Last week my grade level met with one of our local math gurus who is helping lead our district towards better math practices. He was making the point that we want our mathematicians to move towards using more efficient models, like the number line, when solving problems. I totally agree, although in the past few years my efforts at getting there have felt a little clumsy. I asked him this question. "So my kids know what a number line is. They know how it functions with ordered numbers and appropriate spacing. How do I now transition them to using one as a tool?" It seemed like a question I should know the answer to, but I honestly wasn't sure. I'm glad I asked, because his reply led to this post. The following is what he told me to try.
* Give the kids a problem in context.
* Give them a closed number line. (Eventually move to an open number line.)
* Ask them to use the number line to solve the problem. (He actually used the word "force." By providing them with the number line, they're forced to play along. My favorite part is that you don't show them how.)
* Choose a few solutions that exemplify appropriate possibilities and reproduce them on the board.
* Ask questions about what the mathematicians were doing, pressing towards those strategies you hope to see more of.
So today I jumped in with both feet and asked my mathematicians to blindly do the same. I was very impressed. By the way, I didn't show the kids' actual papers, so no one knew whose was whose.
Problem: Amaya found 6 maple leaves. Bradley found 7. How many maple leaves did they find altogether?
They were able to tell me that this mathematician hopped 6 and then 7 more.
We talked about this one hopping on the top instead of underneath. The equation is an added bonus!
This is the one that really excited me. One of our mathematicians explained that this person made big hops of 6 and then 7 more. The author piped up and told us that it was more efficient that way. Oh yeah!
We didn't talk about this one, but I thought it was interesting.
The following is proof that not everyone knew how to use a number line. In fact, most didn't, but I expected that. The good news it that it only takes one or two to make the lesson worthwhile.
Guess what we'll be doing again tomorrow, with a different contextual problem of course. My plan is to do a few of these every week. (It only took about 10 minutes.) I don't think it will take long before most of them can maneuver on the number line fairly well. I'm already envisioning how I can press them further and further to more sophisticated strategies each time.