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”

infinity surface area tasks volume

Lesson Planning; Lesson Participating

Occasionally, I give a task to my students before I have done it myself. Sometimes it is because the solution is fairly straightforward and I can see multiple ways to arriving at it without actually doing it. Other times it is because I want to have no impact on my students’ thought pathways. The practice also makes class time more exciting as students reason through methods that I would not have though of–I am trying to move from a monotonous state of lesson planning to a more exciting one of lesson participation.
infinity investigation pattern sequences and series

Shading Squares

I recently finished up a unit on sequences and series with my grade 11 pre-calculus students. The unit is somewhat of an enigma because it contains relatively simple ideas bogged down in complex notation. This coupled with the overlapping definitions makes for a fortnight of rather rigorous cognitive exercise. 

The unit was supported through group tasks as the topics moved along. Arithmetic sequences and series were linked to linear functions through the toothpick problem. Students were asked to arrange toothpicks into boxes and record how many toothpicks it took to make ‘x’ number of boxes. Their results were extrapolated and tied to variables from the linear functions notation. From there, I introduced the new terms of “common difference” and “term one” instead of slope and y-intercept. The arithmetic portion usually goes smoother than its geometric cousin for two reasons:

infinity pattern

Struggling with Infinity

My fascination with infinity began early on in life. I went to a small private school in Prince Edward Island for my entire elementary school career, and it was outside on the playground where I first tasted the enigma of infinity and the power it held. 

Across the cul-de-sac parking lot stood the swings, slide, and monkey bars; I still remember the first time I encountered infinity under those bars. You see, we had been learning the base-10 number system that day, and my friend Jason and I somehow got into a counting contest of sorts. We began at very small numbers, and gradually cycled through the digits at varying positions until we countered each other with unusually large–and most likely inaccurate–numbers. Trillion, Quadrillion, Bazillion all made appearances until Jason ended the contest with one word–infinity.