### Dates: August 5 – 8, 2015

Location: Washington, DC

## Schedule at a Glance

**Wednesday, Aug 5**

- 5:00 pm – 7:00 pm, Grand Opening Exhibit Hall Reception.
- 5:00 pm – 7:00 pm. James Tanton’s activity
**Impossible Braids a**t the NAMC Exhibit.

**Thursday, August 6**

- 8:15 am – 11:10 am, Mentoring and Outreach Special Session
- 9:00 am – 5:00 pm, Exhibit Hall Open – NAMC booth open!
- 9:00 am – 11:00 am. Presented by Brandy Wiegers,
**Frogs and Toads**, - 1:00 pm – 3:00 pm. Presented by Sommer Gentry,
**Recursive Mountain Climbing (counting)**, at the NAMC Exhibit booth. - 3:00 pm -5:00 pm. Activity by Vi Hart,
**Mathematical Balloons**, at the NAMC Exhibit booth.

**Friday, Aug 7**

- 8:00 am – 8:25 am, History Of Math Circles
- 8:30 am -11:05 am:
- MAA’s 100th Anniversary problems
- Planned State-Wide Math Contest
- Explored the 100 (and 1) Spaces of Prime Climb in a Math Teachers’ Circle
- Growing Math Circles for the Next 100 Years
- 100 Problems Involving the Number 100
- The Cell Phone Dropping Problem
- From 100s in a Number to 100 Squares on a 10×10 Checker Board (Or Are There More?)
- Spinout, The Brain, Gray Code, and 100

- 9:00 am – 5:00 pm, Exhibit Hall Open – NAMC booth open!
- 11:15 am – 1:00 pm. Phil Yasskin presents
**Two person games**at the NAMC Exhibit booth. - 1:00 pm – 3:00 pm. Activity by Joshua Zucker,
**Wolves & Sheep**, at the NAMC Exhibit booth. - 2:00 pm – 2:15 pm, Seeding Mathematical Interest in Inner-City Latino Students
- 3:00 pm – 5:00 pm, Activity by Sam Vandervelde,
**Criss Cross**, at the NAMC Exhibit booth. - 6:00 pm – 9:00 pm, NAMC MathCircle Dinner

**Saturday, Aug 8**

- 9:00 am – 12:30 pm, Exhibit Hall Open, NAMC booth open!
- 9:00 am – 11:00 am,
**Mathematical Tilings**presented at the NAMC Exhibit booth. - 1:00 pm -1:50 pm, A Dozen Proofs that 1=2; A Quirky Overview of Mathematics for High School Students, Parents, and Teachers. Located in the Marriott Wardman Park, Salon 2.
- 2:00 pm – 3:00 pm, SIGMAA-MCST Math Circle Demonstration, Marriott Wardman Park, Maryland A
- 4:00 pm – 5:30 pm, Math Wrangle, Marriott Wardman Park, Maryland A

# The Details

**Wednesday, Aug 5**

- 6:00 pm – 8:00 pm, Grand Opening Exhibit Hall Reception

**Thursday, Aug 6**

9:00 am – 5:00 pm, Exhibit Hall Open8:15 am – 11:10 am, **Mentoring and Outreach Special Sessions**

