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What can Dwight teach us about the signs of products/quotients?

3/26/2014

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Picture
You've probably heard it a million times.
A positive times a positive is a positive
A negative times a positive is a negative
A positive times a negative is a negative
A negative times a negative is a positive.

You've probably even used the little tic-tac-toe chart to remember.

Well here is another one to add to your already long list. I got this idea from a friend of mine, Ms.Goebel, Math teacher at Murrow HS.
Think of the positive sign as love and think of the negative sign as hate.

If someone loves to love that's a positive thing (So a positive times a positive is a positive)
If someone loves to hate that's a negative thing (So a positive times a negative is a negative)
If someone hates to love that's a negative thing (So a negative times a positive is a negative)
If someone hates to hate that's a positive thing (So a negative times a negative is a positive)

If that one doesn't do it for you try looking at it like this:
A positive sign is a friend and a negative sign is an enemy.
A friend of your friend is your friend (So a positive times a positive is a positive)
A friend of your enemy is your enemy (So a positive times a negative is a negative)
An enemy of your friend is your enemy (So a negative times a positive is a negative)
An enemy of your enemy is your friend (So a negative times a negative is a negative)

Just ask Dwight from the office he'll tell you all about it... check out the video below.


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Pi day Reflection

3/14/2014

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Today was a pretty awesome day, it was pi day and I got retweeted by Edward Frenkel. The tweet was about a conversation I had with my students about pi and what it represents. What really surprised me was how deep our conversation got. It started when a student asked: Who invented pi? I saw this as a teachable moment and pounced on it.

"Well no one 'invented' pi, really, pi is something that was discovered".

Queu in the article written by Frenkel "Is the universe a simulation?". The thing that stuck out to me about this article was how clearly Frenkel articulated that the truths of Math are necessary and timeless. For example if no one in Greece 2000 years had discovered pi, someone else eventually would.

So that's what I said to my students.

"No one said 'let's make pi 3.14', it's just something that is what it is, someone discovered that it takes approximately 3 diameters and a bit more of one to make the circumference."

This then led to the last part of our conversation: Is pi something that is part of the "code" the Programmer used to create the simulation Frenkel talks about?

Anyways it was a conversation that left us with more questions than answers, but in in a good way, like in an awe and wonder kind of way.

Which leads to my last point. As much as I love pie, sometimes I do feel that this day should be less about pie and more about pi! The math pi. That's exciting in itself. As Brian Lehrer put it "Celebrating pi day with pies would be like celebrating Martin Luther King day with king size candy bars". I mean there really is no connection between pi and pies, unless of course you see the pie as a circle, have kids measure the circumference, measure the diameter, oh wait on second thought hold the pie, maybe there is a connection here.



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    Math teacher at HSSM in NYC

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