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Mathemagic
Grade: 10-12
Learn how to memorize a deck of cards, influence the flipping of a coin, magically untie yourself from ropes. Is it really magic? No! It's math. This presentation will introduce concepts such as binary and ternary numbers, modular arithmetic, divisibility rules and even topology! |
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Tessellations
Grade: 10-11
We will explore geometry in artwork and nature through tessellations. We will look at the work of artist who used mathematics to enhance their work and even create some of our own tessellation artwork! |
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Fractals
Grade: 11-Calculus
Through artwork and the self similarity of nature, we will investigate the mathematical structure of fractals. Fractals are presented through active play of the Chaos game. The class is asked to work as a team to make decisions that drive the movements of volunteers at the front of the room. The class then records this activity on their own sheets and continues the game, resulting in a fractal pattern, on their own sheets.
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Eulerian Circuits
Grade: 10-11
Presentation without Speaker Notes
Presentation with Speaker Notes
When presenting Eulerian circuits, students are presented with maps of a fictitious pirate land. They are then asked to help the pirates build or remove bridges such that certain criterion can be met. Students work in pairs and attempt to accomplish this task as a team. When requests cannot be completed, the students are asked to rationalize and explain why the request is impossible. We then relate the activity back to a famous problem in mathematics the 7 bridges of Konigsberg.
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Mathematical Jury Duty
Grade: 10-11
A crime has been committed! By exploring various areas of mathematics, such as number theory, probability, graph theory, geometry and more we will see if we can put the guilty party behind bars!
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Toads & Frogs
Grade: 10-Calculus
Presentation without Speaker Notes
Presentation with Speaker Notes
Toads & Frogs is a game that has been utilized at Math Circles for several years. This year, we created supporting material to go hand-in-hand with the game and revive its content. The game involves six student volunteers at the front of the room, being controlled (under game rule sets) by the rest of the class. The students making move decisions are asked one by one what move should be made next; the volunteers then make the corresponding move. Not only is this game excellent for use in classes that need an energy boost, but it also serves to get everyone involved and still allow for exploration of topics such as pattern recognition, difference sequences, solving equations using substituion and elmination and more.
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The game of Nim
Grade: 11adv-Calculus
Presentation without Speaker Notes
Presentation with Speaker Notes
The game of Nim is presented as an introduction to impartial game theory. Students enjoy the manipulation of tokens and often get so involved in the fun of “playing” that they do not realize that they are, in fact, doing mathematics. Binary notation is hidden behind the joy of problem solving.
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Infinity
Grade: 11adv-Calculus
Presentation without Speaker Notes
Presentation with Speaker Notes
While the topic of Infinity can be an intimidating one for many, the attempt was to approach it through real-life situations that are extrapolated into the infinite. We start by telling students that we have a hotel with an infinite number of rooms, and every room is full. We thenask, can we fit 1 more person? 10 more people? An infinite number of people? In this talk we explore the infinite and by answering these questions, introduce students to transfinite arithmetic
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Fibonacci & the Golden Ratio
Grade: 10-Calculus
In this talk students discover the relationship between the Golden Ratio and Fibonacci numbers. We also learn why the Golden Ratio is found throughout nature and listen to Fibonacci number inspired music. |
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Graph Colouring
Grade: 10-11
This talk introduces students to graph theory. We look at the four colour problem, how graph colouring can be used to solve scheduling problems and even lead students through an activity that will classify what graphs can be coloured with 2 colours.
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Planarity
Grade: 10-11
This talk also acts as an introduction to graph theory. We will play the game of sprouts, learn what a planar graph is and why we want to study them. We will then figure out how we can use planar graphs to our advantage to win sprouts!
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Numeral Systems
Grade: 10-Calculus
Take a journey that will take you to the very first systems of numerals in ancient civilizations. Learn the needs that lead the Egyptians to develop clever arithmetic methods to fill their everyday needs, the origin of our system for measuring time and much more!
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Limiting Processes
Grade: Pre-Calculus-Calculus
Through problems like the bouncing ball problem and Zeno’s paradox we will look at infinite sums and explore the concepts behind the limit, without formally defining the limit.
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Tower of Hanoi
Grade: 11-12
The Tower of Hanoi is a very old and very popular problem, it has even been referenced in shows like Survivor and movies like Planet of the Apes. According to Ancient priests there was a temple, which contained a large room with a Tower of Hanoi with 64 golden disks. It was believed that when the last move of the puzzle is completed, the world would end!
In this talk we will explore recurrence relations and use them to solve the Tower of Hanoi problem.
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Population Modelling
Grade: 12-Calculus
Through problems involving frogs and giant lily pads, the Canadian population and zombies, we will investigate population modeling. We will also play with Conway’s Game of Life further explore the complex behavior of populations. |
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Logic & Reasoning
Grade: 10-11
In this talk we will introduce students to formal logic, apply it to some fun activities like the “wolf, goat, cabbage” problem, introduce the idea of 'proof' in a nonthreatening wayand learn that math is not all numbers! |
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Pi
Grade: 10-12
We all know Pi is the ratio of a circles circumference to its diameter and that mathematicians around the world celebrate Pi day, but why else is this number so important and interesting? In this talk we will do some activities that will generate Pi in a surprising way and see why else people love Pi |
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Permutations & Combinations
Grade: 11-12
How many winning poker hands are there? What is the probability in a room of 25 people that two people will share the same birthday? In this talk we will explore permutations and combinations through fun problem solving activities.
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Prime Numbers
Grade: 10-11
Learn how ancient Greeks found prime
numbers, and how huge primes today are the
secret to internet encryption! We will learn some divisibility "tricks",
prove that there are an infinite number of primes, and explore one of the
oldest unsolved problems in mathematics: the Goldbach Conjecture! |
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Circle Geometry
Grade: 12
Presentation without Speaker Notes
Presentation with Speaker Notes
In this presentation we learn about the ancient Greeks and their approach to circle geometry and apply it to some fun problems and paper folding!
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