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The Review Day: Unit Analysis and Scale Factor

There seems to be three sacred cows in mathematics education:

  • the worksheet / exercise set
  • the review day
  • the exam

It is not surprising that these three feed off one another, and make up the bulk of assessment in the typical mathematics classroom (including my own). 

Here’s my disclaimer:
While I have been known to slaughter a few of the sacred cows of the instructional process, I have lagged severely behind in my attention to assessment. I value the complexities of learning that occur when student ideas encounter perturbations, curiosities, and other conceptualizations. The type of assessment that comes out of these mathematical encounters is rich, connected, and constantly evolving. 

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Leaky Faucet Task

This idea is not my own. The only problem is, I don’t exactly know who it belongs to. I remember tweeps talking about about a task where a leaky faucet’s effect was analysed on a water bill. When I encountered the situation at my Uncle’s house, I had to capture the modelling in action.

The best part was the conversation from intrigued (and weirded out) relatives as I ducked and dived around the tap to get a good angle. We got into a conversation about teaching, and they were happy to present any questions that came to their minds.
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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 else who played with or re-posted an original interpretation on the problem.
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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?”
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The Mathematics of Laundry Soap

The grocery store is a brain workout for the mathematically inclined. Not only do the varying metric and imperial conversions tease out the micro-savings of bulk, but neon yellow discount signs encourage percentages and good ole’ multiplication tables. Often you find adults transfixed in a complex division trying to figure out which ham will be cheaper. Once that calculation is complete, they turn their attention to making sure the portion will be enough to feed their whole family. The sheer volume of available estimations overloads me; coupons just complicate the matter–significantly.