__What’s It Like to Be Editor-in-Chief of the Notices of the American Mathematical Society?__

Frank Morgan, Williams College

__Upper Elementary Outreach Mobius Bands and Polyhedra__

Beth Schaubroeck, United States Air Force Academy

__“Energizing” Students__

Elizabeth Yanik, Emporia State University

__Girls in Science: Over 15 Years of STEM Outreach for Middle School Girls__

Susan Kelly, University of Wisconsin – La Crosse

__Expanding Your Horizons at James Madison University: Math and Science Outreach to Middle and High School Girls__

Katie S. Quertermous, James Madison University

Elizabeth Arnold, James Madison University

__Rural STEM Model__

Elizabeth Mauch, Bloomsburg University

__How to Hook Pre-Service Teachers on Professional Development__

Pari Ford, University of Nebraska at Kearney

Amy Nebesniak, University of Nebraska at Kearney

__Impact of 2015 National Math Festival on Undergraduate Mathematics Students__

Alice E. Petillo, Marymount University

Nicole Ferree, Marymount University

__Increasing Diversity in the Classrooms: A Path towards Inclusion in Mathematics__

Li-Sheng Tseng, University of California, Irvine

Alessandra Pantano, University of California, Irvine

__Native American-based Mathematics Materials for Undergraduate Courses__

Charles P. Funkhouser, California State University Fullerton

Miles R. Pfahl, Turtle Mountain Community College

Harriet Edwards, California State University Fullerton

__Creating a Meaningful Undergraduate Research Project__

Brandon Samples, Georgia College & State University

__Supporting the Success of Women Faculty through an NSF ADVANCE Grant: Looking Back, Moving Forward__

Jenna Carpenter, Louisiana Tech University

D. P. O’Neal, Louisiana Tech University

**Friday, Aug 7**

- 8:00 am – 8:25 am,
**A Partial History of Math Circles**

Marriott Wardman Park, Washington 4

Diana White, University of Colorado Denver

Brandy Wiegers, University of Central Washington

Originating in Eastern Europe, Math Circles migrated to the United States in the 1980s. Starting approximately at the same time on both the east and west coast, they have grown to several hundred today. While the inaugural Math Circles in the United States started with a focus on preparing mathematically talented high school age youth for advanced mathematical competitions, their focus has now broadened in scope. There are now Math Circles for all ages of children (preschool through high school) as well as for teachers. In addition, while some focus on preparing for local or national competitions, others focus on providing non-competitive mathematical enrichment experiences for all interested students. In this talk, we provide an overview of this history, focusing on inter-relationships between various Math Circles and how they have both contributed to the development of mathematical communities as well as benefited from it.

- 8:30 am – 11:05 am,
**Math Circle Problems in Honor of the MAA’s 100th Anniversary**

Marriott Wardman Park, Washington 6

A mathematics circle is an enrichment activity for K-12 students or their teachers, which brings them into direct contact with mathematics professionals, fostering a passion and excitement for deep mathematics in the participants. It is usually a weekly or monthly activity, but it can also be an intensive summer experience. Circles provide rich open-ended problems that enable students or their teachers to strengthen their problem-solving skills and deepen their appreciation for and excitement about mathematics. In honor of the MAA’s 100th anniversary, we especially encourage talks that address a problem or topic involving the number 100 that was successful at your math circle.

Organized by: Katherine Morrison, University of Northern Colorado, Philip Yasskin, Texas A&M University, Paul Zeitz, University of San Francisco. Sponsored by SIGMAA MCST.

### Talks include:

- 8:30 am – 8:45 am.
**Coordinating a State-Wide Math Contest. Abraham S. Mantell, Nassau Community College.**

The particulars of coordinating the New York State Mathematics Association of Two-Year Colleges Math League were addressed. Several past problems will be presented, particularly those involving the number 100, in honor of the MAA’s centennial celebration.

- 8:50 am – 9:05 am.
**Abbot and Costello Numbers,**

Mary Garner, Gateway Community Math Center

Virginia Watson, Gateway Community Math Center

The comedy team of Abbott and Costello were famous for a skit in which Costello proves that 7 x 13 equals 28. A Math Circle we led began with the skit and then explored the question “What other three numbers would work in the same way?” We applied some algebra, did some guess and check, played around, and then systematically came up with a list of numbers (less than 100) for which the routine would work. We discussed how we knew there could be no other numbers. We asked if we could extend the algorithm to numbers bigger than 100. This is a simple and fun activity that is accessible to younger students.

