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Teachable Moment: Many answers are a bit simplified but generally a great little web site to explore.

Reference: http://www.howstuffworks.com/

 Teachable Moment: Great, tool for simulating real world experiments. I look forward to seeing this evolve.

Fun, interactive, research-based simulations of physical phenomena from the PhET™ project at the University of Colorado.

Reference: http://phet.colorado.edu/

Teachable Moment: Great collection of math and science activities.

This web site collects math and science activities from major institutions in one place.  A great place to start when looking for projects.

Reference: howtosmile.org

Teachable Moment: NPR's Science Friday is a great show exploring math and science and their web site is a wonderfully rich resource not only for listening to older episodes but also for finding engaging videos and teacher tools.

Science Friday is a weekly science talk show, broadcast live over public radio stations nationwide from 2-4pm Eastern time as part of NPR's 'Talk of the Nation' programming. Each week, we focus on science topics that are in the news and try to bring an educated, balanced discussion to bear on the scientific issues at hand. Panels of expert guests join Science Friday's host, Ira Flatow, a veteran science journalist, to discuss science - and to take questions from listeners during the call-in portion of the program.

Reference: http://www.sciencefriday.com/

Teachable Moment: Great videos that explain advanced engineering concepts in everyday devices. I especially like the tear down videos.

Make called Bill a "brilliant science-and-technology documentarian", whose "videos should be held up as models of how to present complex technical information visually" Wired called them "dazzling." Scientific American's blog called him a "smart, easygoing everyman with a firm understanding of the science." You can see 10 of his best videos below. He takes apart an LCD monitor, demonstrates how fiber optic cables work, rips up a hard drive, explains the wonder of a quartz wrist watch, solves the mystery of black boxes, blows up a light bulb filament, reveals how amazing a pop can tab truely is, shows why a cell phone looks like it does, and explains why you always seem to be in the slowest line.

Reference: http://www.engineerguy.com/

Teachable Moment: At first glance, books like this may seem excessive and exaggerated attempts to tease math out of every day objects, but in an era of graphing calculators, math based 3D modeling tools like OpenScad, and vector based drawing tools, books like this provide a great, real world relevance to the underlying math behind complex shapes. It doesn't hurt that it beautifully put together.

Teachable Moment: Thought you knew the basic types of clouds? This beautifully drawn book from the Cloud Appreciation Society will open your eyes to cloud types you never knew existed.

Our full-colour cloudspotting handbook is now available. This beautiful little publication is filled with amazing photographs from society members of all the common cloud types as well as many rare and unusual clouds and optical effects. ‘The Cloud Collector’s Handbook’ has rounded corners so that it will fit into the pocket easily, allowing cloudspotters to identify a huge range of cloud formations and optical effects anytime and anywhere. But it is not just a reference — it is also a game.

Teachable Moment: This little book cleverly crams complex mathematical concepts into a story of a bad dream.... what more can you say?  If you find numbers interesting, explore them in a whole new way with the help of this little devil.

Twelve year old Robert fears numbers and hates maths. Then, in his dreams, he meets the Number Devil who introduces him to the amazing and magical world of numbers. This international bestseller is an exciting adventure in learning for both adults and children which will do for mathematics what "Sophie's World" did for philosophy.

To Purchase: The Number Devil: A Mathematical Adventure

Authors: Hans Magnus Enzensberger, Rotraut Susanne Berner, Michael Henry Heim

Teachable Moment: Obviously this web site has a soft spot for fun and irreverent teaching and this is probably this math book achieves what most people thought near impossible: make pre-algebra fun and accessible.  What more can I say than that my daughter keeps a dog-eared copy as a reference book with her main math textbook?

Last year, actress and math genius Danica McKellar made waves nationwide, challenging the “math nerd” stereotype—and giving girls the tools to ace tests and homework in her unique just-us-girls style. Now, in Kiss My Math, McKellar empowers a new crop of girls—7th to 9th graders—taking on the next level of mathematics: pre-Algebra. Stepping up not only the math, but also the sass and style, Kiss My Math will help math-phobic teenagers everywhere chill out about math, and finally “get” negative numbers, variables, absolute values, exponents, and more.

Teachable Moment: Lets face it, most science books are meant to look good on your shelf (think "A Brief History of Time") or are too subject specific for a broader audience.  This book is neither: instead, it's and engaging fun book that interweaves history, physics and teaches about perseverance and the scientific process.

Richard Feynman (1918-1988), winner of the Nobel Prize in physics, thrived on outrageous adventures.  Here he recounts in his inimitable voice his experience trading ideas on atomic physics with Einstein and Bohr and ideas on gambling with Nick the Greek; cracking the uncrackable safes guarding the most deeply held nuclear secrets; accompanying a ballet on his bongo drums; painting a naked female toreador -- and much else of an eyebrow-raising nature.  In short, here is Feynman's life in all its eccentric glory -- a combustible mix of high intelligence, unlimited curiosity, and raging chutzpah.

