Radiolab Numbers

Radiolab is so cool. It’s a public radio show you can listen to on your public radio station or online. My dad recently told me about a Radiolab show called Numbers. It originally aired in November 2009. Each show is an hour long and has several segments on a single topic. If you listen to the Numbers show, you’ll first hear a Johnny Cash song, then learn about the innate number sense of infants, and move on to other fascinating topics like Benford’s Law, a surprising observation about the first digits of numbers, and a forensic accountant who uses it to investigate fraud, and on and on. The show is a very human take on numbers. I’m sure you’ll enjoy it.

Scale of the Universe

 

What do Gomez’s Hamburger, Palm Jebel Ali and Mimivirus have in common? They are all found in Scale of the Universe 2 at 2.5 x 1015 meters, 8 x 103 meters, and 4 x 10-7meters, respectively. Scale of the Universe 2 is a cool, interactive website which goes nicely with my earlier blog post about the Powers of Ten lesson and video. Visitors can zoom all the way down to teeny Quantum Foam and then all the way out to the observable universe and the Hubble Deep Field.

Each object has a brief description, so you will not be left wondering what Palm Jebel Ali is (the largest human-made island) and you’ll know Gomez’s Hamburger is a heavenly body, not a menu item. There are commonplace entries like a Boeing 747 and a sunflower, too.

Students can use this site to explore relative magnitude even if they are not yet ready to learn about exponents in math. Author Istvan Banyai has written a wonderful book called Zoom, which does something similar in low-tech. Students might try to create their own book in this format.

John J. Flynn library super-star Corey Wallace brought Scale of the Universe to my attention. This is just another example of how my own universe is constantly expanding with the help of my talented and enthusiastic colleagues.

 

The Powers of Ten

Lee Orlando, fifth grade teacher, kindly contributed this article.

Our Bridges November calendar focuses on decimals and "base-ten fractions," and we've been having some good discussions around the nature of decimal numbers.

Yesterday, we were ordering some numbers that included whole numbers and mixed numbers (expressed as decimals)... one student confidently announced:  "3 is greater than 33.45 because any decimal is smaller than a whole number."   The salient feature for this student was the decimal point, and she was working under the misconception that whenever you see a decimal point, the number is automatically smaller than any whole number.  Just that comment alone kept the students talking and debating for quite a while!

I also did a quick formative assessment: Instead of giving students decimal numbers already arranged appropriately (in a column) in order to add/subtract, I simply gave them the numbers and had them arrange them in order to add (there were four numbers). Perhaps you can guess what many students did. They applied their understanding of place value of whole numbers (ones, tens, hundreds, etc, lining up the numbers from right to left) and totally disregarded the decimal point.  Here were all these decimal numbers, neatly lined up as if they were whole numbers, with the decimal points totally misaligned. These were students who have been adding and subtracting decimal numbers in our weekly math computation practice, but when given the numbers separately - not pre-arranged in a column - their lack of conceptual understanding about decimals and their values was completely transparent.

All this has led to lots of discussions about the power of zero which we had already explored in our Great Wall of Base Ten, but which was now coming back in light of decimal numbers.  I have been digging up some cool resources around this, including this awesome video which you may already know: "The Powers of Ten."

http://www.powersof10.com/film