- 9:10 am – 9:25 am.
**Exploring the 100 (and 1) Spaces of Prime Climb in a Math Teachers’ Circle**

Jialing Dai, University of the Pacific

Christopher Goff, University of the Pacific

Sara Malec, Hood College

Dennis Parker, University of the PacificIn this presentation, we will describe our Math Teachers’ Circle and explain the way that we used the Kickstarter-funded game Prime Climb (formerly Primo) to get middle school teachers thinking about primes, the Sieve of Eratosthenes, and prime factorization.

- 9:30 am – 9:45 am.
**Growing Math Circles for the Next 100 Years. Brandy Wiegers,**

Central Washington University/National Association of Math Circles

Diana White, University of Colorado, Denver/National Association of Math CirclesThe National Association of Math Circles was founded in 2007 with the primary goals to (1) Seed the creation of additional Math Circles in the United States, (2) build a community of Math Circles leaders through which novice and existing leaders are connected, encouraged and inspired, (3) provide high-quality resources that help Math Circles build and sustain effective programs, (4) document and disseminate the impact of Math Circle programs across the nation. The Audience learned about our current work and future plans to promote these goals including the Math Circle Mentorship And Partnership Program (MC-MAP) which started in Fall 2015. The end of the session will include time to share questions and ideas that you have for the growth of the national Math Circle movement.

The National Association of Math Circles was founded in 2007 with the primary goals to (1) Seed the creation of additional Math Circles in the United States, (2) build a community of Math Circles leaders through which novice and existing leaders are connected, encouraged and inspired, (3) provide high-quality resources that help Math Circles build and sustain effective programs, (4) document and disseminate the impact of Math Circle programs across the nation. The Audience learned about our current work and future plans to promote these goals including the Math Circle Mentorship And Partnership Program (MC-MAP) which started in Fall 2015. The end of the session will include time to share questions and ideas that you have for the growth of the national Math Circle movement.

- 9:50 am – 10:05 am.
**100 Problems Involving the Number 100.**

James Tanton, MAA

In this whirlwind of a talk, we offered 100 problems each involving the number 100 that have been used to inspire mathematical musing among students, educators, and general mathematical enthusiasts and circlers.

- 10:10 am – 10:25 am.
**The Cell Phone Dropping Problem**

Japheth Wood, Bard College

Philip B. Yasskin, Texas A&M University

You work for a cell phone company which has just invented a new cell phone protector and wants to advertise that it can be dropped from the N-th floor without breaking. If you are given 1 or 2 phones and a 100 story building, how do you guarantee you know the highest floor it won’t break with the smallest number of trial drops? If you are only given 1 phone you would need to drop it from each floor starting from the bottom, and this might take you 100 drops. If you are given 2 phones, you could drop from every other floor and guarantee you will know the highest floor it does not break with at most 51 drops. Can you do better than 51 drops? How? In what directions does this problem lead?

You work for a cell phone company which has just invented a new cell phone protector and wants to advertise that it can be dropped from the N-th floor without breaking. If you are given 1 or 2 phones and a 100 story building, how do you guarantee you know the highest floor it won’t break with the smallest number of trial drops? If you are only given 1 phone you would need to drop it from each floor starting from the bottom, and this might take you 100 drops. If you are given 2 phones, you could drop from every other floor and guarantee you will know the highest floor it does not break with at most 51 drops. Can you do better than 51 drops? How? In what directions does this problem lead?

Dr. Yasskin was given this problem by a middle school student at SEE-Math who had learned it at MathPath. Yasskin has used it successfully at the TAMU Math Circle with high school students and at a session of 30 Davidson Young Scholars. Dr. Wood developed an information theory proof that you can’t do it with fewer than ? drops (answer withheld until the talk), and is planning to use this problem at the Bard Math Circle this summer.

- 10:30am – 10:45am.
**From 100s in a Number to 100 Squares on a 10×10 Checker Board (Or Are There More?)**

Victoria Kofman, Quality Engineering Education, Inc. Organizing information is an important problem-solving skill. It can be developed when teaching students several topics starting from second-grade material and finishing by algebra level problems.

