After chatting with the Mathalicious crew about a lesson on square roots and irrational numbers, I was inspired to talk math with Tabitha (5 years old).
Me: [With a box of Triscuits at the dining room table] Tabitha! Come here, please! I want to talk to you about something.
Tabitha: I know what this is gonna be about.
Me: Right. I want to know whether you can arrange those in a square.
I hand her four Triscuits.
She quickly forms them into a square.
T: Done. Now can I eat them?
Me: Not yet. Can you do it with these?
I give her nine Triscuits and scramble them up.
She is again successful.
Me: How many more are in this square than in the last one you made?
T: I am really tempted to eat them.
Me: Right. But how many more are there this time?
T: There were 4 before. And now there are 9.
Me: Yes. So how many more in the big one?
Some elaborate Triscuit shuffling goes on, lasting about a minute.
T: Five. Wanna know how I did it?
Do you see the beauty of doing this on a regular basis? Children learn discourse patterns through exposure. Not only can she explain her thinking, she expects to do so.
T: I took 4 away, then there were five left.
Me: Nice. One more.
T: I really want to eat these.
Me: I know. Soon. Can you make a square with these?
I give her 7 Triscuits.
She moves them around. She is not especially systematic in the order she places them.
She ends with this arrangement.
T: If you took this one [i.e. the one in the upper left] away, you’d have a square.
Me: Is that a square?
T: Oh! No. It’s a rectangle.
You do it.
Me: I can’t. See I can do a square with 1 Triscuit.
T: Of course.
Me: Then I can do 4 like you did, and 9 like you did. Four had two Triscuits on a side. Nine has three Triscuits on a side…
But she can no longer hear me over the sound in her head of the crunching of Triscuits.