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.

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

This will be a much more complicated conversation in my house, as we have measuring cups shaped something like this: http://www.lakeland.co.uk/15636/Colourworks-4-Measuring-Cups

I thought this structure was a great way to show learning through play,any child is automatically interested in learning when you make it become fun.brilliant post

Great post – and I love and covet those cups!

“This will lead to good things further down the line.” Also – don’t you think? – this understanding stands as it is, sufficient for plenty of applications. There will always be a further down the line no matter how far we go down it.

I did this with my sixth graders last year. We actually went into the kitchen and I handed them a brownie recipe and a 1/4 cup measuring cup – no other sizes. It was really interesting to hear their conversations!

Lovely, and it was all done with words. What screws up the kids’s brains is a far too rapid introduction of symbols, eg (3/4)/(1/2) (extra brackets(UK) needed for the single liner), and it of course has to have a formal name “division of fractions”, and with a complete disregard for the fact that a fraction is a division anyway, which cannot be written any simpler.

Love to read math discussions that even I can understand!

Lovely way to bring maths home.

Just found your blog. We adopted two children (now 8 and 10)…they came to live with us three years ago and had been given almost zero help academically. We’re playing catch-up something fierce. This summer was filled with math and reading. Today, on the way to a Mexican restaurant, the kids asked why Taco Tuesday is special if you can always get tacos at the restaurant. I explained that each taco is a buck on Taco Tues. Our 8 year old was quiet for a minute, then said, “If all four of us get two tacos, that’s eight dollars!” I responded, “Hey! You just did multiplication! 4 times 2 is 8.” He was ecstatic. “I’ve never done multiplication before! Let’s do more. If ten people get four tacos, that’s…40. And if twenty people get four…that’s 80 dollars!” I was floored. Really hoping we’ve crested a mountain. I’ll be reading here again for more ideas!

Oh, I definitely like the way you think. 2 points for you, next? MamaPat