Imagine three friends play a game. Mia beats Alex, Alex beats Siki, and Siki beats Mia. Which one of the three, if any, should we consider to be overall winner? In this session, we consider the idea of a **tournament, **which is a series of one-on-one win-or-lose games in which every player plays everyone else one time. Continue reading Tournament Winners

# Counting simplified fractions

We all know that many fractions can be simplified, for example, 6/20 may be better written as 3/10. So how many fractions (less than 1) really use a denominator of 20? The answer turns out to be exactly eight… 1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, and 19/20. But is there a rhyme or reason to this answer? Continue reading Counting simplified fractions

# Quadrilaterals

It is hard to believe that this was only our first discussion using Geogebra, the all-powerful program for visualizing geometry problems. In fact we used just a tiny fraction of the tool’s capabilities to explore four-sided figures, or quadrilaterals. Continue reading Quadrilaterals

# Spook-tacular Mental Math

For our Halloween session, presenter Gary Thomas shared some wonderful skills and the abstract concepts that support day-to-day arithmetic. Continue reading Spook-tacular Mental Math

# Multiplication with a slide rule

Anyone can see how to add using a pair of rulers. Say we want to add 3+5. If you slide the “0” of one ruler underneath the “3” of the second ruler, then the “5” of the first ruler appears underneath the “8” of the second ruler. But can we multiply this way? Continue reading Multiplication with a slide rule

# Solids from regular sides

In this session we asked what solids can be made using regular polygons as sides. We investigated this almost entirely by playing around with snap-together polygons. And thanks to our campus 3d printer, we got to handle some of the more obscure shapes too. Continue reading Solids from regular sides

# Fractals and dimension

What is the dimension of a figure? It is natural to say that a segment is 1-dimensional, a rectangle 2-dimensional, and a box 3-dimensional. But what about figures that are not this simple? Continue reading Fractals and dimension

# Ultimate Toothpick Pattern

## Meeting Summary

We met to talk about a very simple, but really interesting, new pattern that can be created in the following way.

- Start with a single toothpick
- Add another toothpick at a right angle to each of the pointy-ends of the pattern
- If two toothpicks, meet at their pointy-ends, don’t add toothpicks to the place they meet.

We started with actual toothpicks, and eventually started to see a neat pattern emerging. And then, things got all mathematical! Continue reading Ultimate Toothpick Pattern

# The BMC is now recruiting for 2015–16

The Boise Math Circle is excited to announce we’ll be continuing our program throughout the 2015–16 school year! The BMC is open to middle and high school students with some experience in algebra. If you like solving problems and want to learn more about the creative side of math, please consider applying. If you have a friend that does, invite them to apply too!

We will begin on Saturday morning, September 19, and meet approximately every two weeks. See our schedule of meeting dates.

- More About the Boise Math Circle
- Program Directors
- Schedule of Circle Meetings
- Recent Circle Meetings
**Apply Now!**

## Teachers

Please help us recruit participants by letting your students know about the program. If you’d like attendance reports for your students (e.g., for extra credit) , please send us an email. You’re of course welcome to join the sessions.

# Boise Math Teacher Circle Summer Workshop

# Agenda

## Wednesday, July 29, 2015

- 8:00 – 9:30 Problem Solving Part 1 (Strategies, 10 Problems, 2 Problems)
- 9:30 – 10:00 Break
- 10:00 – 11:30 Launch + Arithmetic Fun (Overview, Slides)
- 11:30 – 1:00 Lunch (bored?)
- 1:00 – 2:30 Polygons on a Sphere (handout)
- 2:30 – 3:00 Break
- 3:00 – 4:00 Who is a Mathematician?

## Thursday, July 30, 2015

- 8:00 – 9:00 Prep for Field Trip (Arches, Bubbles, Waves, Calculator)
- 9:00 – 9:15 Break
- 9:15 – 11:30 Field trip to the Discovery Center
- 11:30 – 1:00 Lunch
- 1:00 – 2:30 Iteration (handout)
- 2:30 – 3:00 Break
- 3:00 – 4:00 Sona Drawings (handout)