# Boise Math Circles

The Boise Math Students’ Circle is for Treasure Valley young people with some experience with algebra and multiplication tables who want to experience creative mathematics. The Boise Math Teachers’ Circle is a community for Treasure Valley K–12 math educators.

The Boise Math Circle meets weekly or biweekly on Saturdays. Each meeting delivers an elementary topic with deep roots in mathematical theory. Many of these topics are not usually covered in school. The goal is for each participant to feel a spark and discover something new for themselves.

The typical meeting format begins with background and motivating questions, and then transitions into group work and guided discussions. Participants work on open-ended problems together in small groups, and then discuss their findings with the other groups.

Our activities differ from other extracurricular math programs in that it does not provide tutoring or support for school curriculum. The meetings are intended to be stress-free and encouraging. There are no grades, no competition, and no homework. Instead we encourage lots of collaboration and a loose classroom structure.

### Who participates

We welcome Treasure Valley youth in grades 6–12 of all achievement backgrounds who have an independent interest in mathematics. We strongly encourage students from under-represented groups to join.

We try to choose topics that are both accessible to middle and high school students, and interesting to research mathematicians. They may be chosen from any subfield of mathematics including: combinatorics, number theory, game theory, geometry, advanced algebra, set theory, and more. For specific examples of topics, you can always browse our past sessions.

### Who we are

The Circle is hosted by the mathematics department at Boise State University, and run by two of its faculty. The Circle will also feature visitors and guest discussion leaders on a regular basis. For more information about us, visit the faculty bios page!

## What is a math circle?

A math circle is a group of interested individuals who meet to study mathematics for its own sake.

Math circles differ widely and may take up any number of activities such as elementary problem solving or advanced reading. A math circle differs from a tutoring or enrichment program in that it is not supporting school curriculum.

Our particular circle connects secondary school students with university faculty mentors, and uses guided discovery to generate discussions. Read more on our page about the BMC.

The BMC is the first Idaho program to join the 150+ math circles registered with the National Association of Math Circles.

### Student’s circle (BMC)

The Boise Math Students’ Circle is for Treasure Valley young people with some experience with algebra who want to experience creative mathematics.

• 2018-19 BMC calendar
• Past BMC sessions
• Photos from the BMC
• BMC faculty biographies
• What is a math circle?

### Teacher’s circle (BMTC)

The Boise Math Teachers’ Circle is a community for Treasure Valley K–12 math educators.

Check out the current BMTC program
Some past BMTC sessions
You can also see our past programs:

• BMTC 2017-2018
• BMTC 2016–2017
• BMTC 2015–2016

## Boise Math Teachers’ Circle

The Department of Mathematics at Boise State University is proud to announce we will continue a Math Teachers’ Circle for Treasure Valley K–12 mathematics educators

Boise Math Teachers’ Circle promotional flyer
What’s a Math Teacher Circle?
2018–2019 Meetings
Our meetings will take place during the Saturday mornings listed below, from 9:00 AM to noon. Meetings take place on Boise State University campus, Mathematics Building, room 107. Parking is available (contact a circle organizer for the parking code).

Fall 2018:

• Saturday, September 8, 2018
• Saturday, October 13, 2018
• Saturday, November 10, 2018

Spring 2019:

• January 26
• February 9
• March 9
• April 13

After the meetings, information about the activities will be posted in the BMTC archive.

Circle Organizers
Boise State University Mathematics Department
Margaret Kinzel, Mathematics Education
Zach Teitler, Mathematics

Contact

## Recent sessions

### Potpourri

Our first activity was about the problem of writing numbers as sums of three cubes. This Numberphile video with Tim Browning explained the problem. We tried solving for a few numbers like 39.
bmtc-sessions item dated Mar 9, 2019

### Egyptian Fractions

At this session we welcomed some guests: high school students and non-math teachers. It was really exciting to share our math circle more widely!
bmtc-sessions item dated Feb 9, 2019

### Finance

We explored mathematical concepts in statistics and calculus in a context of finance. Jennifer Eldred, who is a teacher at Kuna High School, shared some activities that she prepared as part of her master’s thesis at Boise State. The activities are available on her web site:
bmtc-sessions item dated Jan 26, 2019

