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 ...
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 ...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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 ...
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...
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 ...
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...
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, ...
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 ...
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...
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...
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. ...
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...
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...
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...
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...
This lesson asks participants to classify possible plane sections of cubes. Once the participants think about it a bit, they can experiment with plast...
This lesson guides students through several different definitions of curvature and includes some hands-on activities calculating curvature of orange a...
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...
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...
This topic begins with the concept of a mathematical relation then introduces the division algorithm and works to developing congruences, remainder ar...
These two lectures introduce modular arithmetic as remainder arithmetic by starting with the division algorithm and progressing to congruences and rem...
Introduction to objects and terminology in planar and three dimensional geometry. Participants are asked to provide examples and "formal" explanations...
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...
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...
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...
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...
This Tom Davis lesson presents several deep results from plane geometry related to circles. These include the Nine Point Circle,Ptolemy’s Theorem, M...
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...
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...
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...
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...
Tatiana presented this to our math circle last April. There was a great deal of problem solving involved. The teachers especially appreciated the warm...
This Tom Davis lesson describes the mathematics related ot computer graphics, and uses this as an introduction to homogeneous coordinates and projecti...
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...
The purpose of this lesson is to help students understand better how to solve various inequalities. The lesson starts with some relatively easy exampl...
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 ...
This Tom Davis lesson plan is a basic introduction to Riemann integration. The lesson explores area under curves as well as applications of integratio...
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 ...
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...
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...
KenKen is a puzzle whose solution requires a combination of logic
and simple arithmetic and combinatorial skills. The puzzles range
in difficulty fr...
Kenken is a simple box style puzzle game involving basic mathematical operations. This Tom Davis lesson plan explores the theory behind Kenken and inc...
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...
This math circle lesson plan investigates several basic results in discrete geometry, specifically the Sylvester-Gallai theorem, the Erdos-de Bruijn t...
This Tom Davis Lesson plan explores Mathematical Induction. Included are lists of problems which can be solved with Mathematical Induction with their ...
This lesson plan is based on the lectures: "The secrets of mental math" by A. Benjamin. We practiced mental addition, subtraction, multiplication and ...
This activity is designed to introduce students to the basic modular arithmetic concept and calculations. It can be used before the ISBN Numbers Acti...
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...
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...
The lesson is devoted to an exciting topic -- numerical puzzles. Problems of this type are a valuable resource since they possess both an entertaining...
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...
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...
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...
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...
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 ...
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...
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...
In the Playing with Parity Circle, students learn about parity through playing games and learning magic tricks. The Circle is an opportunity for stude...
In this lesson various problems related to roots, polynomial equations, and irreducibility of polynomials are discussed. A major tool in most of the p...
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...
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...
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...
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 ...
This lesson is about some applications of Viete's formulas and second order linear recursive sequences. Problems involving tiling and Fibonacci sequen...
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...
This activity lets students understand the formulae for the area of a circle, and the volumes of pyramids, cylinders, cones, spheres, plus higher dime...
In this Tom Davis lesson plan the basic foundations of mathematics are constructed. Starting with set theory and finishing up with the construction of...
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...
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...
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...
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...
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...
This is a combinatorics problem that has a number of generalizations.
The following video missed the introduction to the activity. In the introductio...
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...
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...
This lesson builds intuition about surfaces and three-dimensional spaces from a topological perspective. There is a lot of opportunity for imaginatio...
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...
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...
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 ...
This is an introduction to some ideas of combinatorial group theory. Writing a presentation for a group with generators and relations is like creating...
Students will play Function Machines, shift from "in" and "out" to other words, will feel the need for symbols, and therefore invent variables. Then ...
Teachers are introduced to graph theory by exploring patterns using dominoes. Participants examine whether different sets of dominoes can be connected...
The four lessons attached in the following website serve as good warm-up exercises for experienced learners or as problem solving exercises for beginn...
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...
This lesson is a great introduction to multiplying matrices for students who have no experience with this topic. It develops a conceptual understandi...
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...