Fraction Task Testing

The testing of a task went horribly right. Background: Graham Fletcher (@gfletchy) tweeted an Open Middle (@OpenMiddle) prompt for comparing fractions. The thread debated whether or not a representation on a number line would be best.  Many people liked the number line better, but I decided to stick with the inequality signs because: Students see this type of two-bounded inequality notation with domain and range. The number line gave the impression of a single, fixed answer (because the fractions appear a definite, scaled distance away from each other). I gave this question as a starter to a group of my grade …

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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 …

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Mathematics for Bros

Before I begin, I would like to make sure that the title of this post was not misleading. If you are reading because you are fuming at the gender inequality reference in the title, please relax. I am in no way advocating that Mathematics is for Bros; the following post is a collection of the mathematical quips garnered from the “New York Times” bestseller, The Bro Code. It is a sacred cannon passed down from generation to generation of Bros designed to guide the lives and decisions of Bros worldwide. The book takes a humourous look at the superstitions of …

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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 …

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