## The Mathematics of Laundry Soap

The grocery store is a brain workout for the mathematically inclined. Not only do the varying metric and imperial conversions tease out the micro-savings of bulk, but neon yellow discount signs encourage percentages and good ole’ multiplication tables. Often you find adults transfixed in a complex division trying to figure out which ham will be cheaper. Once that calculation is complete, they turn their attention to making sure the portion will be enough to feed their whole family. The sheer volume of available estimations overloads me; coupons just complicate the matter–significantly. When you add the typical male intolerance to shopping, …

## The Linear Relations of Hamburgers

Maybe you have seen the Burger King Stacker commercial where “Meat Scientists” work on an interesting problem. Needless to say, it piqued my curiosity the second I saw it; it was not long until I was trying to suck every ounce of mathematical value from the video. I am sure that I did not accomplish this goal, but I did manage to find some interesting problems and questions. First off, the division of cow by pig seems very contrived. Their result (\$) would seem to suggest that (pig)(\$) = cow. Are cows some sort of expensive swine? The representations of …

## NHL Dream Team

My thoughts have begun to turn to the new school year that will occur in August. This may be jumping the gun, but I like to enter prepared. This is partly due to the possibility of job action, and the surety of football, in the fall. I like to spend the first couple days of school working on basic numeracy skills with my grade 9s and 10s. I find a nice task is much more effective than a few worksheets. I do, however, keep a supply of worksheets on hand to offer to kids who just want the assignment. This …

## Life’s Not Fair

The school year is now over for me. That is a bittersweet statement, because I still have mountains of grading and report card comments to do, but there will be no more direct lessons in the 2010/2011 school year. I found myself nostalgic this morning, and began to recount the good times in the classroom. I recalled the probability mayhem that ensued with my Grade 11s. It was very amusing to see them come up with ways to describe “fair”. I would always tell them that I would only do something if it was “fair”. This, to them, meant a …

## Induction Squared

I came across an interesting problem recently that I gave to my students in need of enrichment.  Given a square and the ability to divide that square into smaller squares, can you divide a square into ‘n’ smaller squares. The squares do not have to be the same size. For which values of ‘n’ is this possible? For which values of ‘n’ is this impossible? Students initial reaction was to draw a square and experiment. I cannot think of a better way to begin this problem. It is organic, and contains some very speedy deductions. We begin with suspicion of …

## Maths’ True Form

I teach mathematics at the high school level, and know all about the various theories surrounding school mathematics. I can still remember the intrigue when the term “Math Wars” was introduced to me through some undergraduate reading. I immediately took to the history of my art, and found a very convoluted and bloody past. The constant pendulum between retention math, new math, back to basics, and now the new-new math is dizzying. Whenever I converse with a colleague about a new way of thinking in math education, I am sure to remind them that we are in a war. It …

## Life Without Euclid

This post has nothing to do with geometry. I guess I can’t say that exactly (because of the possible geometric representations), but I am not dealing directly with these. I am always intrigued when I think like I want my students to think. It is these moments that keep me going into the classroom hoping for new understandings. There have been times this year where students have made connections that I never have. These innocent realizations are mathematics manifested in its purest form. A similar experience happened to me this morning. I had been mulling over a problem posed by …

## Review: The Art of Problem Posing

I consider reading an essential part of my professional development. I enjoy a morning glance through a chapter or two, and like to wind down a winter’s day with a book and a cup of coffee. Sometimes reading is the only way to relax my mind at the end of a day. (Naturally, some professional literature is better at putting me to sleep than others). To this point in my young career, no book has changed my perspective on the teaching and doing of mathematics more than The Art of Problem Posing: Third Edition by Stephen I. Brown and Marion …