Sunday, November 24, 2013

Really Big (and Really Small) Numbers

A couple of months ago, I realized that fractions and decimals were coming up in the third grade textbooks. This would be the first introduction to decimals for most of my students and a far more in depth look at fractions on top of that. So before we got to that point, I would need to make sure they had a handle on place value.

How would Montessori do it? I asked myself. I somewhat regret my decision to drop out of Montessori training. No matter. I could handle it on my own.

So we all got out pieces of paper and some crayons, I went to the white board with my dry-erase crayons, and we accomplished this: (click on the images to view them full sized)

They caught onto the pattern very easily, as I was hoping they would. I started with Ones, Tens, Hundreds, Thousands, Ten Thousands, and Hundred Thousands, noting all of the colors aloud, some of them catching on before the others and verbally prompting me. Then I let them do most of the work. "What comes next?" I asked, and they all replied, "Millions!" "And what color is it?" "Green!" "How many zeroes does it have?" "Six!" We continued in this fashion, hesitating when we reached the next unit. "What comes after Hundred Millions?" I asked. "What comes after Hundred Billions?"

(There was a moment after I asked one of these questions when the class became silent, considering. One student blurted out a concept he vaguely knew as a very large number, "A Google! ... And after that comes a Google Chrome!" I lost it. The entire class burst out laughing. It's a wonderful, carefree memory that I cherish.)

We had to turn to the internet to help us after Hundred Trillions, because I honestly didn't know what came next, and we were able to authentically search for knowledge together.

I ran out of space on the board after Hundred Quintillion, but many of them were eager to go on. I let them go as far as they were able, though the color pattern became a bit skewed for some.

A few days later, we did the same going backwards, which was much more difficult. We didn't go very far, but having done the previous exercise was definitely a benefit.

From there we just followed the textbook, but they were definitely far better off.