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: What?

T: Math.

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.

Me: Yes.

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.

II like this. I wonder if there’d be away to attack the idea of irrational numbers and decimal approximations with the triscuits. The 7-cracker configuration, for example. What if, with older kids, we asked “what would we have to do to make a square out of these?

I did a similar activity during lunch with wheat thins when my kid was 4. I asked her if she could make a shape with them. After easily assembling them into a thin rectangle (2 wide, 4 high) I asked: “So, what did you make?” to which she replied “an apartment building.” lol