## Classroom Adventures in Mathematics: Summer Institute

## 2014 | 2013

### 2014 Program

**The 17 Worlds of Planar Ants**: Dror Bar-Natan, Professor, Department of Math, UofT- Back in early 2000, I got my first digital camera and set out to take pictures of my kids and of symmetric patterns in the plane. There are exactly 17 of those, no more, no less. It is an addicting challenge to walk around looking at buildings, brick walls, people's ties, fabrics, what's not, and to try figure out which of the 17 is each one.
**Similar but new; ‘similarity’ in the xy-plane**: Maria Wesslen, Lecturer, Math and CS, UTM- Similarity is often taught in terms of polygons and other 2D shapes, but rarely in terms of graphs of functions in the xy-plane. Examining similarity of such graphs leads to some surprising results and a better understanding of both topics. This will be a hands-on interactive session where we will work through some problems as well as discuss some general ideas.
**(1/2)!**: Kumar Murty, Professor and Chair, Department of Math, UofT- TBA
**Tic-Tac-Toe: a Gateway to Higher Mathematics**: Shai Cohen, Lecturer, Faculty of Engineering UofT- In this seminar, we will sample a small amount of the mathematics that can be taught using Tic-Tac-Toe. We will look at three- and even four-dimensional versions of the game and examine their use in helping students understand the thinking required for linear algebra in any number of dimensions. If we have time, we may touch upon teaching applications of tic-tac-toe in computer programming, modular arithmetic, and game theory. The talk will end with a discussion of another game played that we can play at a higher dimension than usual.
**Quadratic forms and lattices: from Pythagoras to Minkowski**: Justin Martel, Graduate Student, Department of Math, UofT- Sums and differences of squares is a surprisingly rich topic with connections to several area of mathematics, both classical and modern. The speaker aims to give a concrete and handson introduction to some basic aspects.
**“Who Am I?” : Learning Logarithms through Riddles**: Sa'diyya Hendrickson, PUMP Instructor, Department of Math, UofT- In this lesson, we will explore logarithms in a way that is simple and intriguing. Because logarithms are just exponents in disguise, we will define them using a “Who Am I?” riddle. The main goal of this lesson is to use these riddles to emphasize how a logarithm’s “costume,” which many students find to be intimidating, is simply giving us clues to help uncover which exponent it actually is.
**Mathemagic**: Rick Ross, Alumni, Mathematics, UofT- One of the biggest problems in teaching mathematics is getting students to be interested in what many feel is a complex, difficult and uninteresting subject. On the other hand most people are amazed and fascinated with magic.This presentation/workshop on mathemagic will show how a great deal of magic is based on mathematical principles. By exploring mathematically based tricks the student gets a new appreciation for the power of mathematics to say nothing of increased interest in the subject. We will demonstrate and explain several tricks and the principles behind them.You will have a chance to try your hand at several effects so you can teach them to your students. The approach is based on the philosophy that the best education is when you don't realize you are being educated! Although most effects covered do not use playing cards, bringing a deck of cards with you will help you in trying out those that do. For the rest all you need is a pad and paper.
**Using Astronomy in your Math Classroom for Enrichment and Motivation**: John Percy, Professor, Department of Astronomy and Astrophysics, UofT- Math has advanced astronomy. And astronomy has advanced math. And students find astronomy (and dinosaurs) intensely interesting. In this presentation, I will touch on a dozen topics in astronomy that highlight mathematical concepts such as quantity, structure, space, and change. They range from fundamental (earth-moon-sun relations) to frontier (exoplanets, black holes, cosmology). There will be demonstrations, and ample time for questions and discussion.
**Counting without Counting: the Secret Lives of Coins and Dice**: Steven Rayan, PostDoctoral Fellow, Department of Math, UofT- Being asked to roll a pair of dice and being asked to make change for someone's $5 bill are different, in the sense that the former is governed by chance while the latter is not. (Also, the former is often a stepping stone to fun, while the latter is basically a chore.) Underpinning both tasks, however, is a common mathematical theme: operations on "formal power series". In this talk, we will teach ourselves to count all over again, using coins, dice, and even crazy dice!
**Measuring Seemingly Impossible Things**: Michael Pawliuk, Graduate Student, Department of Math, UofT- How can you figure out the height of your school (without doing anything dangerous)? We will use this question as a motivating project for all sorts of seemingly impossible questions that students can tackle. We will also use this as a point of discussion to contrast "outside the box" thinking with "inside the box" thinking. You should come away from this talk with specific project ideas, many possible adaptations for different learning styles and threads to follow that go beyond the basic projects. Weather permitting the talk will happen outside (details TBA).
**Stamps, coins, and chicken McNuggets**: Matthew Sourisseau, Graduate Student, Department of Math, UofT- We'll develop a mathematical understanding of certain practical problems that are elucidated and unified by combinatorics.
**Games to Foster a Mathematical Mindset**: Lindsey Shorser, PUMP Instructor, Department of Math, UofT- Like math, games have well defined goals, opportunities to build strategies, and a requisite amount of patience. In this session, we will discuss and try out games that can modified to include various mathematical concepts. Through games, we can show students how to think about mathematics in a manner that is both constructive and productive.
**Rotation Equilibrium Hands-on Lesson**: Patrick Finnigan, IEEE- We will design (by solving linear equations both graphically and with matrices), build and test mobiles.

### 2013 Program

**Videos for some of these sessions are available on our Videos Page**

**Day 1**

- Welcome and Introductions
- Keynote Speaker: Professor Dror Bar-Natan, Department of Mathematics, University of Toronto
- Panel Discussion: Current Topics in Mathematics Curriculum and University Expectations
- Lunchtime Workshop: Breaking the Ice with Mathematics

**Day 2**

- Hands-on Workshop: Binary Sorting and Searching by IEEE
- Lecture: Finite-state automata
- Hands-on Workshop: Hands-on Math Activities
- Lunchtime Workshop: Careers in Mathematics

**Day 3**

- Lecture: Math Anxiety
- Lecture: Math and Music
- Lecture and Hands-on Workshop: History of Mathematics (with Historical Instruments)
- Lunchtime Workshop: Historical Instruments Display

**Day 4**

- Lecture: Professor Edward Barbeau, Department of Mathematics, University of Toronto
- Roundtable: Resource Sharing and Open Discussion
- Lunchtime Workshop: Math Trails and Scavenger Hunts

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