Skip to the content of the web site.

Face-to-Face Workshops

Math Circle Presentations

The Waterloo Math Circles is a free weekly enrichment activity for grade 6 to 12 students organized by the Faculty of Mathematics of the University of Waterloo.

Information about the audience, dates and location.

Listed below are summaries of the weekly presentations and related student exercises. These resources are provided for both students and teachers. Please use them!

Fall 2014



Junior Grade 6 Oct 7-8/14 Statistics [pdf, solutions]
Oct 14-15/14 Probability [pdf, solutions]
Oct 21-22/14 Algebra [pdf, solutions]
Oct 28-29/14 Introduction to Game Theory [pdf, solutions]
Nov 4-5/14 Exponents [pdf, solutions]
Nov 11-12/14 Cryptography [pdf, solutions]
Nov 18-19/14 Ratios and Rates [pdf, solutions]
Nov 25-26/14 Gauss Prep [pdf, solutions]
Junior Grade 7 & 8 Oct 7-8/14 Exponents and Roots [pdf, solutions, watch video]
Oct 14-15/14 Angles [pdf, solutions, watch video]
Oct 21-22/14 Sequence [pdf, solutions, watch video]
Oct 28-29/14 Series [pdf, solutions, watch video]
Nov 4-5/14 Pythagorean Theorem [pdf, solutions, watch video]
Nov 11-12/14 How We Make Money [pdf, solutions, watch video]
Nov 18-19/14 Game Theory [pdf, solutions, watch video]
Nov 25-26/14 Gauss Prep [pdf, solutions]
Intermediate Oct 8/14 Geometry I: Angles [pdf, prob set, solutions, watch video]
Oct 15/14 Geometry II: Side lengths [pdf, prob set, solutions, watch video]
Oct 22/14 Geometry III: Circle Geometry [pdf, prob set, solutions, watch video]
Oct 29/14 Geometry IV: More Circle Geometry [pdf, prob set, solutions, watch video]
Nov 5/14 Equations and Inequalities I [pdf, prob set, solutions, watch video]
Nov 12/14 Equations and Inequalities II [pdf, prob set, solutions, watch video]
Nov 19/14 CSIMC Sample [prob set, solutions, watch video]
Nov 26/14 CIMC and Puzzles [prob set, slideshow, watch video]
Senior Oct 8/14 Number Theory I [pdf, prob set, solutions]
Oct 15/14 Number Theory II [pdf, prob set, solutions]
Oct 22/14 Number Theory III [pdf, prob set, solutions]
Oct 29/14 Recurrences I [pdf, prob set, solutions, slideshow]
Nov 5/14 Recurrences II [pdf, prob set, solutions, slideshow]
Nov 12/14 Recurrences III [pdf, prob set, solutions, slideshow]
Nov 19/14 Optimization and Operations Research I [pdf, prob set, solutions, slideshow]
Nov 26/14 Optimization and Operations Research II [pdf, prob set, solutions, slideshow]

Winter 2014



Junior Grade 6 Feb 4-5/14 Introduction to Statistics [pdf, solutions]
Feb 11-12/14 Graph Theory I [pdf, solutions]
Feb 18-19/14 Graph Theory II [pdf, solutions]
Feb 25-26/14 Unique Geometry [pdf, solutions]
Mar 4-5/14 Pascal's Triangle [pdf, solutions]
Mar 18-19/14 Circuits [pdf, solutions]
Mar 25-26/14 Gauss Prep [pdf, solutions]
Mar 1-3/14 Modular Arithmetic [pdf, solutions]
Junior Grade 7 & 8 Feb 4-5-6/14 Operations with Sets [pdf, solutions, watch video]
Feb 11-12-13/14 Counting I [pdf, solutions, watch video]
Feb 18-19-20/14 Counting II [pdf, solutions, watch video]
Feb 25-26-27/14 Probability [pdf, solutions, watch video]
Mar 4-5-6/14 Graph Theory I [pdf, solutions, watch video]
Mar 18-19-20/14 Graph Theory II [pdf, solutions, watch video]
Mar 25-26-27/14 Gauss Prep [pdf, solutions, watch video]
Apr 1-2-3/14 Modular Arithmetic [pdf, solutions, watch video]
Intermediate Feb 5/14 Contest Prep I [pdf, prob sets, prob set answers, solutions, watch video]
Feb 12/14 Contest Prep II [pdf, prob sets, prob set answers, solutions, watch video]
Feb 19/14 Contest Prep III [pdf, prob sets, prob set answers, solutions, watch video]
Feb 26/14 Diophantine [pdf, solutions, watch video]
Mar 5/14 Diophantine II [pdf & solns, slideshow, watch video]
Mar 19/14 Cryptography I [pdf, solutions, watch video]
Mar 26/14 Cryptography II [pdf, solutions, watch video]
Apr 2/14 Cryptography III [pdf, solutions, watch video]
Senior Feb 5/14 Cryptography I [pdf, solutions]
Feb 12/14 Cryptography II [pdf, solutions]
Feb 19/14 Cryptography III [pdf, solutions]
Feb 26/14 Linear Recurrence Relations [pdf, solutions]
Mar 5/14 Linear Recurrence Relations II [pdf, solutions]
Mar 19/14 Linear Recurrence Relations III [pdf, solutions]
Mar 26/14 Math Modeling [pdf]

