You will not catch me claiming that problems need to be real world in order to be relevant. I would much rather think of classroom materials as either mind numbing or thought provoking. This continuum can be applied to hypothetical, practical, or genuine scenarios (a classification system neatly summarized in a chart in this article). I see the greatest potential in scenarios that provide elegant entrance to mathematical reasoning. If it happens to contain a real world context, fantastic. Either way, it needs to be thought provoking. Take a look at the chart below: If you don’t follow the NBA …

Continue reading »# Category: systems of equations

## Candies, Pennies, and Inequalities

I want students to solve systems out of necessity. I want them to feel the interconnectedness of the two (or three) equations. In the past, I’ve asked small groups to build a functional 4×4 magic square. Soon they realize that changing a single number has multiple effects; this is the nature of the system. Unfortunately, abstracting the connections results in more than two variables. This year, I wanted to create the same feeling with only two variables. (The familiar x & y). Enter: Alex Overwijk.We blitzed through a task of his for systems of equations when I participated in a …

Continue reading »## Visualizing Linear Systems

My Grade 9 students don’t see an equation for the first two weeks of their unit of solving linear equations. That is because I think students get all bogged down in the notation, and lose their problem solving intuition. Instead, I play around with a key metaphor for solving linear equations–the balance scale. I’ve used the metaphor before, but only verbally alongside an algebraic representation. I would say things like, “What you do to one side, you must do to the other”, or “What would we have to do to keep the scales balanced?” The whole time, I only referenced the metaphor; …

Continue reading »## 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, …

Continue reading »## When School Math Falls Short

Warning: the following post contains algebra; I just thought I should be transparent. If three-space, divisibility, or inequalities make you queasy, please escape while you can. This afternoon, I was re-united with an old problem that I had managed to shunt into the back of my memory. Maybe because I remember it being incredibly frustrating, but (most likely) because it doesn’t fit nicely into a niche of school mathematics. The problem is summarized as follows: You need to buy exactly 100 pets. You have exactly $100 to do so. Dogs cost $15, Cats cost $1, and Mice cost $.25. How …

Continue reading »