### Fractals

We looked at fractals, and even made our own! This session was led by Teri Willard and Mandy McDaniel. We cut and folded pieces of paper to illustrate the first four “phases” in the iteration for a fractal. We used our models to investigate a number of patterns, such as counting the number of rectangular faces and determining their measurements at each step, to finding the total area or volume of the fractal. That involved geometric series. We discussed how this activity could go into a classroom and the many things that a student might get from it. This was a “low floor, high ceiling” activity—anyone can have fun making the paper models, and the mathematical investigation can go as far as you want it to go.
bmtc-sessions item dated Nov 10, 2018

### Rationals and Irrationals

We looked at irrational and rational numbers. We figured out which real numbers have terminating, repeating, or eventually repeating decimal expansions. And we found some patterns in the periods of repeating decimal expansions: for a prime number $p$, the decimal expansion of $1/p$ always has a period which is a factor of $p-1$. We saw how to prove that some numbers are irrational, including $\sqrt{2}$ and $\log_2(3)$ (the logarithm of $3$ in base $2$).
bmtc-sessions item dated Oct 13, 2018

### Introduction to trees

Continuing with our introduction to combinatorics, this time we explored the structure side of things and introduced graph theory.
bmc-sessions item dated Sep 29, 2018

## Archive of BMC sessions

Sep 29, 2018 Introduction to trees

Sep 15, 2018 Introduction to graph theory

Sep 8, 2018 Introduction to combinatorics

Apr 28, 2018 Regular tessellations

Oct 28, 2017 Graphs and cycles

Oct 14, 2017 Functions and Pairing

Oct 7, 2017 Binomial coefficients and Catalan numbers

Sep 23, 2017 Modular counting and the table setting problem

Sep 16, 2017 Recursion and the four numbers game

Sep 2, 2017 The greatest common divisor and probability

Apr 22, 2017 Sending coded messages

Apr 1, 2017 Recognizing patterns

Mar 11, 2017 Falling chickens

Feb 25, 2017 A tree of fractions

Feb 11, 2017 Patterns in data

Jan 28, 2017 The logic of calculators

Jan 14, 2017 Parametric equations

Dec 10, 2016 The secret lives of permutations, part two

Dec 3, 2016 The secret lives of permutations

Nov 12, 2016 Bart vs Lisa vs Fractions

Oct 29, 2016 Mental math, version two

Oct 15, 2016 Adding together infinitely many numbers

Sep 24, 2016 Ovals upon ovals!

Sep 10, 2016 Mars moon mission

May 21, 2016 The game SET

Apr 30, 2016 Cave person games

Apr 16, 2016 Taking in the whole room

Apr 2, 2016 Multiplying points in the plane

Mar 12, 2016 Graph isomorphism

Mar 5, 2016 Toroidal doodles

Feb 20, 2016 Sudoku and latin squares

Feb 6, 2016 STEM exploration day

Jan 16, 2016 Toroidal polyhedra

Dec 5, 2015 Tournament Winners

Nov 21, 2015 Counting simplified fractions

Oct 31, 2015 Spook-tacular mental math

Oct 17, 2015 Multiplication with a slide rule

Oct 10, 2015 Solids from regular sides

Oct 3, 2015 Fractals and dimension

Sep 19, 2015 The ultimate toothpick pattern

May 19, 2015 Origami and geometry

May 12, 2015 Games with modular arithmetic

Apr 18, 2015 Hyperbolic surfaces

Apr 4, 2015 Moving points

Mar 14, 2015 Three point one four one five something

Mar 9, 2015 Infinite counting numbers

Feb 21, 2015 Patterns in the Fibonacci numbers

Feb 7, 2015 STEM exploration day

Jan 24, 2015 Ways to write numbers

Jan 17, 2015 Shapes and motions

Dec 6, 2014 Number graphs

Nov 8, 2014 Numbers on clocks

Nov 1, 2014 Beguiling tilings

Oct 25, 2014 Coloring maps

Oct 18, 2014 Polygons and area

Oct 11, 2014 Spheres and geometry

Sep 27, 2014 Downtown walking distances

Sep 20, 2014 Sona sand drawings

Boise Math Circles
Joe Champion, Samuel Coskey, Margaret Kinzel, Zach Teitler
scoskey@boisestate.edu