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## Shoe Sale Remake

I transferred schools at the end of last year, so for the first time in seven years, every one of my students I meet on the first day of school will be a stranger. This means that the first hour I have with each of the four classes is not only their introduction to the course, but also their introduction to me. It won’t take long for them to make an impression of me, of mathematics, of their classmates, and how I expect us all to co-exist for the next five months or so.

I have written on first day tasks before, but not for several years. In that post I identify four “attributes” of an effective first-day task*. One of the tasks I settled on for this year was The Shoe Sale task from Peter Liljedahl. (Other bloggers have documented work with the problem as well: e.g. Fawn Nguyen and Chris Hunter).

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## Fraction Talks

Discussion is one of the organic ways through which human interaction occurs, but not all discussion is created equal in the math classroom. The tone of discussion relies on the mode of listening (Davis, 1996). Most classroom talk focuses on an evaluative mode of listening. Students are expected to share, compare, and contrast solutions to problems.

I do think that justification of their solutions gets at some important points regarding mathematical reasoning, but would like to move the discussion to center around that exact feature–the reasoning.

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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.
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The difference between what should happen and what does happen is a difficult distinction for students. They are so used to finding exact answers in the back of textbooks, that differing experimental results create an sense of uneasiness. At an early age (Grade 9 in my province) we begin to introduce students to the ideas of sampling and experimental probability.

The topic is usually approached with a project or survey of schoolmates. The results are then tallied and then used to create “probabilities” of various things such as favourite sports team, food, or colour. I love the philosophy behind the project approach; student initiative and autonomy is a powerful thing. I, however, don’t like that the experiment involves humans. Here’s why…
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