My Hero, Zero!

Teachers,

I've seen some amazing seasonal themed lessons this week:  predicting the number of pumpkin seeds, using pumpkin seeds for number bond manipulatives, estimating pumpkin weight, etc. If you are looking for a mathematical theme for tomorrow consider, Zero.  Why Zero? Did you know that zero has a scary past? Zero is so unusual and interesting it has its own "biography", Zero: The Biography of a Dangerous Idea, by Charles Seife. Seife states, "as natural as zero seems to us today, for ancient peoples zero was a foreign - and frightening - idea." The Greeks banned it!

Zero doesn’t' behave like other numbers. Add a number to itself and it changes. Not with zero,

0 + 0 = 0, no change. Zero is neither positive or negative. It is the only number separating these two number realms on the number line. In our decimal system zero is the only number that can act as a placeholder and not as a number. In fact look at your computer keyboard, your phone - where is zero? It isn't before the one; it's after the nine. This is a remnant of viewing zero as a placeholder only and not as a number itself. Does zero matter? Start counting. 1, 2, 3, looks like we don't need it, but wait, 8,9, 10. There it is as a placeholder. We can approach infinity with 0 as a placeholder. Place value is all about the power of zero to allow us to only use 10 digits to represent numbers as large as we need. But, sometimes zero as a number acts as if it doesn't matter at all. Add 0 to 7,

still 7,  The Identity Property of Addition. But multiply 7 by 0. Ahh! Zero is suddenly very powerful as a number. Poof! Zero is all that is left, The Multiplicative Property of Zero. Zero can by scary - we wouldn't want to multiply any student by zero because we like them, right? :) When zero becomes a multiplier it destroys everything in its path - Wow! Wait, there's more, what about division? 7/0, what is that? Well, we can check division by multiplication, correct? Let's see, what if 7/0 =0,  0 times 0 would have to equal 7. But, 0 times 0 = 0 and the last time I checked 0 was not equal to 7, so we have a huge problem. Dividing any number by 0 throws our mathematical system out of whack. ERROR - is what your calculator tells you. But, divide by a number that approaches but is not quite equal to zero and we approach infinity. Crazy, isn't it?

Dress zero up in a hero costume and you have a 3 minute classic on Zero as a place holder from Schoolhouse Rocks, "Zero, my Hero, how wonderful you are": http://www.youtube.com/watch?v=Nvc2PPTlW7k

So, zero ... hero or ...?

Happy last weekend in October,

Lorinda