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Great Explanations

Trick for teaching basic trigonometry

Posted by Diego Fonstad
Diego Fonstad
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on Monday, 11 June 2012
in Great Explanations

Teachable Moment: Nice simple and straight forward trick to remember 

From the Blog:

"During my middle-school teaching days I noticed that often kids would arrive in my 8th-grade class with a half knowledge of sine, cosine, tangent. There were two major problems they often had in solving for unknown sides in a right triangle using trig:

1. They couldn't visually distinguish opposite side vs. adjacent side. Many middle-schoolers I taught had a poor consistency (if any) with recognizing what "opposite" and "adjacent" meant in a diagram; it was just too abstract for them, even though I tried to explain how to look for the sides "across" the triangle, etc.

2. They couldn't figure out whether to use sine, cosine, or tangent in a given situation.

Follow the link below to read more. 

Reference: http://untilnextstop.blogspot.com/2011/02/trick-for-teaching-basic-trig.html

Tags: Math
Hits: 110622

Michael Faraday Watches a Candle

Posted by Mathai Mammen
Mathai Mammen
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on Tuesday, 27 December 2011
in Great Explanations

Teachable Moment: A beautiful reminder from Michael Faraday of the power of observation:  Observe....everything. Think about...everything. And don't interfere. Then do it again until you are sure you have it.

We take for granted that we understand the simple, and have moved on to the less simple. Michael Faraday gave an annual lecture on the burning candle, which is reproduced here. A beautiful read - and even better when spoken and delivered emphatically.

References: http://www.bartleby.com/30/7.html
http://www.fordham.edu/halsall/mod/1860Faraday-candle.asp#Lecture%20I

Hits: 34253

Cool math trick: Converting between miles and kilometers

Posted by Diego Fonstad
Diego Fonstad
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on Monday, 12 September 2011
in Great Explanations

Teachable Moment: The Fibonacci sequence is a great introduction to math in nature and this little trick even provides a nifty practical use of the numbers.

From the blog: "The Fibonacci sequence is made up of numbers that are the sum of the previous two numbers in the sequence, starting with 0 and 1. It's 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… 1 is 0+1, 2 is 1+1, 3 is 1+12, 5 is 2+3, and 8 is 3+5. The number after 144 is 233, or 89+144. The Fibonacci number describes the golden spiral, an ideal form much beloved by designers everywhere. Interestingly, it also neatly matches the relationship between kilometers and miles. Three miles is five kilometers, five miles is eight kilometers, eight miles is 13 kilometers. It's not perfect, eight miles is actually 12.875 kilometers, but it's close enough in a pinch. If you need to convert a number that's not on the Fibonacci sequence, you can just break out the Fibonacci numbers, convert, and add the answers. For instance, 100 can be broken down into 89 + 8 + 3, all Fibonacci numbers. The next numbers are 144, 13, and 5, which add up to 162. 100 miles is actually equal to 160.934. Again, close enough. Math is cool."

References: http://www.mnn.com/earth-matters/wilderness-resources/blogs/cool-math-trick-converting-between-miles-and-kilometers

Tags: Math
Hits: 53198

Cricket Chirps: Nature's Thermometer

Posted by Diego Fonstad
Diego Fonstad
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on Tuesday, 09 August 2011
in Great Explanations

Teachable Moment: I'm not sure what I like more about this idea: the practical nature of it or the fact that the correlation between temperature and cricket chirp rate was documented by one of the inventors of the radio telephone.

From Farmer's Almanac:

Did you know that you can tell the temperature by counting the chirps of a cricket? It's true! Here's the formula:

To convert cricket chirps to degrees Fahrenheit, count number of chirps in 14 seconds then add 40 to get temperature.

Example: 30 chirps + 40 = 70° F

To convert cricket chirps to degrees Celsius, count number of chirps in 25 seconds, divide by 3, then add 4 to get temperature.

