I didn't completely understand the magnitude of my decision to move from first grade to fifth grade. I thought I did. I've switched grades plenty of times before, but this one was a little more difficult in some ways and a whole lot of wonderful in other ways. I always like to get the bad out of the way first, so let's start with difficult. My file cabinets are empty. Totally empty. There's nothing in there to pull out and use. I'm making everything from scratch. I've already had to plan for 4 sub days-math training, art training x2, and reading benchmarks and I had nothing easy to pull out and leave for a substitute. That's just difficult. But on the wonderful side, oh boy, is it wonderful. They get my jokes, they can quietly work for more than 2 minutes, I'm always amazed at how much they can do and it's so fun to see them start really thinking. Which actually brings me back to magnitude. It turns out that I'm not the only one misunderstanding magnitude.
Our first unit is place value and my kids are having no difficulty whatsoever with looking at the number 6,375,293 and telling me that the 7 stands for 70,000. They know what each digit stands for, but they seemed to have no understanding of the magnitude of a number or for more targeted thinking such as how many tens are in 3215. So I just kept backing up and finally I hit how many tens does it take to make 100 and everyone got it. I was blown away that my students could read and write large numbers, but didn't have much understanding beyond that. Where was their flexibility with numbers and their understanding of magnitude?
Remember I've been a first grade teacher for years. I'm used to asking students to build something when they don't understand. So to show my students the magnitude of large numbers, I asked them if they thought they could use graph paper to build up to one million. It was a unanimous YES. "Really," I asked, then I started impersonating Amy Poehler. "Really? Really? REALLY????" The challenge was on, so I told them to start with one and build each place until they reached one million. With a ream of graph paper and plenty of tape they went to work.
Going from one to ten to one hundred was easy.
Putting together ten hundreds to make a thousand, not too bad either. But when they started putting together ten thousand, I started to hear kids changing their thinking. The confidence that they could build one million was wavering.
When the first group reached one hundred thousand and realized that to make a million they would have to first make 10 groups of 100,000, I stopped the class and we gathered around to talk about what we could see. I couldn't get the entire hundred thousand in my photo, but it's huge. Before we taped it to the wall we carried it outside and laid it down on the playground. Then we traced around it and measured out ten of them to show one million. Seeing how big one million would be quickly changed the minds of these 10-year old mathematicians. No longer did they think they could build to one million easily. We also really cemented in the idea that each place is ten times bigger than the previous place. The magnitude of one million now has more meaning for them. We didn't finish until after lunch and I had to do a bit of juggling around in my plan book but it was worth it. We ended the day with a discussion of how many hundreds they had to use to make 1000, 10,000 and even 100,000. It was so amazing to see how this activity completely changed our original conversation. It may have taken a lot of time, but we have a deeper understanding of numbers now, which should help us move a little faster as we progress through the year.
I hope you take the opportunity to slow down and dig a little deeper.