Fall 2013



Junior Grade 6 Oct 8-9/13 Algebra [pdf, solutions]
Oct 15-16/13 Binary and Beyond [pdf, solutions]
Oct 22-23/13 Dimensional and Unit Analysis [pdf, solutions]
Oct 29-30/13 Shapeshifting [pdf, solutions]
Nov 5-6/13 Multiplication [pdf, solutions]
Nov 12-13/13 Divisibility [pdf, solutions]
Nov 19-20/13 History of Cryptography [pdf, solutions]
Nov 26-27/13 Origami & Math Trivia [pdf, solutions]
Junior Grade 7 & 8 Oct 8-9-10/13 Algebra [pdf, solutions, watch video]
Oct 15-16-17/13 History of Numbers [pdf, solutions, watch video]
Oct 22-23-24/13 Finance [pdf, solutions, watch video]
Oct 29-30-31/13 Logic Puzzles [pdf, solutions, watch video]
Nov 5-6-7/13 Similarity & Congruence [pdf, solutions, watch video]
Nov 12-13-14/13 Mathematical Gems [pdf, solutions, watch video]
Nov 19-20-21/13 Mathematical Games [pdf, solutions, watch video]
Nov 26-27-28/13 Origami Math Trivia [pdf, solutions, watch video]
Intermediate Oct 9/13 Ratio [pdf, problem set, solutions, watch video]
Oct 16/13 Rates I [pdf, problem set, solutions, watch video]
Oct 23/13 Rates II [pdf, problem set, solutions, watch video]
Oct 30/13 Rates III [pdf, problem set, solutions, watch video]
Nov 6/13 Counting I [pdf, problem set, solutions, watch video]
Nov 13/13 Counting II [pdf, problem set, solutions, watch video]
Nov 20/13 Counting III [pdf, problem set, solutions, watch video]
Nov 27/13 Favorite Problems [pdf, watch video]
Senior Oct 9/13 Problem Solving I [problem set, solutions, slideshow]
Oct 16/13 Problem Solving II [problem set, solutions, slideshow]
Oct 23/13 Problem Solving III [problem set, solutions, slideshow]
Oct 30/13 Surfaces I [pdf-combined, problem set I , solutions]
Nov 6/13 Surfaces II [problem set II, solutions]
Nov 13/13 Surfaces III [problem set III, solutions]
Nov 20/13 Sequences and Series I [pdf]
Nov 27/13 Sequences and Series II [pdf]