To Purchase: Surely You're Joking, Mr. Feynman! (Adventures of a Curious Character)

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

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

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

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

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/

Teachable Moment: This is a wonderful example of the power of conceptual blending and the need for scientists to nurture a wide  breadth of interests.

In the early 1920s, Niels Bohr was struggling to reimagine the structure of matter. Previous generations of physicists had thought the inner space of an atom looked like a miniature solar system with the atomic nucleus as the sun and the whirring electrons as planets in orbit. This was the classical model.

But Bohr had spent time analyzing the radiation emitted by electrons, and he realized that science needed a new metaphor. The behavior of electrons seemed to defy every conventional explanation. As Bohr said, “When it comes to atoms, language can be used only as in poetry.” Ordinary words couldn’t capture the data.

Bohr had long been fascinated by cubist paintings. As the intellectual historian Arthur Miller notes, he later filled his study with abstract still lifes and enjoyed explaining his interpretation of the art to visitors. For Bohr, the allure of cubism was that it shattered the certainty of the object. The art revealed the fissures in everything, turning the solidity of matter into a surreal blur.

Teachable Moment: The Challenger disaster was blamed on gas escaping from a faulty o-ring and much debate and discussion has emerged about how engineers should have known that that could have happened.  The data is readily available for students to analyze and plot themselves and can lead to a great case study or discussion.

Richard Feynman was one of twelve members appointed to a commission tasked with investigating the 1986 explosion of the space shuttle Challenger. Feynman's experiments showed that the tragedy was caused by a failure of the craft's rubber-like O-rings. Made of material with reduced resilience at temperatures below freezing, the rings were cracked by freezing weather, cracks which led to the escape of hot gasses leading to the fatal explosion. Much to the annoyance of commission chair William P. Rogers, Feynman used a glass of ice water and an O-ring to conclusively show the seal's vulnerability — at a press conference in front of live television cameras.

Teachable Moment: When I first heard this story I was told the iron was made from the failed Quebec Bridge, which I guess isn't true but the ceremonial message of responsibility still holds... this ring is a great reminder of how important engineering decisions can be.

The Ritual of the Calling of an Engineer has a history dating back to 1922, when seven past-presidents of the Engineering Institute of Canada attended a meeting in Montreal with other engineers. One of the speakers was civil engineer Professor Haultain of the University of Toronto. He felt that an organization was needed to bind all members of the engineering profession in Canada more closely together. He also felt that an obligation or statement of ethics to which a young graduate in engineering could subscribe should be developed. The seven past-presidents of the Engineering Institute of Canada were very receptive to this idea.

Teachable Moment: "Applied Math" can often be full of tortured attempts to make a math problem relevant by layering a story... but real life failures!  That's fun and memorable ;-)
Use the second link in the reference for the answer key.

Story 1: On September 23, 1999 NASA lost the $125 million Mars Climate Orbiter spacecraft after a 286-day journey to Mars. Miscalculations due to the use of English units instead of metric units apparently sent the craft slowly off course - - 60 miles in all. Thrusters used to help point the spacecraft had, over the course of months, been fired incorrectly because data used to control the wheels were calculated in incorrect units.

Lockheed Martin, which was performing the calculations, was sending thruster data in English units (pounds) to NASA, while NASA's navigation team was expecting metric units (Newtons).

Problem 1 - A solid rocket booster is ordered with the specification that it is to produce a total of 10 million pounds of thrust. If this number is mistaken for the thrust in Newtons, by how much, in pounds, will the thrust be in error? (1 pound = 4.5 Newtons)

Teachable Moment: Great science experiments are indistinguishable from magic and this little video is a wonderful example using viscocity to demonstrate laminar flow.

As explained on the web site: http://panda.unm.edu/flash/viscosity.phtml

The Reynolds number R is the dimensionless combination:

in which ρ is the density, ν the speed of the fluid, R the size of the flow, and η the viscosity. When R ≤ 1, friction dominates inertia and the fluid flows in layers (laminar flow).Here we are using corn syrup which has a viscosity of 5 (Pa s); its viscosity is 5000 times that of water, and the Reynolds number R is less than unity.This experiment is being demonstrated by Kevin Cahill for his Biophysics II students.The couette cell used in this experiment was fabricated by John DeMoss in the Machine Shop of the Department of Physics and Astronomy at the University of New Mexico.

Teachable Moment: This brilliant little video made by the Royal Observatory in Greenwich covers the concepts of parallax, doppler and red-shift and shows how they are all used together to measure the universe.

Teachable Moment: This video illustrates how asking "why" can lead to novel discoveries even around phenomena many others have already observed.

 Teachable Moment: Simple little visual proof of the formula for the area of a circle. 

Teachable Moment: This is a great synthesis of how a series of clearly important, yet seemingly disparate, equations have been used together to provide us modern conveniences.

