Lesson Plans
Math Circle Problem Collection Home | Math Circle Problem Sets | Math Circle Problem List | Math Circle Lesson Plans

Lesson Plan Level and Difficulty Description Owner
Polynomials, the Arithmetic of Dinner Rolls, and Endekaphiles

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I'm thinking of a polynomial with whole number coefficients. When x = 1, the value of the polynomial is 22. When x = 25, the value of the polynomial ... midhudsonmathcircle
3 x 3 Magic Square

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This is a circle that takes 1 to 2 sessions but can be extended to 4 or 5. The starting question is: How many solutions are there to the 3x3 magic ... craig
6C3

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This is a list of problems with answer 6C3. It introduces the idea of a bijective proof and helps students practice their organization skills. It was ... auckly
Algorithms & Flowcharts

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Introduction to algorithms and flowcharts, adaptable to many levels. wmueller
An Interesting Way to Combine Numbers

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In this Joshua Zucker and Tom Davis lesson plan that explores varying approaches for different skill levels to the problem: Imagine that all the nu... pignov
Balloon Numbers

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This lesson is one of the activities that has been used in Julia Robinson Mathematics Festivals. At most of these festivals there are many pages listi... auckly
Bard Math Circle problem sets, 2012-2013

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These are the 2012-2013 problem sets used by the Bard Math Circle in the middle school math circle housed at the Kingston Library in Kingston, NY. Thi... japheth
Base 2, Division, Paper Folding, and Convergence

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This lesson has a nice collection of problems. Highlights include a paper folding algorithm to fold a strip of paper into perfect thirds, and the divi... auckly
Basics of Mental Math

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The focus of this lesson is to show mental math tricks to students. The worksheet groups the problems according to the tricks taught in the powerpoint... AlexZ
Big Numbers

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This lesson describes some of the largest finite numbers that have ever been written down. It is likely that anyone reading it will see a number large... auckly
Big Numbers

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This Tom Davis Lesson plan explores unconventionally large numbers from different perspectives. pignov
Bin Packing

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This Tom Davis lesson considers several problems related to bin packing. It starts with the question of filling a grid polytope with dominoes, moves t... auckly
Binary Trick

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In this trick, someone is asked to pick an integer from 1 to 31 and identify which of five cards contains the number. The person running the trick can... auckly
Braids

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This lesson describes a mathematical theory for three strand braids with the ends at the top joined to a rod and the ends at the bottom joined to a se... auckly
Buffon's Experiment and Approximating Pi

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This is a placeholder to make sure this is in the right place. chris.cunningham
Building Blocks

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This lesson is one of the activities that has been used in Julia Robinson Mathematics Festivals. At most of these festivals there are many pages listi... auckly
Bulgarian Solitaire

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Starting with 15 coins. Move the coins into any amount of piles of any size. Now, each move consists of taking one coin from each pile and creating a ... brandy
Card Tricks

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This lesson introduces several mathematically based card tricks. It is due to Tom Davis. http://www.geometer.org/mathcircles/ auckly
Catalan numbers

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This Tom Davis lesson explores appearances of the Catalan numbers in combinatorics. http://www.geometer.org/mathcircles/ auckly
Chomp the Graph

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Chomp the Graph is a mathematical game of strategy in which two players take turns removing vertices and edges from graphs. Players move in turn rath... mhomp3
Circle of Differences

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Place numbers at the vertices of a regular polygon. A square makes a good beginning. Then at the midpoint of each side, place the difference of the ... auckly
Circles and Angles

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This short lesson gives four basic facts relating circles and angles. It leads into other Tom Davis lessons. http://www.geometer.org/mathcircles auckly
Circles of Apollonius

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Teachers will begin with the famous problem of Apollonius, to find circles that are tangent to three given circles, and to count how many such circles... Debbie Williams
Clip Theory

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What is the next term of the sequence $1, 2, 4, 8, 16, \cdots$? In this activity the next number is not $32$! This lesson touches on Euler's formula, ... auckly
Coins in Twoland

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In Twoland the coins have value 1, 2, 4, 8, 16, and so on. The most interesting town there is Twoville, where the law requires you to pay with exact ... auckly
Coloring

