Experiencing Scale in Higher Dimensions

A colleague and I have often bemoaned our attempts to teach the concept of scale factor in higher dimensions. A topic that has such beautiful and elegant patterns and symmetries between the scale factors consistently seems to sail directly past the experience of our students. I have tried enacting several tasks with the students including some favourites from the #MTBoS (Mathalicious 1600 Pennsylvania and Giant Gummy Bear). Each time, the thinking during the task seems to dissipate when new problems are offered. It just seems like students have a hard time trusting the immense rate that surface area and volume …

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The Scale of Coffee Cups

A colleague is a religious McDonalds’ coffee drinker. One day she showed up with a medium coffee and a cream on the side. It was in two separate cups: I asked her for her cups when she was done. (She is also a math teacher so understands that this is not a creepy request. It is no weirder than the time I bought 400 ping pong balls, or 1500 bendy straws). I then made her a request to buy a large and small coffee in the future and save me the cups. The result was a family of coffee cups …

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Basketball Golf Task

The other day, a future teacher asked what one piece of advice I would give to a soon-to-be mathematics teacher. I immediately had several. I settled on one that I felt encapsulated my belief both in and out of class: Honour curiosity.  In class, this finds me wandering through student suggestions and constantly posing new problems that create relevant challenges. Curiosity (both student and teacher) keeps a vibrant ecology going, and I would argue that the intellectual tension so often provided through curiosity is necessary for a positive ecology to thrive.Outside of class, this has me interacting with my curios …

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On a Smaller Scale

I was watching Saturday morning cartoons when this commercial was aired. High energy music and neon flashes of light are often used to sell car related toys on these stations, but this commercial caught my eye. Upon first viewing, I thought I saw them advertise speeds of  1500 mph I was initially surprised at this huge velocity, but then figured that the station was using a play on units to exaggerate. They never mentioned what the abbreviation “mph” actually stood for–I had assumed miles per hour. I wrote down the name of the toy and made a mental note to write a …

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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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Merit to Mathematics Labs

There is widespread turmoil among teachers and students when it comes to the practicality of mathematics. School mathematics, at the middle and high school levels, has moved out of the elementary niche of rudimentary skills, but has yet to make it into the realm of complexity necessary to apply it back into the world. Our happy compromise, as teachers, is to go with a two-pronged attack: 1. Tell the students that the practicality comes later 2. Create word problems about trains leaving stations or people tossing balls off cliffs Every teacher of mathematics (from the wide-eyed rookie to the well-weathered …

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