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The division by zero @NCTM webinar was really cool! Thank you @Joannbarnett and @ChondaLong for putting it together!
I& #39;ll share some of my own thoughts in this thread. #NCTM100 (1/n)
I& #39;ll share some of my own thoughts in this thread. #NCTM100 (1/n)
I really liked the deliberate emphasis on making something that can be so abstract into something concrete and relatable. That& #39;s really important to our younger (and older!) students to be able to make sense of mathematics as not just a collection of "rules". (2/n)
Side note: I also was quite relieved when the two models of division were just called "measurement" and "sharing." I know they& #39;re formally called "partitive" and "quotative" but for the live of me I can never remember which is which! 
https://abs.twimg.com/emoji/v2/... draggable="false" alt="đ
" title="Smiling face with open mouth and cold sweat" aria-label="Emoji: Smiling face with open mouth and cold sweat"> (3/n)
Regarding the idea of "18 apples Ă· 0 friends", I& #39;ve usually dismissed that as "the question doesn& #39;t make sense" and left it at that. But they had a really interesting way to think about it that I had never considered before. (4/n)
The gist was "How tall are those 0 friends? What are their hair colors? You can& #39;t say anything about those 0 friends, much less how many candies they got."
That is a mind-blowingly interesting way to think of the problem. (5/n)
That is a mind-blowingly interesting way to think of the problem. (5/n)
Jumping into "higher-math mode", your set of friends is an empty set â
. But then, for any predicate P, any statement of the form "âxââ
, P(x)" is AUTOMATICALLY true â vacuously! I wonder if there& #39;s any way to dive deeper into that aspect of the problem, just for fun. (6/n)
Then, as for the "18 candies Ă· 0 candies in each bag" problem, it was really interesting that so many people had the answer of "as many as you want" â and mentioned their students often have the same thought. Our kids are astoundingly creative and insightful. (7/n)
As expected, "infinity isn& #39;t a number" was the response to that line of reasoning. I do think that& #39;s a rabbit-hole topic of its own, but it& #39;s definitely one that might be worth exploring at some point. What IS a number, anyway? https://abs.twimg.com/emoji/v2/... draggable="false" alt="đ€" title="Thinking face" aria-label="Emoji: Thinking face"> (8/n)
I do have my own thoughts on the topic of division by zero and its relation to infinity (which if you look at my profile should be obvious https://abs.twimg.com/emoji/v2/... draggable="false" alt="đ" title="Winking face with tongue" aria-label="Emoji: Winking face with tongue">), but it& #39;s always great to hear the perspectives of other teachers. They lead to awesome new thoughts and questions. (9/n)