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This Tom Davis lesson plan explores coloring on grids as well as other partitioned geometric objects. pignov
Combinations and Permutations

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This is a description of combinations and permutations and counting techniques. By itself it is not a self contained math circle lesson. These notes a... auckly
Combinations and Permutations

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This Short Tom Davis Lesson Plan explores counting, combinations and permutations. pignov
Combinatorics problems by Tom Davis

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This is a collection of combinatorics problems submitted by Tom Davis. http://www.geometer.org/mathcircles/ General discussion may be found at [... auckly
Constructing voting paradoxes with logic and symmetry; Arrow's Theorem

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The material is roughly for three one to one-and-half hour Math Circle sessions. Each part is self-contained and could be done independently. The fir... Elena
Construction problems

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This is a short collection of straight edge and compass construction problems by Tom Davis. http://www.geometer.org/mathcircles/ It goes along w... auckly
Contest Geometry

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This hand out lists many results from geometry that are useful for math contests. It is from Tom Davis. http://www.geometer.org/mathcircles auckly
Conway's Rational Tangles

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John Conway introduced the notion of a rational tangle in a foundational paper on knot theory. He also devised a wickedly cool dance to explain them. ... auckly
Counting

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This is a set of notes and problems related to combinatorics. It is due to Tom Davis http://www.geometer.org/mathcircles/ Compare with [[Comb... pignov
Counting Cube Colorings

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I first saw this topic presented to a group of middle and high school students at the Boston Math Circle at Northeastern University. The presenter was... viajera
Counting Poker Hands

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This short Tom Davis article gives the mathematical probabilities for different poker hands. pignov
Counting Shapes

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The focus of this lesson is to teach students how to find patterns and count shapes. However, this lesson will also teach them the importance of organ... AlexZ
Coupon Collector

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Learning about Expected Value and the Law of Large Numbers through the classic Coupon Collector problem. potto
Crack the Graham

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There are many more sequences than arithmetic, sequences such as 1,4, 7, 10, 13,... and geometric sequences such as 2, 6, 18, 54, 162, .... In fact, t... auckly
Criss Cross

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Criss-Cross is a game presented by S. Vandervelde in his Circle in a Box book of Math Circle activities and planning documents. The game is...
brandy
Cryptography

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This is a collection of coded jokes starting with simple shift ciphers up to some frequency analysis. Students of many ages can work on it without muc... auckly
Cryptography

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This is a set of notes on Cryptography by Tom Davis. http://www.geometer.org/mathcircles/ Compare with [[Huffman Encoding]]. auckly
Cube Slicing

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This lesson asks participants to classify possible plane sections of cubes. Once the participants think about it a bit, they can experiment with plast... auckly
Curvature and Euler Characteristic

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There are many things that can be done under this heading, and this lesson relates to many other lessons. It is... auckly
Curvature, Angle Defect, and the Gauss-Bonnet Theorem

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This lesson guides students through several different definitions of curvature and includes some hands-on activities calculating curvature of orange a... greenlinda
Curves in Computer Graphics

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This Tom Davis lesson plan explores 3D computer graphics and their transformations and rotations. pignov
Dance to Deeper Understanding of Transformations

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Contradancing is a type of dance much like square dancing or the Virginia Reel, performed to the same kind of country music. Groups of four dancers li... vwatson
Derangements

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This lesson plan by Brian Conrey and Tom Davis asks the question if a sold out crowd was seated randomly in an area, what is the probability that some... pignov
Dice, airplane, sequences, and a card game (start w/ computer explorations).

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Several challenging discrete math problems that invited computer explorations to generate insight, make conjectures, and suggest proof strategies. ... kawski
Die Game

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This game came from a Renaissance fair via Phil Yasskin. The die game is played as follows: A goal number is chosen (usually 31). The first player ... auckly
Division Algorithm and Remainder Arithmetic

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This topic begins with the concept of a mathematical relation then introduces the division algorithm and works to developing congruences, remainder ar... brandy
Division Algorithm and Remainder Arithmetic

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These two lectures introduce modular arithmetic as remainder arithmetic by starting with the division algorithm and progressing to congruences and rem... tinkadavis
Dots and Dashes

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This lesson explores cool patterns that arise when one considers the frequency sequence of a given sequence. It is a sample from James Tanton, M... auckly
Dynamics of Holes in Knots and Mobius Strips.

