Category: tasks

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 great task to get students tinkering with probability before defining its inter-workings theoretically. A great description of their function can be found on the PlusMath website written by Dr. Grime himself. They are available for purchase from MathGear.co.uk.

investigation set theory tasks

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 verbiage. I wanted them to become comfortable using words like set, subset, and disjoint throughout the task. I did not introduce them to the idea of intersection and union–those were to be formalized through the task.

classroom structure PBL surface area tasks volume

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.

classroom structure scale tasks unit analysis whiteboards

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 else who played with or re-posted an original interpretation on the problem.

factors games numeracy primes tasks

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/

circles circumference factors pattern tasks

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 bike.

factors tasks unit analysis

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?”

area circles Pythagorean theorem right triangles tasks

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 hear about them–they need to see them.

I can remember the look on my mother’s face when I broke out the silverware to show her that the restaurant table corner was not square. Without a ruler, I showed her that trigonometry allows us to rely on ratio rather than set measurements. As I was in the midst of showing her that the 3-4-5 knife-length rule was breached, the waitress came. Mom was horrified; I was thrilled.

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Unexpected Lesson Extension

Post author By natbanting
Post date April 6, 2012
1 Comment on 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.

cylinder sphere tasks volume

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 skills” that they are honing with their work. Estimation, problem solving, critical thinking, diagnostics, peer work, spatial reasoning and the like.