shreveport

As Math Teachers’ Circle leaders we are always looking for new ideas for problems for our meetings. When I heard that a 15th pentagon had been found that would tile the plane I knew there was a session idea involved! I will share how I took the newly discovered tiling and created a hands-on activity for the North Louisiana Math Teachers’ Circle. The teachers enjoyed the session so much they decided that the pentagon tiling should be part of our new t-shirt.

Mary Garner, Kennesaw State University

Virginia Watson, Kennesaw State University

One of our favorite math circle problems comes from Exploratory Problems in Mathematics by F.W. Stevenson. As with all the problems from this book, the author presents the problem in such a way that there is a guaranteed entry point, and a series of questions that definitely requires problem-solving stamina. There is also the potential to engage a wide range of mathematical principles, from very basic to more advanced. The specific problem is titled “The Check is in the Mail” and it is concerned with 12 checks and 12 envelopes and how many of the checks are in the correct envelopes. In this session, we’ll discuss our experience with middle-grades math teachers and examine what several math circles have published about problems involving derangements. We’ll also mention one other favorite problem from the book - the Josephus problem in disguise.

Chris Bolognese, Columbus Academy

Raj Shah, Math Plus Academy

Is it possible to measure all possible integer lengths on a ruler without marking every integer on that ruler? In particular, can you construct the most efficient ruler that can measure all integer lengths from 1” to 36” on a yardstick using the least number of marks? And if so, what is the minimum number of marks needed and where should they be placed? A trivial solution would be to mark the ruler at one inch and simply measure objects by moving the ruler along the object one inch at a time. So, we constrain this exploration to using the ruler without moving it along the object. This problem was investigated by our local area mathematics teachers' circle. Participants at the circle started by analyzing a 6" ruler and found that marks at 1" and 4" produced a perfect ruler (that is, one with the least marks that can still measure all the lengths as before). Exploring this problem further, participants developed a number of conjectures, such as key locations to place marks, and how symmetry could be used to find other possible solutions. Participants also developed digital tools to help in the analysis using Javascript and Ruby code. The perfect rulers task served as an exemplary circle topic since it was easy to access and extend and promoted collaboration and discussion.

Diana White, University of Colorado, Denver/National Association of Math Circles

Brandy Wiegers, Central Washington University/National Association of Math Circles

Math Circles have spread rapidly over the past 15 years and through their growth we have seen the development of broader informal mathematical outreach efforts. The National Association of Math Circles (NAMC, http://www.mathcircles.org/) has done the first attempt to survey this growing group and learn more about their contribution to the national picture of mathematical outreach and enrichment. The initial data collection occurred over the spring of 2016, when the NAMC administered a basic information gathering survey to the more than 180 Math Circle programs across the country who have registered on the NAMC website. This talk will summarize the information we learned. In addition, we will provide information on future NAMC initiatives and plans with regard to training, resources, evaluation and research, and partnerships with other informal learning groups.

Sandra Richardson, National Science Foundation

This session will highlight manipulatives and tools used to foster communication among middle and high school mathematics teachers in a Math Teachers' Circle (MTC). Examples of how participants effectively communicate mathematical concepts, representations, and approaches in reasoning through favorite MTC problems will be shared.

Robert Sachs, George Mason University

A Math Circle session devoted to iterative approximation went really well and focused on some important and beautiful mathematics. The "hook" is to ask how the Babylonians might have found the highly accurate approximation to the square root of 2 found on YBC 7289. The topic lends itself to many variations depending on the group and can branch in many ways and be approached at various levels of sophistication.

Douglas B. Meade, University of South Carolina

Fractals are everywhere, and involve beautiful and accessible mathematics. The presentation was originally prepared for use in a Math Teachers' Circle for middle school teachers. The material is easily adapted for use with teachers of other levels -- or for a traditional Math Circle for students.

The presentation includes a balance of theory (geometry, self-similarity, sequences, series, recurrence relations), application (graphical, 3D printing), and hands-on construction (origami).

To participate in the origami component, bring 12 business cards to build a level 0 Menger sponge (a cube) or 192 cards to build a level 1 Menger sponge.

Alessandra Pantano, University of California, Irvine

In this talk, we address the transition of our math circle from a program for talented youth, serving the mathematical elite, to a program with a stronger community outreach objective, serving socio-economically disadvantaged students and their parents. Shifting gears in scope and audience required substantial curriculum modifications, with the obvious challenge of designing mathematically stimulating problems for students who often lack mastery of even the most basic fundamental concepts.