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Starter Activity: Hand-cuff Knot http://mathssquad.questacon.edu.au/the_handcuffs_puzzle.html Watch our instructors doing the activity: http://www... brandy
Easy problems for beginning elementary school students

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Warm-Up Mr. and Mrs. Boo have three daughters. Each of them have two brothers. How many children are in the family? Ancient numbers 2500 ... jbrodsky
Elementary Geometry

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Introduction to objects and terminology in planar and three dimensional geometry. Participants are asked to provide examples and "formal" explanations... lgawarec
Equations and Unknowns

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In this lesson plan we solve story problems involving one unknown and one equation and then systems of equations with up to 3 unknowns. We also introd... lgawarec
Euler's Theorem

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This Tom Davis lesson plan explores Euler's Theorem using simple geometric figures. pignov
Explaining Fractions and Decimals Visually

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The focus of this lesson is to explain fractions and decimals to students that either have only just learned about fractions and decimals or have no e... AlexZ
Exploring Pascal's Triangle

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In this Tom Davis lesson plan the mathematics embedded in Pascal's Triangle are explored. pignov
Exploring Platonic Solids

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This lesson explores the connection between two dimensional polygons and three dimensional polyhedra. Establishment of Euler’s formula is one of th... ccrowe
Fibonacci and Other Special Numbers

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Part 1 is an exploration of some different ways of thinking about Fibonacci numbers and some Fibonacci number identities (based in part on James Tanto... DPatrick
Folding and Pouring

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This lesson starts with a mixing problem, moves to a paper folding question that is the same problem in disguise and relates both to the analogue of d... auckly
Folding Patterns and Dragons

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This lesson investigates the interesting patterns that result from repeatedly folding a strip of paper in half. It is a sample from James Tanton... auckly
Four Points on a Circle

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This Tom Davis lesson presents several deep results from plane geometry related to circles. These include the Nine Point Circle,Ptolemy’s Theorem, M... auckly
Four Square Problem

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This problem is perfect for students who need practice in basic arithmetic and are up for a challenge. The students repeat subtraction over...
brandy
Fractal Dimension and Sierpinski’s Triangle

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This was the 5th meeting of the Spring 2013 meetings for the Islander Math Circles. Se...

joedachamp
Fractions

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What is a fraction, anyway? Why do the rules you learned in school actually work? The attachment is a handout, followed by teacher notes, followed... joshuazucker
Fractions and Decimals

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This Tom Davis lesson plan explores the relationship between fractions and decimals and exposes the student to the question "does $0.999...=1$? pignov
Game of Nim

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This math circle lesson intends to develop, through the use of selected examples and questions, some key insights into the game of Nim necessary for... auckly
Games

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In this lecture we discuss different problems related to various games. We will see what the right winning strategy is in order to win games for break... grandim
GCD, LCM, Euclidean Algorithm

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This lesson has a hand-out that describes some facts related to the Euclidean Algorithm together with some related problems. There is also a second ha... auckly
Geodesic Domes

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This Tom Davis lesson plan explores the construction of a Geodesic dome. pignov
Geometry and Geography

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In this Tom Davis lesson plan many geometric problems are presented in the setting of familiar Geography. pignov
Geometry from Ancient Iraq

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October 9, 2012 Title: Geometry from Ancient Iraq Abstract: We will study the tablet, BM (British Museum) #15285, which is an Old Babylonian series o... Judith Montgomery
Graph Theory Problems and Solutions

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This Tom Davis lesson plan lists problems in Graph theory as well as their solutions. pignov
Grid Power/ Tatiana Shubin 4/2011

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Tatiana presented this to our math circle last April. There was a great deal of problem solving involved. The teachers especially appreciated the warm... gbrooks
Homogeneous Coordinates and Computer Graphics

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This Tom Davis lesson describes the mathematics related ot computer graphics, and uses this as an introduction to homogeneous coordinates and projecti... auckly
How big is the universe?

