One of my favorite things to do is talk math with my own kids. Today, Barbara asks me how old I'll be when she is 10. I love this question and ask her what she thinks.
She has no idea, so I ask, "how old are you now?" 6.
"How old am I now?" I don't remember.
She is silent for a while, then says 41. I ask her how she got 41 and she says, "I counted." I ask how and she gives me a vague answer. I wish I could go back in time and probe more here - this is a good mathmistakes.org -like situation, and I wish I could have asked for direct evidence of her thinking.
Instead, I say, well it's not right, so let's try a different way. She wants to get it right. I say again, "How old am I right now?...and how old are you right now?"
Me: "How old will you be next year?"
Me: "And how old will I be next year?"
Me: "And what will happen after that?"
...and then I close my mouth and wait. Of all the things in this conversation, this was by far the most effective thing I did - I just waited. I also think the "what will happen" question is the right one, as opposed to "what about the next year?" or "how old will we be next?"
After a long pause, Barbara starts..."I will turn 8..."
Still waiting. I'm pretty sure she'll get there.
"...and you will turn 34."
Got it; she's on the way.
"...and then I'll be 9, and you'll be 35..."
Me: "How did you get that?"
Barbara: "I counted."
Me: "Tell me how you counted."
Barbara then walks me through her start process, starting with "this year I'm 6 and you're 32, so next year..." and ending with "then I'll be 10 and you'll be 36."
Then we were interrupted, so there was no chance to extend this or apply the same reasoning elsewhere...at least not immediately.
@trianglemancsd I am not, but I thought - despite the initial hiccup - this one went fairly well.