n+n-1 vs. n+(n-1)

We were studying patterns this morning and as I walked around the room I took note of who wrote their formula in a different way.  After having a couple students share their methods and then having the class prove their equivalence, I asked a third student if she was the one who had “n+(n-1)” (because I couldn’t remember whose paper it was).  The other students yelled out, “obviously that’s the same as 2n-1” but I shushed them and had her share.  After the presentation, one of the students who had said it was obviously the same announced “that’s a totally different approach! It’s the same thing to say n+n-1 and n+(n-1) but the parentheses mean something really different here”  I was thrilled, because that was exactly the point I was trying to make and he couldn’t have said it better if I’d given him a script.  This is the same student who 5 minutes before was blowing on his phone (who invented an app that involves blowing on the screen??).  He may not be 100% on task, but I’ll take an easily distracted student who shares insights with enthusiasm over an obedient one any day.

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