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Distances and magnitudes of the Sun and planets are re scaled to the size of everyday objects. We then move to the Milky way and other galaxies. lgawarec
How to Lead a Math Circle (Tom Davis)

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This just gives one perspective on running a math circle by Tom Davis http://www.geometer.org/mathcircles/ Math circles are for high school o... auckly
Huffman Encoding

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This is a set of notes describing Huffman Encoding. The notes describe some very nice theory, but there are not many explicit problems or activities f... auckly
Huffman Encoding

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This Tom Davis Lesson Plan explains telephone numbers, encoding and compressing information. pignov
Inequalities

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The purpose of this lesson is to help students understand better how to solve various inequalities. The lesson starts with some relatively easy exampl... grandim
Infinity

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This Tom Davis lesson plan explores the cardinality of the integers and real numbers, and also discusses the construction of the infinite ordinals. pignov
Intersection Math

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This lesson explores an interesting "multiplication" operation. It is a sample from J. Tanton, Mathematical Outpourings: Newsletters and Musings... auckly
Introduction to Diophantine Equations

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This Tom Davis lesson plan explores solving basic Diophantine equations with tools such as the Euclidean Algorithm. pignov
Introduction to Mathematical Biology

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This lesson presents a pair of math circle activities related to biology. The first considers a rabbit population. The second is a game that models a ... auckly
Introduction to Matrices

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This Tom Davis lesson plan explores Matrices, from basic operations to interesting applications. pignov
Introduction to the Riemann Integral

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This Tom Davis lesson plan is a basic introduction to Riemann integration. The lesson explores area under curves as well as applications of integratio... pignov
Introduction to Topology

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This lesson focuses on introducing students (primarily 5th graders, but could be modified for younger or older students). It is helpful to know a bit ... East Lansing Middle School Math Circle
Investigating the Mathematics of Sona: Sand Drawings from Angola

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Sona are sand drawings used by the Cokwe people of Angola in storytelling. Some of the simpler drawings are done by tracing closed curves around a rec... longjh
ISBN Numbers and Check Digits

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This activity focuses on the use of modular arithmetic in using check digits in development of ISBN Numbers. skilic-bahi
ISBN Numbers and Check Digits_CAM

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This activity focuses on the use of modular arithmetic in using check digits in development of ISBN Numbers. skilic-bahi
Iterated Functions

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This Tom Davis lesson plan explores iterated functions, from basic radicals and trig functions to Markov process and Newton's method. pignov
Kayles on graphs

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Kayles is a 2 player game where each player takes turns coloring in either a single vertex of a given graph, or two adjacent vertices. The player to c... ssharif
KenKen

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KenKen is a puzzle whose solution requires a combination of logic and simple arithmetic and combinatorial skills. The puzzles range in difficulty fr... hbreiter
Kenken for teachers

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Kenken is a simple box style puzzle game involving basic mathematical operations. This Tom Davis lesson plan explores the theory behind Kenken and inc... pignov
Knot Symmetry

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This lesson is a follow-up to the well known rational tangle lesson plan. Help! My little siblin... auckly
Light bulbs

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This activity encourages students to explore a number of sequences and a dynamical system that maps sequences to sequences. It is related to the prime... auckly
Linear Geometric Forms

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This Tom Davis lesson plan explores matrices and liner equations and their relationships to geometric objects and rotation/scaling. pignov
Lines and Points in the Plane

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This math circle lesson plan investigates several basic results in discrete geometry, specifically the Sylvester-Gallai theorem, the Erdos-de Bruijn t... ben.braun
Math Dance

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Karl Schaffer and Erik Stern have developed many innovative ways to connect mathematics and dance. His website lists many activities that could be ... auckly
Math Introduction

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(Photo included below) This is a mathematical way to introduce a group of around 20 people, but this ice-breaker can be modified to work with diffe... uptime
Math Yoga

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This is a short physical math circle activity related to graphing. Watch Brandy lead the activity in the following video. auckly
Mathematical Biology

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This Tom Davis lesson plan explores the Biological mathematics of genetics. pignov
Mathematical Induction

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This Tom Davis Lesson plan explores Mathematical Induction. Included are lists of problems which can be solved with Mathematical Induction with their ... pignov
Mathematical Origami: PHiZZ Dodecahedron

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In this session we will learn how to make a dodecahedron using Tom Hull's PHiZZ modular origami units.