Winter 2013



Junior Grade 6 Feb 5-6/13 Working with Sets [pdf, solutions]
Feb 12-13/13 Working with Abacuses [pdf, solutions]
Feb 19-20/13 Estimation [pdf, solutions]
Feb 26-27/13 Measurement [pdf, solutions]
Mar 5-6/13 Mean Median Mode [pdf, solutions]
Mar 19-20/13 Fractions [pdf, solutions]
Mar 26-27/13 Pythagorean Theorem [pdf, solutions]
Apr 2-3/13 Math Contest [pdf, solutions]
Junior Grade 7 & 8 Feb 5-6/13 Fibonacci Series [pdf, solutions]
Feb 12-13/13 Pascals Triangle [pdf, solutions]
Feb 19-20/13 2D Geometry [pdf, solutions]
Feb 26-27/13 3D Geometry [pdf, solutions]
Mar 5-6/13 Graph Theory [pdf, solutions]
Mar 19-20/13 Circles, Circles, Circles [pdf, solutions]
Mar 26-27/13 Gauss Preparation [pdf, solutions]
Apr 2-3/13 Review Challenge [pdf, problem set, solutions]
Intermediate Feb 6/13 Contest Preparation I [problem set, solutions]
Feb 13/13 Contest Preparation II [problem set, solutions, slideshow, watch video]
Feb 20/13 Analytic Geometry I [pdf, problem set, solutions]
Feb 27/13 Analytic Geometry II [review, problem set, solutions, watch video]
Mar 6/13 Number Theory I [pdf, problem set, solutions, watch video]
Mar 20/13 Number Theory II [pdf, problem set, solutions, watch video]
Mar 27/13 Sequences & Series I [pdf, problem set, solutions, watch video]
Apr 3/13 Sequences & Series II [pdf, problem set, solutions, watch video]
Senior Feb 6 & 13/13 Inversive [pdf, problem set]
Feb 20/13 Inequalities [pdf, problem set, solutions]
Feb 27/13 Graph Theory I [slides, problem set, solutions]
Mar 6/13 Graph Theory II [slides, solutions]
Mar 20/13 Graph Theory III [pdf]
Mar 27 & Apr 3/13 Number Theory [pdf, solutions]

Fall 2012



Junior Grade 6 Oct 9-10/12 Patterns [pdf, solutions]
Oct 16-17/12 Logic [pdf, solutions]
Oct 23-24/12 Tessellations [pdf, solutions]
Oct 30/12 Percent [pdf, solutions]
Nov 6-7/12 Binary Numbers [pdf, solutions]
Nov 13-14/12 Rates and Ratios [pdf, solutions]
Nov 20-21/12 Kinematics [pdf, solutions]
Nov 27-28/12 Math Contest [pdf, solutions]
Junior Grade 7 & 8 Oct 9-10/12 Sequences and Series [pdf, solutions]
Oct 16-17/12 Sets and Venn Diagrams [pdf, solutions]
Oct 23-24/12 Counting [pdf, solutions]
Oct 30-31/12 Geometric Arithmetic [pdf, solutions]
Nov 6-7/12 Cryptography [pdf, solutions]
Nov 13-14/12 Factors and Primes [pdf, solutions]
Nov 20-21/12 Probability [pdf, solutions]
Nov 27-28/12 Gauss Math Contest [pdf, solutions]
Intermediate Oct 10/12 Geometry I - Angles [pdf, problem set, solutions]
Oct 17/12 Geometry II [pdf, problem set, solutions, watch video]
Oct 24/12 Geometry III [pdf, problem set, solutions, watch video]
Oct 31/12 Geometry IV [pdf, problem set, solutions, watch video]
Nov 7/12 Problem Solving [pdf, problem set, solutions]
Nov 14/12 Equations & Inequalities - 1 Variable
[pdf, problem set, solutions, watch video]
Nov 21/12 Equations & Inequalities - 2 Variables [pdf, problem set, solutions]
Nov 28/12 Linear Optimization [pdf, problem set, solutions, watch video]
Senior Oct 10/12 Basics of Set Theory [pdf]
Oct 17/12 Infinite Sets [pdf, problem set]
Oct 24/12 Equivalence Relations and Infinite Sets [pdf, problem set]
Oct 31/12 Symbolic Logic I [pdf, problem set, solutions]
Nov 7/12 Symbolic Logic II [pdf, problem set, solutions]
Nov 14/12 Mathematical Induction [pdf, problem set, solutions]
Nov 21/12 Iterated Functions I [pdf, problem set]
Nov 28/12 Iterated Functions II [pdf, problem set]

