MP3 – Construct viable arguments and critique others’ reasoning.

Puzzling Pairs

By:

Topic(s):

Combinatorics, Number Theory, Parity / Invariants, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Lesson Plan, References

Langford pairings are sequences in which a set of N pairs, {1, 1, 2, 2, …, N, N}, is arranged so that every pair, {k, k}, appears in the sequence with k numbers between the pair. Langford pairings have been actively studied by mathematicians since the 1960s for their applications...

Stomachion (Archimedes’ Box)

By:

August Raybould

Topic(s):

Geometry, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Handouts, Lesson Plan, References

The Stomachion puzzle, attributed to the Ancient Greek scholar Archimedes and preserved within the Archimedes Palimpsest, is considered to be the oldest known mathematical puzzle. The puzzle contains 14 pieces in 12 distinct shapes that fit perfectly into a square. Since its discovery, the underlying structure of the puzzle has...

Racial Profiling

By:

Scott Kapralos

Topic(s):

Mathematical Modeling, Social Justice Mathematics

Supporting Resources:

Handouts, Lesson Plan, References, Virtual Tools

To investigate situations in the real world, we sometimes create a mathematical model. A mathematical model is a simplified version of the real world that allows us to understand the real world a little better. Over time we can change this model so that it gets closer and closer to...

Cup Stacking

By:

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...

Percents

By:

Alexandra Edwards, Dyan Palmer

Topic(s):

Algebra / Arithmetic

Supporting Resources:

Facilitator Guides, Handouts

Developed as part of the Math Circles of Inquiry project, this module has students grapple with different representations of percents in various contexts in order to solve real life problems. Students need fluency in percentages for real world applications such as shopping, eating at restaurants, commission based careers, etc. Understanding...

Rational Numbers

By:

Elizabeth Livorsi, Maureen Aguglia, Sara MacKenzie

Topic(s):

Algebra / Arithmetic, Number Theory

Supporting Resources:

Facilitator Guides, Handouts

Developed as part of the Math Circles of Inquiry project, this module is an introductory activity for rational numbers, likely aligned with Grade 7. Students will be given five points on a number line and will be asked to estimate the values of each in a 3-part task and explain...

Liar’s Bingo

By:

Bob Klein, Steve Phelps

Topic(s):

Mathematical Games, Number Theory, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Handouts, References

From recognizing a pattern to generating terms, to abstracting and making inferences, tasks based on patterns embody the “low-threshold, high-ceiling” trait of good problems. Liar’s Bingo is all about patterns. This session involves recognizing patterns and searching for underlying structure, number theory, numeration, and potentially binary arithmetic. Sometimes, as in...

Lockers: An Open-and-Shut Case

By:

Elgin Johnston

Topic(s):

Number Theory

Supporting Resources:

Handouts

A classic Math Circle problem! At a large high school, there are 10000 lockers. The lockers are numbered, in order, 1, 2, 3, . . . , 10000, and to start, each locker is closed. There are also 10000 students, also numbered 1, 2, 3, . . . , 10000....

Mathemagical Card Tricks

By:

Stephanie Santorico

Topic(s):

Algebra / Arithmetic, Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides, References

There are many card tricks based on simple mathematics as opposed to sleight of hand. In this session, participants will play with a number of such tricks, test them out and work on discovering the math underneath, with a goal to formalize the mathematics that makes the trick work.

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...

MathCircles.org

Mathematical Practice: MP3 - Construct viable arguments and critique others' reasoning.

Puzzling Pairs

Stomachion (Archimedes’ Box)

Racial Profiling

Cup Stacking

Percents

Rational Numbers

Liar’s Bingo

Lockers: An Open-and-Shut Case

Mathemagical Card Tricks

Mathematical Games