We begin with a discussion of the Plato...

auckly
Mathematical Tiling

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Tiling allows us to mathematizes the world around us, providing game play with classroom tile floors or kitchen counters. The nice aspect of ...
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Mental Math

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This lesson plan is based on the lectures: "The secrets of mental math" by A. Benjamin. We practiced mental addition, subtraction, multiplication and ... lgawarec
Modular Arithmetic

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Modular Arithmetic - the 11 hour clock

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Participants create mod 11 multiplication table and solve equations in mod 11 arithmetic. lgawarec
Modular Arithmetic-CAM

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This activity is designed to introduce students to the basic modular arithmetic concept and calculations. It can be used before the ISBN Numbers Acti... skilic-bahi
Multipication Graphs

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A multiplication graph is formed by choosing a positive integer n, numbering a collection of n-1 points from 1 to n-1, then drawing an edge between an... auckly
Musical Symmetry

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Frieze patterns are enjoyable to look at at pose a... auckly
Number Bracelets

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Choose two numbers in f0; 1; : : : ; 9g to begin a sequence of dig- its. The next digit in the sequence is the units digit of the sum of the two pre... auckly
Number Theory and the abc Conjecture

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A collection of problems in number theory, including an exploration of the Euclidean Algorithm. Also includes a discussion of the abc Conjecture,... auckly
Numerical Puzzles

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The lesson is devoted to an exciting topic -- numerical puzzles. Problems of this type are a valuable resource since they possess both an entertaining... ania_burago
On Reflection

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This lesson investigates the dynamics of billiards in certain lattice rectangles. This is a sample from James Tanton, Mathematical Outpourings:... auckly
Optics and Geometry with Applications to Photography

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This Tom Davis lesson plan explores the mathematics of optics. pignov
Ovals and Diamonds and Squiggles, Oh My! Mathematics of the game of SET

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Both a handout and solutions are included in this document which can be used to guide MTC participants through activities which explain the game of SE... mhomp3
Owls and Voles

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This lesson shows students how mathematics may be used to model the balance between predators and prey in an ecosystem. It includes roll playing and s... auckly
Parity for 4th and 5th graders

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This lesson plan starts with odd and even number addition and then moves to knights on a chess board and or gears in order to have the kids figure out... auckly
Parking Sequences

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We are going to take a look at a problem that deals with parking cars in a one-way parking lot. Each driver in a line of cars will choose which parki... pfordne
Peering Through Tubes

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This activity addresses the question: how much can we see through a tube? Students take measurements and gather data and then search for patterns in ... M Fenn
Permutation Groups

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This Tom Davis lesson plan explores the basic group theory of permutations, with some interesting study of the Rubik's cube as well. pignov
Pick's Theorem

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This Tom Davis lesson plan explores Pick's Theorem by showing how to calculate the area of varying polygons on a lattice. pignov
Pile Splitting

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This is a lesson plan by James Tanton based on the Pile Splitting activity. It will be presented at the 2011 Circle on the Road workshop. DESCRIPTION... auckly
Planar graphs

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This hour and a half lesson introduces planar graphs, i.e., through the Handshake Lemma and Euler's formula. The "Planar Graph Basics" attachment prov... ach3
Platonic Solids

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In this lesson we explore why there are only five platonic solids. This lesson was adapted from a session at the Houston Circle on the Road. In thi... judith.covington@lsus.edu
Playing with Parity

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In the Playing with Parity Circle, students learn about parity through playing games and learning magic tricks. The Circle is an opportunity for stude... auckly
Polya's Counting Theory

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This Tom Davis lesson plan explores Polya's counting theory and the combinitorial problems it can be used to solve. pignov
Polygons

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This short Tom Davis lesson plan gives a definition of a polygon as well poses a few questions to students concerning polygons. pignov
Polynomials and Complex Numbers

