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Great Explanations

Sparky and the Meaning of Subtracting Negatives

Posted by Diego Fonstad
Diego Fonstad
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on Sunday, 13 February 2011
in Great Explanations

Teachable Moment: Subtraction of negatives can be very confusing and Danica provides a clever analogy of walking a dog to explain this difficult concept. Click on the limage to see concept larger.

An explanation from "Kiss My Math" that uses walking a dog as a way of explaining subtraction of negatives.

References: http://www.kissmymath.com/

Tags: Math
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Occam's Razor

Posted by Diego Fonstad
Diego Fonstad
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on Friday, 11 February 2011
in Great Explanations

Teachable Moment: Occam's razor has many applications but recently I used it as a coach for a First Lego League team.  The children were making increasingly complex Lego contraptions and in order to reign them in, I introduced the concept of Occam's razor which didn't dismiss their complex efforts but challenged them to think of simpler solutions.  After a while, all I had to do was simply say "is this consistent with Occam's razor" and they'd go back and find a better solution.

From Wikipedia: Occam's razor (or Ockham's razor[1]), often expressed in Latin as the lex parsimoniae, translating to law of parsimony, law of economy or law of succinctness, is a principle which generally recommends selecting the competing hypothesis that makes the fewest new assumptions, when the hypotheses are equal in other respects.[2] For instance, they must both sufficiently explain available data in the first place.

References: http://en.wikipedia.org/wiki/Occam's_razor

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Schrodinger's Cat

Posted by Diego Fonstad
Diego Fonstad
Diego Fonstad has not set their biography yet
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on Sunday, 09 January 2011
in Great Explanations

Teachable Moment: Frankly, quantum entanglement is a pretty complex idea... but if anything's going to start cracking your brain open to it, this is a pretty good start.

In 1935, Schrodinger wrote a paper about the state of Quantum Physics wherein he posited the following:

"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts"

Tags: Physics
Hits: 15369

Rule of Thumb... for gauging distances

Posted by Diego Fonstad
Diego Fonstad
Diego Fonstad has not set their biography yet
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on Sunday, 09 January 2011
in Great Explanations

Teachable Moment: What I like about this is how practical it is as a tool while simultaneously teaching ratios and entry level trigonometry.

Your arm is about ten times longer than the distance between your eyes. That fact, together with a bit of applied trigonometry, can be used to estimate distances between you and any object of approximately known size.

Imagine, for example, that you're standing on the side of a hill, trying to decide how far it is to the top of a low hill on the other side of the valley. Just below the hilltop is a barn, which you feel reasonably sure is about 100 feet wide on the side facing you.

Tags: Math
Hits: 66115