inequalities infinity reflection

Second-hand Student-ing

Billy: “Banting, I have a question for you.”

It was 5-minute break between classes and I was trying to reset the random seating plan, open up the electronic attendance system, and load the image that would serve as a starter for the day’s lesson. During this small window of time, questions are usually about missing binders, requests for future work due to mid-semester holiday plans, or updates on my ever-present pile of grading. In short, I usually do not want to deal with them. Begrudgingly, I obliged.

Billy: “I need a piece of paper and a pen”

fractions inequalities problem posing tasks

Fraction Task Testing

The testing of a task went horribly right.
Graham Fletcher (@gfletchy) tweeted an Open Middle (@OpenMiddle) prompt for comparing fractions.
inequalities linear functions systems of equations tasks

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.

inequalities numeracy systems of equations

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 many of each pet do you have to buy?
(You must buy at least 1 of each)