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In this lesson various problems related to roots, polynomial equations, and irreducibility of polynomials are discussed. A major tool in most of the p... grandim
Polynomials and pyramids

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The starting point of this lesson is the following question: how many golf balls will make a perfect triangular pyramid? Tabachnikov
Polyomino Exploration

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Polyominoes are geometric figures that are composed entirely of squares. Some examples of different types of polyominoes are: • Dominoes: made f... Burns1
Popcorn Prank

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What would it take to ll this room with popcorn? How many people in the world are talking on their cell phones at this instant? If everyone in the co... auckly
Power of a Point

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In this lesson problems related to power of a point relative to a circle are discussed. The level of the problems ranges from AMC10 to IMO. The lesson... grandim
Practical Calculation of Polygonal Areas

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This Tom Davis lesson plan explores ways of calculating areas of polygons with a focus on practicality. pignov
Practical Probability: Casino Odds and Sucker Bets

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This Tom Davis lesson plan explores casino games and their probabilities, also discussed is the famous non-intuitive Monty Hall problem. pignov
Probability Polynomials and Weird Dice

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In this lesson we explore the probability of different sums appearing when two dice are rolled. We then look at how we could renumber 4 sided (tetrahe... midhudsonmathcircle
Projective Geometry

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In this Tom Davis lesson plan Projective Geometry is explored. From simple perspective in drawings to homogeneous coordinates. pignov
Public Key Cryptography

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Participants find a key-number pair using mod 100 arithmetic to create their public and private keys. They reveal the public key and keep the private ... lgawarec
Pumpkin Numbers

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LESSON PLAN – PUMPKIN NUMBERS (Students Invent Their Own) This lesson is intended to be done after exploring other number types that have names –... Rodi Steinig
Puzzles!

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A collection of puzzles. Used to discuss problem-solving techniques. Used as the "kick-off" meeting for the year for the 2012-13 San Diego Math Te... DPatrick
Pythagorean Tuning vs the Equitonal scale

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What can mathematics say about frequencies that sou... auckly

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This lesson is about some applications of Viete's formulas and second order linear recursive sequences. Problems involving tiling and Fibonacci sequen... grandim
Recursive Functions and Computability

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This is a description of the theory of computation. By itself it is not a self contained math circle lesson. These notes are by Tom Davis http://ww... auckly
Regular polygons

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Presenting one idea together with a collection of problems based on that idea is the comfort food of math circle lesson plans. This Razvan Gelca less... auckly
RSA Encryption

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This Tom Davis lesson plan explores the common digital security method, RSA Encryption, using elementary applications of basic number theory. pignov
Solid Geometry

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This activity lets students understand the formulae for the area of a circle, and the volumes of pyramids, cylinders, cones, spheres, plus higher dime... auckly
Solving BAMO Problems

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This Tom Davis lesson plan details strategies for the Bay Area Mathematical Olympiad exam. pignov
Something from Nothing

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In this Tom Davis lesson plan the basic foundations of mathematics are constructed. Starting with set theory and finishing up with the construction of... pignov
Special Session at Marianna Kistler Beach Museum of Art

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This lesson of Math Circle Seminar at Kansas State University is a special session co-organized with Marianna Kistler Beach Museum of Art. The group... Natasha
Stomp Rockets

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Stomp rockets are great for STEM outreach events. Students construct rockets out of construction paper and then hypothesize which rocket will...
brandy
Straightedge and Compass constructions

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This is a set of notes on geometric constructions by Tom Davis. http://www.geometer.org/mathcircles/ The [[Construction problems]] can be used a... auckly
Subdividing a pile

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This Tom Davis lesson plan sets up a classroom discussion over a simple game of dividing up a stack of chips. The discussion can be modified to a vari... pignov
Symmetric Polynomials

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Various problems related to symmetric polynomials and power sums. In the majority of the solutions, Newton's identities are used. grandim
Tessellations via Tanton

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This lesson investigates tessellations of the plane, including aperiodic ones. This is a sample from James Tanton, Mathematical Outpourings: New... auckly
The Fourth Dimension

