A propos of nothing one day, I ask Griffin (9 years old at the time, finishing up fourth grade) a question.

Me:Griff, imagine you are baking cookies and you need cup of sugar, but you only have a cup measure. How would you get cup?

He thinks about this for a moment.

Griffin(9 years old): You put cup of whatever you’re measuring.

Me:Sugar.

G: Does it matter?

Me:No. I suppose not.

The conversation could end here and I would be delighted. But it does not end here.

G: You put that into the bowl, then you fill the cup halfway and put that in.

Me:And that’s cup?

G: Yes.

Me:How do you know?

G: Because is a half, and then half of a half.

Me:Yeah. That is what you just described. How do youknowthat that’s right?

G: Like a square. If you shade in half of it, and then half of what’s left, that’s the same as shading of it.

## So What Do We Learn?

One question division helps answer is *how many of this are in that?* My question of Griffin asked *how many halves are in three-fourths?* This is a division question.

Griffin may not know that it is a division question. That is fine. He is thinking about a specific example of *how many of this are in that?* This will lead to good things further down the line.

That he sees “sugar” as a non-essential detail of the story is lovely. This will serve him well.

Griffin’s mental image for this task is a common one. He can see three fourths of a square in his mind, and he can see that this is the same as one-and-a-half halves of a square.

Finally, we learn (because I am about to tell you) that this scenario could never really happen when baking in our home. I have an awesome set of measuring cups (pictured below): , , , , , 1 and . (A friend—and friend of the project—has pledged to donate her cup measure to the *Talking Math with Your Kids* cause.)

## Starting the Conversation

There are so many ways to raise the question *how many of this are in that?* Measure each other in inches, wonder how many feet tall that is. Count your quarters, wonder how many dollars that is. Repeat with nickels, or dimes. Bake a batch of cookies using only the cup measure.

And you can read through previous division posts for more ideas.