3rd – 5th – MathCircles.org

Fold & Cut

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Topic(s):

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Handouts, Photos & Videos, References, Virtual Tools

What shapes can result from the following fold-and-cut process?
Take a piece of paper.
Fold it flat.
Make one complete straight cut.
Unfold the pieces.
Are all shapes possible?

Cup Stacking

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Topic(s):

Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides, Handouts, Photos & Videos, References

Begin with a row of cups and end with all of the cups in a single stack. Rules: 1. Count the number of cups in a stack. That stack must jump that number of spaces. For example, 1 cup can only move 1 space; 2 cups have to move 2...

Locked Out: A Breakout Box Session for Your Circle

By:

Donna Farrior, Kimberly Adams

Topic(s):

Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, References

Escape Rooms and “Bomb Disposal” activities are growing in popularity as a form of team building and entertainment. This session blends the two ideas to create a cooperative math activity where the challenge is to solve math problems whose solutions generate combinations to open a locked box. The math problems...

Mathematical Games

By:

Tatiana Shubin

Topic(s):

Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides

This session includes 15 games using manipulatives or paper and pencil. The goal is to decide which one of the two players has a winning strategy. To solve a game means to find a winning, or a non-losing, strategy for one of the players. An answer must include a detailed...

One, Two, Three, Four: Building Numbers with Four Operations

By:

Michael Nakamaye

Topic(s):

Algebra / Arithmetic, Number Theory

Supporting Resources:

Facilitator Guides, Featured in MCircular

What numbers can you make with 1, 2, 3, and 4, using the operations of addition, subtraction, and multiplication? Work on these problems builds arithmetic fluency and provides opportunities to identify patterns, develop and defend arguments, and create conjectures. This investigation also highlights how thin the boundary is between a...

Piece of Cake; Delectable Fractions and Decimals

By:

Heather Danforth-Clayson

Topic(s):

Algebra / Arithmetic, Number Theory

Supporting Resources:

Facilitator Guides, Featured in MCircular, References

While exploring the relationship between fractions and decimals, participants will have the opportunity to practice operations with fractions, notice and explain patterns, review understandings of place value and number sense, and justify their reasoning. You can get a taste of math research by repeating these two steps: Think about an...

Pick’s Theorem

By:

Aimee S. Johnson, Joshua M. Sabloff, Tom Davis

Topic(s):

Geometry

Supporting Resources:

Facilitator Guides, Handouts, Virtual Tools

Austrian mathematician Georg Pick first stated this theorem in 1899. However it wasn’t brought to broad attention until 1969. In this exploration, participants will use rates of change to aid them in discovering Pick’s famous formula by finding a relationship between the area of the figure, the number of perimeter...

Primes, Divisibility, and Modular Arithmetic

By:

Joshua Zucker

Topic(s):

Number Theory

Supporting Resources:

Facilitator Guides

Number theory is all about adding and multiplying integers: pretty simple stuff, good for elementary school or for PhD mathematicians. Dr. Arnold Ross says of number theory, that the purpose is “to think deeply of simple things.” So let’s do that together. This session includes multiple problem sets beginning with...

Recruiting Change for a Dollar

By:

Craig Collins, Cynthia Kramer, Elizabeth Donovan

Topic(s):

Combinatorics, Number Theory, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Handouts

How many different ways are there to make change for a dollar? As mathematicians we often search for patterns in a problem. However, for this problem, there is no simple, predictable pattern to build to an answer, encouraging participants to reach outside their comfort zones and ponder alternative strategies in...

Simplex Locks

By:

Amy Myers

Topic(s):

Combinatorics

Supporting Resources:

Facilitator Guides

A simplex lock is a type of combination door lock that involves pushing-in buttons. Given the set of rules for using a 5-button simplex lock, how many different combinations are there?

Audience: 3rd - 5th