Without equations, most of our technology would never have been invented. Of course, important inventions such as fire and the wheel came about without any mathematical knowledge. Yet without equations we would be stuck in a medieval world.

Teachable moment:  just because the basic periodic table format designed by Mendeleev is the most commonly taught format, it doesn't mean it works for everyone, this image explores and illustrates the various ways people have tried to organize the elements.  

Reference: http://www.keaggy.com/periodictable/ 

Teachable Moment: Most of us have a very narrow understanding of which resources we use are non-renewable.  This highly informative graphic illustrates the range of non-renewable resources and helps initiate a discussion about prioirities.

Reference: http://www.bbc.com/future/story/20120618-global-resources-stock-check

Teachable Moment: This >500 year old image raises the age old question of credit in discovery: what does it mean to be the first person to document what others know.  The high resolution image can also be printed and cut out as a lesson in how to project a sphere onto a flat surface.

In 1507, German cartographer Martin Waldseemüller made the first known maps naming America.  In 2007 Germany gifted one of the known versions of this map to the Libray of Congress calling it the "Birth Certificate of America."  Recently, another copy was discovered and was "released" by the Ludwig-Maximilians-Universität (LMU) München on the Internet on July 4, 2012.  Here's a link to the high resolution PDF: http://epub.ub.uni-muenchen.de/13138/1/Cim._107-2.pdf

For the press release and more pictures go here: http://www.en.uni-muenchen.de/news/newsarchiv/2012/spotlight/tdw_ub_fund.html

Teachable Moment: This stunning image from the USGS illustrates shows both the relative scarcity of water on our planet and challenges our thinking of volume.  We all know that the earth is almost 97% covered with water, but how many of us realized how thin a layer that represented and what that was relative to the land mass?  Follow the link to a larger image and the underyling math.

Reference: http://ga.water.usgs.gov/edu/2010/gallery/global-water-volume.html

Teachable Moment: The next time you hear about the sun unleashing a solar flare, solar wind a.k.a. a CME (Coronal Mass Ejection) check out this nifty web site to see if you'll have an aurora in your area.  Oh, and if you want to hear about future events, send an email to  This email address is being protected from spambots. You need JavaScript enabled to view it.  

From the NASA Web Site:

"OVATION: An empirical model of the intensity of the aurora. The model uses solar wind conditions and the IMF at the L1 point as inputs.

The Display: Shows the intensity and location of the aurora as expected for the time shown at the bottom of the map. This forecast is based on current solar wind conditions and the average time for the solar wind to propagate from the ACE satellite at L1 to Earth.

The model produces an estimate of the intensity of the aurora. In this product a linear relationship between intensity and viewing probability is assumed. This relationship was validated by comparison with data from the UVI instrument on the NASA POLAR Satellite .

The sunlit side of Earth is indicated by the lighter blue of the ocean. The sub-solar point is also shown as a yellow dot but only if the sub-solar point is in the view of the choosen image. The day-night line or terminator is shown as a yellow line. Note that the aurora will not be visible during daylight hours and it may be an hour or more before sunrise or after sunset that the aurora can be seen from the ground."

Reference: http://helios.swpc.noaa.gov/ovation/

Teachable Moment: This blog collects images and stories of various modern inventors and provides a great insight into what leads people to invent.

They say that necessity is the mother of invention. I’m interested in the rest of the family.

Teachable Moment: It's fun to see how much his mind wandered and the breadth of his interests.

Go to the Library of Congress for the full sketchbooks

The Atlantic Article has a great selection of images from the sketchbooks.

From the Atlantic Article:

It was on March 10, 1876 that Alexander Graham Bell made the first successful telephone call. "'Mr. Watson--come here--I want to see you," he said to his assistant, who was in the next room. Bell recorded those early telephone experiments in his lab notebooks from the time, as he did with countless other experiments and ideas.

Teachable Moment: The Lemelson-MIT Program on invention focuses on promoting invention but I really like the story of how Lemelson himself invented the mechanism that became ubiquitous in the Sony Walkman because he wanted to devise a better way to search patents. 

From the bio on the web site: "Lemelson first struck on the idea of using magnetic tape to store images when he and his wife were doing a manual search at the United States Patent Office. Frustrated by the daunting task, Lemelson began to think of ways to mechanize the system.

Teachable Moment: This is a great example of how stepping away from a problem can often lead to novel solutions.  It can also be used to illustrate how working with a mock-up of the target can provide novel insights.

From the Cosmos Article: FOR 10 YEARS, Graeme Clark had been working tirelessly to develop an implant that would help the deaf to hear. The theory made sense. The electronics had been developed, and the design was near finalised.

Teachable Moment:This TED video discusses the invention of the GPS as a perfect example of open innovative systems where "chance favors the connected mind".  I also like it because it provides a good example of how innovation can be as simple as merely the inversion of our thinking... in this case, one group of scientists had discovered how to track a moving object in space from a fixed point on the ground... and another one pushed them to think about tracking a moving object on the ground from a fixed point in space.