Sessions by Topic
This is a collection of materials developed for Math Circle sessions for teachers and students. These materials were primarily designed as a guide for session leaders rather than for classroom use. Please keep visiting this page, as we are always adding new materials and refining old ones. We welcome your contributions to this list!
“Have Colors, Will Paint” |
Featured Sessions
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We feature different session materials in each issue of our newsletter, MTCircular. These sessions are marked with a star ( ) in the list below.You can also browse our archive of newsletter resources. If there is a session you’d like to see featured in an upcoming newsletter, let us know! |
All Session Materials
Materials featured in our newsletter are marked with a star.
- General Problem Solving
- NEW! Knights and Knaves: A journey to the land of logic (Altha Rodin)
- NEW! Hats and More! (Lorenzo Sadun)
- NEW! Pigeonhole Principle and Parity Problems (Brian Conrey, Corinne Cristiani)
- How to solve it (Dan Freed)
- Introduction to Problem Solving (Joshua Zucker)
- The 1-to-100 Problem (Joshua Zucker and Tom Davis)
- The Power of Wishful Thinking: handout and hints (Altha Rodin)
- Problem-Solving Warmups (Elgin Johnston; TeX files available upon request)
- Problems to Tease and Teach (Tatiana Shubin)
- So You’re Going to Lead a Math Circle (Emily McCullough & Tom Davis)
- Mathematical Games
- NEW! Can you Spot It! (Thomas Clark)
- KenKen (Tom Davis)
- Mathematical Card Tricks (Tom Davis)
- Mathemagical Card Tricks: Participant and Leader documents (Stephanie Santorico)
- Mathematical Games (Tatiana Shubin)
- Mathematical Games (Paul Zeitz)
- The Mathematics of Sudoku (Tom Davis)
- One-Player Games (Joshua Zucker)
- SET (Brian Conrey and Brianna Donaldson)
- Spot It!: A Mathematical Analysis (Deepu Sengupta; TeX files available upon request)
- Spot It! (Tom Clark and Calvin Jongsma)
- Algebra & Arithmetic
- NEW! Optimal Locations of Firehouses (Josh Sabloff)
- NEW! Plimpton 322 and Pythagorean Triples (Bruce Yoshiwara)
- NEW! Pizza & Ice Cream! (Liza Cope)
- NEW! License Plates and Divisibility (Penny Dunham)
- NEW! Curious issues with Order of Operations (Josh Taton)
- NEW! Game 24 and extensions (Matt Seguin)
- Coins in Twoland (Joshua Zucker)
- Exploding Dots, or Dots and Boxes (James Tanton): Instructor notes, Student materials
- Fractions, Decimals, Ratios, Percents, Proportions (Tatiana Shubin)
- Fun with Folding and Pouring: handout, notes (Steve Dunbar & Anne Schmidt)
- Function Diagrams (Henri Picciotto)
- Geogebra Problems (Altha Rodin)
- Shapes and Numbers (Alexander Beloposky)
- Combinatorics & Probability
- NEW! Intersection Math (James Tanton)
- NEW! Simplex Locks (Amy Myers)
- NEW! Count Me In (Marilyn Howard)
- NEW! Hercules and the Hydra (an exploration of patterns that maps onto Peano’s Axioms) (Josh Sabloff)
- NEW! Magic Squares and the Magic Sum (Katie Haymaker)
- Bad Squares on Board Games (Amy Myers)
- Catalan Numbers (Tom Davis)
- Combinations and Permutations (Tom Davis)
- Combinatorial Problems (Tom Davis)
- Counting (Harold Reiter; TeX files and solutions available upon request)
- Counting dots on cubes and tetrahedra (Andrew Gillette)
- Counting Things (Tom Davis)
- Derangements (Brian Conrey & Tom Davis)
- Euler Characteristic & Worksheet (Sam Vandervelde)
- Exploring Pascal’s Triangle (Tom Davis)
- Game of Criss-Cross & Worksheet (Sam Vandervelde)
- The Futurama Theorem (Cheryl Grood)
- Graph Theory Problems (Tom Davis)
- Handshakes and Graph Theory (Elgin Johnston; TeX files available upon request)
- Handshakes: A Trio of Friendly Problems (Mary Fay-Zenk)
- How to Gamble If You Must (Paul Zeitz)
- I Walk the Line(s) (Aimee Johnson & Joshua Sabloff)
- The Mad Veterinarian on Mathematical Safari: notes and slides (Gene Abrams)
- Magic, Latin, and Sudoku Squares (Matthias Beck)
- Magical Questions about Magic and Squares and Magical Graphs: handout and notes (Alison Marr)
- Polya’s Counting Theory (Tom Davis)
- Tilings (Sam Vandervelde)
- Parking Functions (Matthias Beck)
- Probability (Elgin Johnston; TeX files available upon request)
- Rubik’s Slide (Aimee Johnson & Joshua Sabloff)
- Solving Problems with Graphs (Nick Zufelt)