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The student studies the nets of a cube to find out what the three dimensional projection of a fourth dimensional cube might look like. vwatson
The Game of Life

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Life is played on a grid of square cells--like a chess board but extending infinitely in every direction. A cell can be live or dead. Cells are born o... lgawarec
The Handshake Problem

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This is a classic problem and is a lot of fun for this age group (and older children, who could move through it at a faster pace). The basic proble... auckly
The Math Salute

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The math salute is a physical challenge that demonstrates the "work backwards" problem solving strategy. It is a very short lesson. Just show your aud... auckly
The Math Salute

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The math salute is a physical challenge that demonstrates the "work backwards" problem solving strategy. It is a very short lesson. Just show your aud... mahantesh
The Mathematics of Sodoku

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This Tom Davis lesson plan explores the mathematics behind the popular newspaper puzzle Sodoku. pignov
The Monty Hall Problem

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The lesson simulates the Monty Hall problem from the show Let's Make a Deal. angelone
The Stern Brocot Tree

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This lesson examines a remarkable enumeration of the rational numbers that is related to Euclid's algorithm and continued fractions. It is a sample... auckly
The TV Problem

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“Your cousin has just gotten a new job as an announcer on the Golf Channel, and is so excited for you to watch every broadcast. While you may enjoy... fulcrum-deploy
The Watermelon Problem

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This is a combinatorics problem that has a number of generalizations. The following video missed the introduction to the activity. In the introductio... auckly

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This lesson investigates numbers that are triangular and square at the same time, and relates these numbers to a well known approximation scheme for t... auckly
Think Extreme

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Presenting one idea together with a collection of problems based on that idea is the comfort food of math circle lesson plans. This lesson lists prob... auckly
ThinkFun River Crossing

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ThinkFun produces a wonderful collection of games and puzzles. It is possible to run a math circle, or part of ... auckly
Tiling and Induction

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There are many wonderful math circle activities related to tiling problems. There is a collection of tiling problems that may be solved via colorin... auckly
Topology of Surfaces and Three-Dimensional Spaces

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This lesson builds intuition about surfaces and three-dimensional spaces from a topological perspective. There is a lot of opportunity for imaginatio... greenlinda
Touching Pennies

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For which numbers is it possible to arrange a collection of exactly that number of pennies in the plane so that each penny touches exactly three other... auckly
Towers of Hanoi for Elementary students

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A lesson used at the East Lansing Elementary Math Circle for exploring the Towers of Hanoi with second-fourth graders. Includes an introduction to re... ashleyahlin
Traffic Jam

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This lesson starts with a physical component, a game students play out of their seats. From there, they play both smaller and larger versions of the ... M Fenn
Turning Laughter into Insight

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This is an introduction to some ideas of combinatorial group theory. Writing a presentation for a group with generators and relations is like creating... auckly
Untuition By Brian Conrey

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We used manipulative to lead us to solve basic questions. I will place three here. Can You place 21 one-by three tiles on a * by * chessboard witho... fulcrum-deploy
Using Function Machines to Invent Variables

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Students will play Function Machines, shift from "in" and "out" to other words, will feel the need for symbols, and therefore invent variables. Then ... Rodi Steinig
UsingDominoes to explore Graph Theory

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Teachers are introduced to graph theory by exploring patterns using dominoes. Participants examine whether different sets of dominoes can be connected... midhudsonmathcircle
Various exercises

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The four lessons attached in the following website serve as good warm-up exercises for experienced learners or as problem solving exercises for beginn... Pi
Visualizing Algebra

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The focus of this lesson is to teach students how to visualize algebraic word problems. This handout helps define concepts such as variables (ex. what... AlexZ
What is a Matrix? What good are Matrices?

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This lesson is a great introduction to multiplying matrices for students who have no experience with this topic. It develops a conceptual understandi... joedachamp
What is the color of my hat?

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The principles of coding theory can be demonstrated with so-called hat problems: participants put on either a black or red hat without looking, so tha... ssharif
Zome Patterns

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In this Tom Davis lesson plan patterns are found with the mathematical building toy Zome. pignov