Winter 2012



Junior Grade 6 Feb 8/12 Arithmetic Tricks [pdf, solutions]
Feb 15/12 Math Puzzles [pdf, solutions]
Feb 22/12 Number Theory I [pdf, solutions]
Feb 29/12 2D Geometry [pdf, solutions]
Mar 7/12 Measurement and Geometry [pdf, solutions]
Mar 21/12 Probability of Games [pdf, solutions]
Mar 28/12 Intro. Caribou Mathematics Competition [pdf, solutions]
Apr 4/12 Mathifed Jeopardy [pdf, solutions]
Junior Grade 7 & 8 Feb 8/12 Speedy, Speedy Arithmetic [pdf, solutions]
Feb 15/12 Ancient Geometric Constructions [pdf, solutions]
Feb 22/12 Algebraic Approaches [pdf, solutions]
Feb 29/12 Spatial Visualization and Origami [pdf, solutions]
Mar 7/12 Introduction to Graph Theory [pdf, solutions]
Mar 21/12 Circuits [pdf, solutions]
Mar 28/12 Gauss Contest Preparation [pdf, solutions]
Apr 4/12 Math Olympics [pdf, solutions]
Intermediate Feb 8/12 Pascal & Cayley Contest Preparation [pdf, Problem Set, Solutions, watch video]
Feb 15/12 Pascal & Cayley Contest Preparation II [pdf, Problem Set, Solutions, watch video]
Feb 22/12 Pascal & Cayley Contest Preparation III [pdf, Problem Set, Solutions, watch video]
Feb 29/12 Linear Diophantine Equations I [pdf, Problem Set, Solutions, watch video]
Mar 7/12 Linear Diophantine Equations II [pdf, Problem Set, Solutions, watch video]
Mar 21/12 Probability [pdf, Solutions, watch video]
Mar 28/12 Probability: Expectation and Ruination [pdf, Solutions, watch video]
Apr 4/12 The Unreasonable Effectiveness of Mathematics [watch video]
Senior Feb 8/12 Combinatorics [pdf]
Feb 15/12 Combinatorics II Set Theory [pdf]
Feb 22/12 Combinatorics III [pdf, solutions]
Feb 29/12 Probability, Statistics, and Bayes' Theorem I [pdf]
Mar 7/12 Probability, Statistics, and Bayes' Theorem II [pdf]
Mar 21/12 Probability, Statistics, and Bayes' Theorem III [pdf]
Apr 4/12 Elementary Knot Theory [pdf]

Fall 2011



Junior Grade 6 Oct-5/11 Simplifying Equations [pdf, solutions]
Oct-12/11 Math Magic [pdf, solutions]
Oct-19/11 Ancient Number Systems [pdf, solutions]
Oct-26/11 Introduction to Number Theory [pdf, solutions]
Nov-2/11 Matrices I [pdf, solutions]
Nov-9/11 Fibonacci and the Golden Ratio [pdf, solutions]
Nov-16/11 Introduction to Topology [pdf, solutions]
Nov-23/11 Jeopardy [pdf, solutions, game]
Junior Grade 7 & 8 Oct-5/11 Mental Division [pdf, solutions]
Oct-12/11 Modular Arithmetic [pdf, solutions]
Oct-19/11 Prime Numbers [pdf, solutions]
Oct-26/11 Fractals [pdf, solutions]
Nov-2/11 Dimensional Analysis [pdf, solutions]
Nov-9/11 Logic Puzzles [pdf, solutions]
Nov-16/11 Polygonal Numbers [pdf, solutions]
Nov-23/11 Jeopardy [pdf, solutions]
Intermediate Oct-5/11 Ratios [pdf, Problem Set, Solutions, watch video]
Oct-12/11 Rates I [pdf, Problem Set, Solutions, watch video]
Oct-19/11 Rates II [pdf, Problem Set, Solutions, watch video]
Oct-26/11 Counting I [pdf, Problem Set, Solutions, watch video]
Nov-2/11 Counting II [pdf, Problem Set, Solutions, watch video]
Nov-9/11 Counting III [pdf, Problem Set, Solutions, watch video]
Nov-16/11 Math Contest Preparation I [pdf, watch video]
Nov-23/11 Math Contest Preparation II [pdf, watch video]
Senior Oct-5/11 Finite Machines [pdf, Problem Set]
Oct-12/11 Regular Languages [pdf, Problem Set]
Oct-19/11 Regular Languages & Beyond [pdf, Problem Set]
Oct-26/11 Geometry I [pdf]
Nov-2/11 Geometry II [pdf]
Nov-9/11 Geometry III [pdf]
Nov-16/11 Solid Geometry I [pdf]
Nov-23/11 Solid Geometry II [pdf, Solutions]