- Shuffling, Cycles, and Matrices (Elgin Johnston; TeX files available upon request)
- Where Can I Park? (Elgin Johnston; TeX files available upon request)
- Geometry
- NEW! Animated Activities (Steve Garland)
- NEW! Brownies and Word Problems (Josh Taton)
- NEW! Playing with geoboards and coins: An exploration towards Pick’s theorem (Christopher Woodward)
- Icebreaker
- Activity
- Alternate Handout (Iuliana Radu)
- NEW! Non-Euclidean Geometries (Samantha Pezzimenti)
- NEW! Polygon explorations with pattern blocks (Christopher Woodward)
- Mysteries of Bicycle Tracks (James Tanton)
- NEW! Patterns and math in quilts (Matt Roscoe)
- NEW! Puzzles, Bands, and Knots (Jennifer Mann)
- Any Conic Section (So Long As It Is a Parabola) (Tatiana Shubin)
- Big Box Problems (Harold Reiter; TeX files and solutions available upon request)
- The Biggest, the Smallest… (Tatiana Shubin)
- Classical Geometric Construction (Tom Davis)
- Curves in Computer Graphics (Tom Davis)
- Euler’s Theorem (Tom Davis)
- Four Points on a Circle (Tom Davis)
- Geodesic Domes (Tom Davis)
- Geogebra Explorations and the Parallel Postulate (Altha Rodin)
- Geogebra Problems (Altha Rodin)
- (Geogebra) Straightedge and Compass Construction (Altha Rodin)
- Geometry and Geography (Tom Davis)
- Grid Luck (Tatiana Shubin)
- Have Colors – Will Paint (Tatiana Shubin)
- Homogeneous Coordinates for Computer Graphics (Tom Davis)
- (Mostly) Simple (Mostly Area) Problems with Solutions (Tatiana Shubin)
- Pick’s Theorem (Aimee Johnson & Joshua Sabloff)
- Pick’s Theorem (Matthias Beck)
- Pick’s Theorem (Tom Davis)
- Polyhedral Symmetry (Sam Vandervelde)
- Practical Calculation of Polygonal Areas (Tom Davis)
- Projective Geometry (Tom Davis)
- The Circles of Apollonius (Chris Goff)
- The Mathematics of Sona (Sand Drawings from Central Africa) (Paul Ellis)
- The Mathematics of Zome (Tom Davis)
- Number Theory
- NEW! Prime Numbers (David Patrick)
- NEW! Prime Climb (Chris Goff)
- Card Shuffling and Repeated Decimals (Steve Pelikan & Steve Phelps)
- Codes, Ciphers, and Secret Messages (Matthias Beck)
- Coins, M&M’s, and Generating Functions (Matthias Beck)
- Compositions (Joshua Zucker): Session notes, Teachers’ guide
- Cryptography (Tom Davis)
- Digital Delirium (Harold Reiter; TeX files and solutions available upon request)
- More Digital Delirium (Harold Reiter; TeX files and solutions available upon request)
- Divisibility Tests (Matthias Beck)
- Factor Game (PBS Mathline)
- Factorials and Squares (Estelle Basor)
- Fractions and Decimals (Tom Davis)
- Friday the Thirteenth: handout and slides (Sheila Krilov)
- Introduction to Diophantine Equations (Tom Davis)
- Introduction to Finite Systems: Z6 and Z7 (Harold Reiter; TeX files and solutions available upon request)
- The Jug Band (Elgin Johnston; TeX files available upon request)
- Lockers: An Open-and-Shut Case (Elgin Johnston; TeX files available upon request)
- Patterns in Decimal Expansions (Brian Conrad): slides and exercises
- Place Value Problems (Harold Reiter; TeX files and solutions available upon request)
- Primes, Divisibility, and Modular Arithmetic (Joshua Zucker)
- Product Game (Judith Montgomery, via NCTM)
- RSA Encryption (Tom Davis)
- Prime Number Card (Paul Zeitz)
- Repeating Decimals (Elgin Johnston; TeX files available upon request)
- Using the Euclidean Algorithm (Harold Reiter; TeX files and solutions available upon request)
- Miscellanea
- Transfinite Numbers (Martin Rudolph)
- Big Numbers (Tom Davis)
- Coloring (Tom Davis)
- Conway’s Rational Tangles
- Notes from Tom Davis
- Slides and videos (Part 1, Part 2) using individual tabletop tangle cards, from Altha Rodin
- Notes from James Tanton
- Escher Tilings (Altha Rodin)
- Euler’s Formula (Kovan Pillai)
- Frogs and Toads (East Texas MTC via Cut the Knot)
- Infinity (Tom Davis)
- Introduction to Matrices (Tom Davis)
- Mathematical Puzzles in Literature (Elizabeth Jaffe)
- Permutation Groups and Rubik’s Cube (Tom Davis)
- Sucker Bets (Tom Davis)
- Visualization in Algebra (Tom Davis)
- NEW! A Potpourri of Delightful Mathematical Curiosities (Joy Hsiao)
- NEW! Mathematical Magic for Muggles (Paul Zeitz)
- NEW! How do you connect the dots? (Andrew Gillette)
- NEW! Fun with filtering(Andrew Gillette)
- NEW! Liars Bingo(Bob Klein and Steve Phelps)
