Fair Dice Task

The recent curriculum renewal has placed a (well-deserved) heightened emphasis on counting, set theory, and probability. Just under a half of a Grade 12 “Foundations of Mathematics” course now covers the three topics. This is a huge improvement from the token, disjointed topics strewn around the last courses. It allows teachers to set a different tone–a tone of curiosity that seems inherent in probability. I came across the idea of Grime Dice (named and pioneered by Dr. James Grime @jamesgrime) late last year after I knew I was to be teaching probability this winter. I knew right away this was a …

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Sorting Set(s)

Set Theory, Counting Methods, and Probability are probably my three favourite topics to teach. For the first time under our new curricular framework, I got to teach these topics to a group of seniors. I decided to build up large themes and understandings through introductory tasks; my goal was to create an “unflippable” entry point where students could work together to complete tasks and filter out necessary details such as rules, notation, etc. I began our study of Set Theory with this task.The students were introduced to the idea of what a set is. They also were given some elementary …

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Project Work Scaffold

There are two schools of thought when it comes to PBL: Start with a large-scale project and fit the specific outcomes within it, or Build toward a larger project with smaller tasks. I love the idea of large projects, but also aim to make my work as accessible as possible for those who want to take it and improve on it. I just don’t see option one working within my traditional classroom of 35 students for one hour a day. The existence of an overarching curriculum only further decreases its accessibility. As for option two, there is an art in equipping students for project …

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Gummy Bear Revisited

The giant gummy bear problem has been floating around the blogosphere for a while. When I first saw it, I knew I wanted to use it. I finally have the perfect opportunity in Foundations of Mathematics 20 this year. (Saskatchewan Curriculum). History of the Problem (As far as I know) Originally presented by Dan Anderson here. Included original Vat19 video and driving question about scale. Adapted by John Scammell here. Edited video and new driving question. Dan Meyer provided a 3Act framework for the problem here. Blair Miller adapted his own 3Act structure here. My apologies go out to anyone …

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The Guess Who Conundrum

Every so often, an idea comes out of left field. I woke up with this on my mind–must have been a dream. Back in the day, my family had a dilapidated copy of the game “Guess Who?” My siblings and I would take turns playing this game of deduction. You essentially narrowed a search for an opponent’s person by picking out characteristics of their appearance. http://www.flickr.com/photos/unloveable/2398625902/ I vividly remember playing with my younger sister one time at a family cottage. She–foolishly–chose a female person for me to identify. Anyone who has played the game before knows that the males far …

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Bike Trail Task

There is two hour parking all around University of Saskatchewan. I once went to move my car (to avoid a ticket) and found that the parking attendant had marked–in chalk–the top of my tire. I wanted to erase the mark so began driving through as many puddles as possible. I then convinced myself to find a puddle longer than the circumference of my tire–to guarantee a clean slate and a fresh two hours.  As I walked back to campus, I got thinking about the pattern left behind by my tires. For simplicity, let’s take the case of a smaller vehicle–a …

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Painting Tape

I came across the following situation while shopping for paint at a local home improvement store: Admittedly, the three varieties were not positioned like this, but this positioning does raise an interesting question. “We can see the packages are the same height, what is that height?” I see this question going one of two ways: The students realize that really any conceivable measurement is possible. (Barring, of course, zero and the negatives) One could make the argument that it also cannot be irrational, but this would be nit-picking. Can a roll of tape have a width of pi/6? Exactly? The …

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Sprinkler Task

I am frustratingly mathematical. Ask my wife. I see the world as a combination of, in the words of David Berlinski, absolutely elementary mathematics.(AEM). The path of a yo-yo, the tiles in the mall, and the trail of wetness after a bike rides through a puddle are all dissected with simple, mathematical phenomenon. The nice part about AEM is that I can talk about it to almost anyone. People are (vaguely) familiar with graphs, geometric patterns, and circles even if they can’t decipher what practical implications they have on their city block. Unfortunately, people (and students) don’t often want to …

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Unexpected Lesson Extension

It is very hard to develop an active atmosphere in a math classroom–especially at the high school level. I believe there are two main reasons for this: 1) Students have been slowly trained throughout their schooling that a “good” math student is one that listens, absorbs, and repeats. 2) The content often reaches beyond what most teachers deem to be “constructable”. Rather than fight with these two restraints, I began my implementation of Problem Based Learning in a class with manageable curriculum content filled with students who never learned to sit still in the first place. As time progressed, the room …

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Finding a Radius

I designed a class around the pedagogy of Project Based Learning this semester. As the school year passes by at mach speed, I have adapted certain activities and projects to fit my students’ needs. The result is a class based around providing tools, and tackling interesting tasks with them. Each set of problems (or unit) is capped with a large project. We are in the midst of a surface area and volume unit. We have tackled the major solids and prisms. Netting, superimposing grids, converting units, analyzing packaging etc. Throughout the entire class, I have been highlighting the various “employable …

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