Winter 2011



Junior Grade 6 Feb-9/11 Cryptography and Tangrams [pdf, solutions]
Feb-16/11 Surface, Area and Volume [pdf, solutions]
Feb-23/11 Distance, Speed and Time [pdf, solutions]
Mar-2/11 Counting [pdf, solutions]
Mar-9/11 Combinations [pdf, solutions]
Mar-23/11 Gauss Contest Preparation [pdf, solutions]
Mar-30/11 Jeopardy [pdf, solutions]
Junior Grade 7 & 8 Feb-9/11 Cryptography and Binary Numbers [pdf, Solutions]
Feb-16/11 Commission, Taxes & Discounts [pdf, Solutions]
Feb-23/11 Markup & Markdown [pdf, Solutions]
Mar-2/11 Probability I [pdf, Solutions]
Mar-9/11 Probability II [pdf, Solutions]
Mar-23/11 Gauss Contest Preparation [pdf, Solutions]
Mar-30/11 Jeopardy [pdf, Solutions]
Intermediate Feb-9/11 Math Contest Preparation I [pdf, Problem Set, Solutions, watch video]
Feb-16/11 Math Contest Preparation II [pdf, Problem Set, watch video]
Feb-23/11 Number Theory I [ Problem Set, Solutions, watch video]
Mar-2/11 Number Theory II [ Problem Set, Solutions, watch video]
Mar-9/11 Number Theory III [ Problem Set , watch video]
Mar-23/11 Analytic Geometry I [pdf , Problem Set , Solutions, watch video]
Mar-30/11 Analytic Geometry II [pdf , Problem Set , Solutions, watch video]
Senior Feb-9/11 Probability I [pdf, Problem Set]
Feb-16/11 Probability II [Problem Set]
Feb-23/11 Number Theory I [Problem Set]
Mar-2/11 Number Theory II [Problem Set]
Mar-9/11 Number Theory III [Problem Set]
Mar-23/11 Invariants I [Problem Set]
Mar-30/11 Invariants II [Problem Set]

Fall 2010



Junior Grade 6 Oct-6/10 Exponents and Binary Numbers [pdf]
Oct-13/10 Tessellations I [pdf]
Oct-20/10 Tessellations II [pdf]
Oct-27/10 Multiplication [pdf]
Nov-3/10 Order of Operations [pdf, Solutions]
Nov-10/10 Algebra [pdf, Solutions]
Nov-17/10 Sequences [pdf, Solutions]
Nov-24/10 Jeopardy [pdf]
Junior Grade 7 & 8 Oct-6/10 Graphs and Transformations [pdf, Solutions]
Oct-13/10 Percents and Ratios [pdf, Solutions]
Oct-20/10 Statistics I [pdf, Solutions]
Oct-27/10 Statistics II [pdf, Solutions] Pascal's Triangle [pdf, Solutions]
Nov-3/10 Number Theory [pdf]
Nov-10/10 Logic [pdf]
Nov-17/10 Game Theory [pdf, Solutions]
Intermediate Oct-6/10 Geometry I [pdf, watch video]
Oct-13/10 Geometry II [pdf, watch video]
Oct-20/10 Geometry III [pdf, watch video]
Oct-27/10 Sequences and Series I [pdf, watch video]
Nov-3/10 Sequences and Series II [pdf, Problem Set, watch video]
Nov-10/10 Sequences and Series III [pdf, Problem Set, watch video]
Nov-17/10 Equations and Inequalities I [pdf, watch video]
Nov-24/10 Equations and Inequalities II [pdf, watch video]
Senior Oct-6/10 Induction and Sequences I [pdf, tutorial]
Oct-13/10 Limits of Sequences I [pdf]
Oct-20/10 Limits of Sequences II [pdf]  Series [pdf]
Oct-27/10 Linear Programming I [pdf]
Nov-3/10 Linear Programming II [pdf]
Nov-17/10 Length, Area and Volume [pdf, Problem Set]

