Reflections* is a monthly column for teachers, by teachers on topics of interest to mathematics educators: lesson plans, book/resource reviews, reflections on classroom experiences, and more. If you are interested in sharing your own ideas with mathematics educators in the province (and beyond), consider contributing to this column! Contact us at thevariable@smts.ca.*

**A Summer of Math: Waterloo Math Conference Reflections
**

*Amanda Culver*

Most math enthusiasts have heard of the University of Waterloo—it’s *the* math place to be in Canada. Last month, I was lucky enough to attend—for the second time in three years—their annual Math Teachers’ Conference.

The conference consists of two and a half days of sessions, where participants are fed breakfast, lunch, and dinner and can stay in campus residence (free of charge, with registration). Sessions are led by both professors and teachers, and topics vary widely, from drawing Metamobius surfaces, to applications of mathematics, to problem solving, and more.

As the University of Waterloo—or more specifically, the CEMC (Centre for Education in Mathematics and Computing)—is known for its large offering of math contests and problems, we started off the conference with a session on problem solving. What was great was that we got to work on the problems ourselves, which is what I loved about the conference two years ago and what drew me (and two of my colleagues) back this year.

On the first day, Jason Van Rooyen led a session called *Integrating Problem-Solving in Grades 9 and 10* and J.P. Pretti led *Algorithmic Problem Solving*, and both sessions provided some great take-home problems that I’ll definitely be using with students. I was also introduced to Binary Sudoku, which is quite a fun challenge (head to the following site for instructions and puzzles: http://www.binarypuzzle.com/index.php).

The afternoon session took a more artistic turn, when Ted Gibbons taught us how to draw some Metamobius surfaces. As I am venturing into teaching some arts education courses this year, I might have to include this topic in a lesson. I became obsessed and drew about a dozen. Check out my favourite:

Day Two was just as great. Five professors from the Department of Mathematics talked to us about their various fields, giving us examples of why math is important and why one should obtain a Bachelor of Mathematics. I found this of particular interest, as students never stop asking “Why do we need this?” in math class. Did you know that to compress files, the cosine function is used? Almost everything around us is based on some field of mathematics, such as Pure Mathematics (the math that happened *before* people said, “hey, that’s useful!”), Actuarial Sciences and Statistics (how much money should we save now so that we can have a long retirement?), Combinatorics (the basis of GPS systems and finding the shortest distance from A to B), and Computer Science (image compression and modification, which is very useful in health sciences, among other fields).

Ian Vanderburgh, who is this years’ recipient of the Canadian Mathematical Society’s Excellence in Teaching Award, led a great session on geometry, which is unfortunately not a huge part of our Canadian math curriculum. We played with some interesting geometrical problems, including some involving circle geometry (which *is* in the Saskatchewan Grade 9 curriculum). An interesting point he made was that although we do so much teaching, we rarely get time to sit down and do some math ourselves. So he provided us with some really tough questions that pushed our thinking. Here’s one that we worked on:

*N* lines are drawn. No two lines are parallel. No three lines are concurrent (that is, they won’t share an intersection point). How many regions are formed when *N* lines are drawn?

Next, David Hagen showed us how he flipped his classroom. The general idea is that students do the learning at their own pace at home, via teacher-made videos, and then work on practice questions in the classroom. I’ve attended a few sessions on the flipped classroom, but what made this one unique was that he actually showed us how he films! It definitely gave me some inspiration to flip some lessons in my own classroom.

The last session I got to attend was Carmen Bruni’s *Patterns and Sequences*. The problems he had us work on were ones that could be adapted for a variety of classes, from Grades 7 to 12. Here’s one that I particularly enjoyed (you can find some of the answers at the end of this post):

A slime number is a number that, when “sliced,” leaves behind prime numbers. You can “slice” before or after the number and anywhere in between. For example, 23 is slime because 2/3 gives 2 and 3, both of which are prime; also, 23/ and /23 gives 23, which is also prime.

1. Find the first three even slime numbers.

2. Find the first three square slime numbers.

3. Find the first three cubic slime numbers.

4. Find two consecutive slime numbers. Find three consecutive slime numbers. Can you find an arbitrarily large sequence of slime numbers?

5. A number is super-slime if no matter how you slice the number, all of the slices are prime (e.g., 23 à 2/3, /23, 23/). Show that there are only finitely many such numbers and find them.

Overall, the conference was wonderful, yet again, and I am so glad I was able to spend almost 72 hours with math teachers and math enthusiasts from around the world. Next year, the conference will also make its way to Winnipeg, making the trip more accessible to us prairie teachers. In the meantime, be sure to check out the CEMC website, where you can find a vast collection of past and upcoming contests, fully-developed courses (they are working to include courses from Grades 7-12, and already have some Grade 12 material available, free of charge), and, my personal favourite, their Problem of the Week (which will also be offered in French for the 2016-2017 school year!).

*Answers to the slime problem: *

- a) 2, 22, 32
- b) 25, 225, 289
- c) 27, 343, 729
- d) Two consecutive slime numbers: (2,3), (22, 23), (32, 33); Three consecutive slime numbers: (331, 332, 333); No, an arbitrarily large sequence does not exist, as you can’t find a sequence of 4 or 5 consecutive slime numbers

Amanda Culver has been a French and mathematics secondary teacher within the province of Saskatchewan for four years. She aims to make her classroom a safe and supportive space to be and to learn mathematics. Amanda’s closet is full of math t-shirts, and she got a “pi” tattoo on Ultimate Pi Day. Needless to say, she loves math!