We just started limits in PreCalc this week (today was Day 2). One of my favorite things to do is to get out the personal whiteboards and have kids create graphs that fit certain criterion; for example, the limit as x approaches 1 of f(x) is 3 but f(1) dne.
My last question asks the kids to create a graph where the left- and right-hand limits are both 2 but the full limit does not exist.
They always stare at the Smart Board. Then they stare at their whiteboard. Then they draw something. Erase it. Repeat.
I’ll coyly say something like, “If you’re having some trouble, talk with your partner and see if you can figure it out together.”
After a while I asked the kids to show me their whiteboards. One kid had written “Trick question.” I laughed out loud. I told the class that I did, in fact, see a correct solution, and I asked this kid to show the class his whiteboard.
Everyone laughed. 🙂
I’ve implemented the wonderful “2 Nice Things” routine when I her a kid say something mean. I heard an unkind comment today, and asked, “Is that two nice things?”
“Yes,” the girl said without hesitation. “I like your shirt and I think you’re pretty,” she said to be student she offended.
“Thank you,” I said. And I was so pleased at how quickly those words of kindness were offered.
We have come a long way.