Example: 48 chirps /(divided by) 3 + 4 = 20° C

Tags: Biology
Hits: 29481

The Physics of Angry Birds

Posted by Diego Fonstad
Diego Fonstad
Diego Fonstad has not set their biography yet
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on Friday, 01 April 2011
in Great Explanations

Teachable Moment: It is important to realize that making science "relevant" doesn't always mean solving real world problems... it can be as simple as showing how proper use of science makes games better.

The article asks the question: 

"But what about the physics? Do the birds have a constant vertical acceleration? Do they have constant horizontal velocity? Let’s find out, shall we? Oh, why would I do this? Why can’t I just play the dumb game and move on. That is not how I roll. I will analyze this, and you can’t stop me."

Follow the reference to find out.

 

References: http://www.wired.com/wiredscience/2010/10/physics-of-angry-birds/

Tags: Physics
Hits: 76248

Why don't planets twinkle as stars do?

Posted by Diego Fonstad
Diego Fonstad
Diego Fonstad has not set their biography yet
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on Friday, 01 April 2011
in Great Explanations

Teachable Moment: This thought experiment can be used at so many levels.  At its core, it teaches basic concepts of astronomy but it also can be used to explore the properties of light and even of the concept of infinity. As the distance of the object approaches infinity, the impact of the atmosphere is stronger and stronger.

Stars twinkle. Planets shine steadily. Why?

Stars always twinkle because they’re so far away from Earth that, even through large telescopes, they appear only as pinpoints. And it’s easy for Earth’s atmosphere to disturb the pinpoint light of a star.

Hits: 132039

Turtles all the way down

Posted by Diego Fonstad
Diego Fonstad
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on Thursday, 31 March 2011
in Great Explanations

Teachable Moment: What do we really know and how solid is the foundation of that knowledge?  That's the fundamental question of all science and, as Hawking so brilliantly realized, the turtle story makes this question tangible and fun to think about.

In Stephen Hawking's 1988 book A Brief History of Time, he starts with the following story:

A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever", said the old lady. "But it's turtles all the way down!"

References: Hawking, Stephen (1988). A Brief History of Time. Bantam Books. ISBN 978-0553053401.
http://en.wikipedia.org/wiki/Turtles_all_the_way_down#cite_note-0

Hits: 29998

Infinite Monkey Theorem

Posted by Diego Fonstad
Diego Fonstad
Diego Fonstad has not set their biography yet
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on Wednesday, 30 March 2011
in Great Explanations

Teachable Moment: This wonderful thought experiment is a great way of exploring probabilities as they apply to multiple random events.  The mere fact that it has infused its way into popular culture is a testament to its ability to engage thinkers.

The infinite monkey theorem, originally posited by Emile Borel, states that a monkey pressing keys at random on a keyboard for an infinite amount of time would eventually type a finite text.

The probability of typing that text is straight forward:

Tags: Math

Maxwell's Demon

Posted by Diego Fonstad
Diego Fonstad
Diego Fonstad has not set their biography yet
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on Tuesday, 29 March 2011
in Great Explanations

Teachable Moment: First, let's admit...it's a cool name... so cool, that rock bands chose it to have geek "cred."
But it's also a fascinating thought experiment that challenges a "law" of thermodynamics.

In 1867, James Clerk Maxwell pictured two chambers, A and B, each filled with gas at the same temperature and with a door between them. Theorists later had a demon open the door (without doing any work) to let the fastest-moving molecules pass from A into B, and the slowest from B to A. Over time, the speed of the atoms (and therefore the temperature) increases in B — a violation of the second law of thermodynamics.

References: http://physicsworld.com/cws/article/news/26939
http://www.wired.com/science/discoveries/magazine/15-06/st_best
http://en.wikipedia.org/wiki/Maxwell%27s_demon

Hits: 17858

Book Stacking Problem

Posted by Diego Fonstad
Diego Fonstad
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on Saturday, 05 March 2011
in Great Explanations

Teachable Moment: Great visual way of thinking of and understanding harmonic series.

How far can a stack ofn books protrude over the edge of a table without the stack falling over? It turns out that the maximum overhang possible d_nfor n books (in terms of book lengths) is half the nth partial sum of the harmonic series.

 

 

Tags: Math
Hits: 64307