Winter 2010


Sorry! Please download mp3 files to play


Junior Feb-3/10 Number Theory I [pdf, download mp3, listen]
Feb-10/10 Number Theory II [pdf, download mp3, listen]
Feb-17/10 Exponents [pdf, download mp3, listen]
Feb-24/10 Patterns [pdf, download mp3, listen]
Mar-3/10 3D Geometry I [pdf, download mp3, listen]
Mar-10/10 3D Geometry II [pdf, download mp3, listen]
Mar-24/10 Data Analysis [pdf, download mp3, listen]
Mar-31/10 Gauss Preparation [pdf]
Intermediate Feb-3/10 Contest Preparation I [pdf]
Feb-10/10 Contest Preparation II [pdf]
Feb-17/10 Contest Preparation III [pdf]
Feb-24/10 Linear Equations I [pdf, download mp3, listen]
Mar-3/10 Linear Equations II [pdf, download mp3, listen]
Mar-10/10 Linear Equations III [pdf, download mp3, listen]
Mar-24/10 Random Walks I [pdf]
Mar-31/10 Random Walks II [pdf]
Senior Feb-3/10 Game Theory I [pdf]
Feb-10/10 Game Theory II [pdf]
Feb-17/10 Game Theory III [pdf]
Feb-24/10 Probability and Expectation [pdf]
Mar-3/10 Counting Techniques and Probability [pdf]
Mar-10/10 Distribution and Probability [pdf]

Fall 2009


Junior Oct-7/09 Counting [pdf, download mp3, listen]
Oct-14/09 Sets [pdf, download mp3, listen]
Oct-21/09 Probability [pdf, download mp3, listen]
Oct-28/09 Algebra I [pdf, download mp3, listen]
Nov-4/09 Algebra II [pdf, download mp3, listen]
Nov-11/09 2D Geometry I [summary, lesson, download mp3, listen]
Nov-18/09 2D Geometry II [pdf, download mp3, listen]
Nov-25/09 2D Geometry III [pdf, download mp3, listen]
Intermediate Oct-7/09 Ratios [pdf]
Oct-14/09 Rates [pdf]
Oct-21/09 Rates II [pdf]
Oct-28/09 Counting I [pdf]
Nov-4/09 Counting II [pdf]
Nov-11/09 Counting III [pdf]
Nov-18/09 Diophantine Equations I[pdf]
Nov-25/09 Diophantine Equations II [pdf]
Senior Oct-7/09 Infinite Series I [pdf]
Oct-14/09 Infinite Series II [pdf]
Oct-21/09 Infinite Series III [pdf]
Oct-28/09 History of Equations I [pdf]
Nov-4/09 History of Equations II [pdf]
Nov-11/09 History of Equations III [pdf]
Nov-18/09 Graph Theory I [pdf]
Nov-25/09 Graph Theory II [pdf]

Winter 2009


Junior Intermediate Senior
Began in Oct. 2009 Feb-4/09 PCF_Preparation I
Feb-11/09 PCF_Prep. II
Feb-25/09 PCF_Sequences
Mar-4/09 Series
Mar-11/09 Sequs. & Series
Mar-25/09 Analytic Geo I
Apr-1/09 Analytic Geo II
Feb-4/09_Conics I
Feb-11/09_Conics II
Feb-18/09 Conics III
Feb-25/09 Geometry I
Mar-4/09 Geometry II
Mar-11/09 Geometry III
Mar-25/09 Equations

Fall 2008


Junior Intermediate Senior
Began in Oct. 2009 Oct-8/08_Num_Theory_I
Oct-15/08 Num_Theory_II
Oct-22/08 Num_Theory_III
Oct-29/08 Geo_I
Nov-5/08 Geo_II
Nov-12/08 Geo_III
Nov-19/08 Prob_I
Nov-26/08 Prob_II
Oct-8/08_Num_Theory I
Oct-15/08 Num_Theory_II
Oct-22/08 Num_Theory_III
Oct-29/08 Trig_I
Nov-5/08 Trig_II
Nov-12/08 Trig_III
Nov-19/08 Prob_I
Nov-26/08 Prob_II