Today, a few 7th grade boys came in after school today and wanted to help with some things around my room: tidy up desks, organize whiteboards, etc. There was a box of 100 manilla folders that I had just brought back from the office. I needed 80 of the folders and would later return the remaining folders to the office.
Here's my exchange with the student we'll refer to as Albert:
Me: I need 80 folders from that box. Albert, think of a quick way you could get those 80.***Let's pause. How would you (the reader) quickly get 80 folders from this box?
Albert: I could count in 5's.
Me: Okay. Any quicker than that?
Albert: By 10's.I get what Albert is trying to do. He doesn't want to count to eighty by ones. To that point, I would say his initial two responses made sense and are practical, in the mind of a 7th grader. I thought maybe I'm asking the question incorrectly, so I try it again.
Me: Right. That would be a good way to organize the folders to keep track of them as you count. Albert, I'd like you to think of a way to quickly get those folders out of the box.I can see the look on his face is one of confusion. Not that look like he's trying to figure it out, but that look like he has no idea what I'm asking. So after a minute, I mistakenly ask another question (in hindsight, I wish I would've stopped the conversation and let him do his thing).
Me: How many folders are in the box?
Me: How many do I need?
Me: Is there a way to get me the 80 without counting all 80?Albert has no idea. I like this question because now it's specific. His challenge is to get me 80 folders without actually counting all 80. After a minute. He needs some prompting.
Me: If the box has 100 and I need 80, how many will be left?
Me: So 80 plus 30 is 100?
Albert: No wait, 20.
Me: Okay, so I will send 20 back to the office. How can I get 80 folders out of the box without counting all 80?Albert has no idea. This exact exchange continued for another round. I'd like to say that Albert eventually came to an efficient way on his own, but he didn't. I tossed 100 up on the whiteboard. We subtracted 80 and wrote 20. I thought after Albert saw the 20 on the board, he might realize to count 20 folders from the box, take out the remaining folders and switch them with the 20.
This is quite common. The number sense (or lack thereof) my students have (or don't yet) is quite fascinating. I have a lot of work ahead of me this year. One thing is for sure. I can get better at asking shorter questions. I can get better at looking for these learning opportunities. I can get better at not looking for one answer when asking questions of students. As Max Ray would say, "2 > 4."