Given that our audience is also generally under-educated in a number of other subjects, our team has recently decided to try to broaden the educational value of our program by designing a mathematically challenging curriculum that addresses topics of high societal impact (e.g., water conservation, environmental protection, health care). The overarching goal is developing an appreciation for mathematics as a truly trans-disciplinary field.

Li Feng, Albany State University

Janis T. Carthon, Albany State University

Courtney L. Brown, Albany State University

An quadratic equation can have two distinct real roots, or one repeated real solution, or two conjugate complex solutions. The first two cases can be visualized by looking at the x-intercept(s) of the graph of the corresponding quadratic function. In the case when there are two conjugate complex solutions, its graph does not have any x-intercepts. So we cannot use the x-intercept to locate the complex roots. In this paper, we will use a new approach to visualize the two complex roots. We will use a special circle and look at the intersection points of circle and the axis of symmetric of the quadratic function. We pointed out those intersection points are the two conjugate complex roots and hence it provides us a way to visualize the complex roots.

Thomas Clark, Dordt College

In this talk I'll share about a Math Teachers' Circle session I recently ran centered around the children's game Spot it! This game has some very interesting mathematics behind it and naturally begs to be explored with inquiry. I'll describe the way I led teachers to ask questions about the game, the way the teachers then explored the topic, and the mathematics behind it all. Materials available.

Crystal Lorch, Ball State University

John Lorch, Ball State University

A Sudoku puzzle is a 9 X 9 grid, divided into nine 3 X 3 subsquares, in which some of the cells already contain numbers (called clues) from the symbol set {1,2,..., 9}. To solve the puzzle one must fill the remaining cells with symbols such that no symbol is repeated in any row, column, or subsquare. "How many sudoku solutions are there?" and "What is the fewest number of clues that can be used to determine a unique Sudoku solution?" are among the natural questions about Sudoku. Answers to both questions are known (6670903752021072936960 and 17, respectively) though the second question stood open until 2012 and currently can only be verified by an exhaustive and time-consuming computer search. In the Yorktown Middle School Math Circle we investigated these questions by considering a smaller version of Sudoku, called Shidoku, in which one uses symbols {1,2,3,4} and a 4 X 4 grid divided into four 2 X 2 subsquares. Students used the ideas of multiplicative counting, relabeling, symmetry, and equivalence classes (the latter we called "teams"; these were represented by "team captains") to show that there are 288 Shidoku solutions and that four is the fewest number of clues that can be used to determine a unique Shidoku solution. In this presentation we describe how students were introduced to the ideas listed above and the activities that led them to their results about Shidoku.

Angie Hodge, University of Nebraska Omaha

This Math Circle session gives the standard river crossing problems a fun new twist with pirate zombies. In this session, I'll explain how to run the session, provide helpful tips on how to make this session run smoothly, and also give a sampling of the problems used in this circle. Be ready for audience participation!

Including Diana White, NAMC and Brianna Donaldson, AIM.

**6:00pm - 8:00 NAMC MathCircle hosted Appetizers and self-hosting Dinner **

Location: Dick's Last Resort, 343 N. Front Street, #100, Columbus, OH

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

**9:00am - 12:00 pm, Exhibit Hall Open - Visit the NAMC Booth.**

**1:00pm - 1:50 pm, Special Presentation for High School Students, Parents, and Teachers
The Astounding Mathematics of Bicycle Tracks. Location: Hayes **

Speaker: James Tanton, MAA

Sir Arthur Conan Doyle asked a question: If you come across a pair of bicycle tracks in the snow, could you determine in which direction the bicycle went? He got the answer wrong! So let’s ride a bicycle, look at its tracks, and get the answer right. Even though this puzzle is now classic in the mathematics community (thanks to the charming MAA book Which Way did the Bicycle Go?... and Other Intriguing Mathematical Mysteries by Konhauser, Velleman, and Wagon), there is still much more we can say and do with bicycle tracks, all leading to some astounding surprises for students, teachers, mathematicians, and math enthusiasts alike. Hold on to your wheels for this one! This is a general outreach lecture presented by James Tanton of the MAA and designed to inspire relevant and exciting mathematical thinking and doing for the high-school classroom. All are so welcome to attend!

**2:00pm - 3:30 pm, Math Teacher's Circle Demonstration. Location: Morrow **

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 designed for local students. While students 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.

Presenter: Dr. Amanda Serenevy, Riverbend Community Math Center

Moderator: Bob Klein, Ohio University.

Sponsored by SIGMAA MCST

**4:00pm - 5:30 pm, Math Wrangle, Location: Morrow **

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 Math Fest 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.

Mark Saul, American Math Competitions

Ed Keppelmann, University of Nevada

Sponsored by SIGMAA MCST

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