In second grade, many students have difficulties with finding the quantity of tens or hundreds in large numbers. At Vika School, students learn this material by solving problems where tens are represented as rectangles and hundreds as triangles. Using our triangles-rectangles model, The flag of Great Britain, a rectangle with a vertical line, a horizontal line, and two diagonals, represents 1,690. The exercise not only helps students understand tens and hundreds, but teaches them strategies for organizing information.

The next topic that can be used to foster skills of organizing information is probability: drawing “trees” based on well-organized structures helps in calculating the number of combinations.

On Algebra level, the students might be proposed to find a total number of squares on a 10×10 international checkers board. If a student can solve this problem using more than one approach, the student has mastered the skill of organizing information.

- 10:50am – 11:05am.
**Spinout, The Brain, Gray Code, and 100**

George McNulty, University of South Carolina

Nieves McNulty, Columbia College

Douglas B. Meade, University of South CarolinaSpinout and the Brain are two classic puzzles with a common theme: both are based on Gray codes. This presentation focuses on the Gray code, including its history and applications (not just fun puzzles) in a format suitable for use with a Math (Teachers’) Circle. In recognition of the MAA’s 100th anniversary, we will certainly learn that 100 is the 5th number in Gray code; we might even find some time to determine how to determine the 100th number in the Gray code.

- 2:00 pm – 2:15 pm,
**Seeding Mathematical Interest in Inner-City Latino Students**

Themed Contributed Paper Sessions: TCPS 15 – Democratizing Access to Authentic Mathematical Activity

Alessandra Pantano, University of California, Irvine

Li-Sheng Tseng, University of California, Irvine

Andres Forero, University of California, Irvine

The UCI Math Circle initiated a pilot program to work with a group of about 30 middle school Latino students from a low-performing public school in nearby Santa Ana, CA. During the 2014–2015 academic year, we ran 16 sessions of mathematical explorations on a variety of topics including algebra, number theory, and geometry. The program is open to all the students interested in mathematics, with no regards to their mathematical abilities. We will describe our experience working with students in grade 6–8 with a wide range of math background, and share our insights in creating educational material that increases both the students’ mathematical competence and their interest in “doing math.”

- 6:00pm – 9:00pm
**NAMC MathCircle hosted Appetizers and self-hosting Dinner**

**Saturday, Aug 8**

- 9:00 am – 12:30 pm, Exhibit Hall Open – NAMC booth open!
- 1:00 pm – 1:50 pm, Special Presentation for High School Students, Parents, and Teachers:

**A Dozen Proofs that 1=2: An Accessible and Quirky Overview of Mathematics for K12 Teachers and Their Students.**

Marriott Wardman Park, Salon 2

James Tanton, The Saint Mark’s Mathematics Institute and MAA

Guidobaldo del Monte (1545-1647), a patron and friend of Galileo Galilei, believed he had witnessed the creation of something out of nothing when he established mathematically that zero equals one. He thereby thought he had proven the existence of God! James Tanton doesn’t claim to be so bold, but he is willing to prove instead that one equals two. And, moreover, just to convince you that he is right, he will do so a dozen times over, drawing upon a wide spectrum of mathematical techniques: school algebra and arithmetic, probability and mechanics, pure thought and physical action! Will you be able to find fault with any of his “proofs?” This will be a math talk of the like you’ve never seen before. All are welcome!

- 2:00 pm – 3:30 pm,
**SIGMAA-MCST Math Circle Demonstration**, Marriott Wardman Park, Maryland A

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.

Katherine Morrison, University of Northern Colorado

Japheth Wood, New York Math Circle

Sponsored by SIGMAA MCST

- 4:00 pm – 5:30 pm,
**Math Wrangle**, Marriott Wardman Park, Maryland A

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