Cocoa Puff or Cocoa Puffs: The language of nothing

In honor of Tabitha turning 11 this week, here’s a conversation from 6 years ago. 

We have a little family tradition. When we go grocery shopping the weekend before your birthday, you can choose one box of any cereal you want-no restrictions. In the weeks and months leading up to the grand event, much time is spent in the cereal aisle weighing the advantages of the various sugar-laden options.

The week before turning five, Tabitha nearly dropped the ball. She just grabbed the first box of anything at hand. I don’t remember what it was, but it seemed out of character for her. I reminded her of the cereals she had been coveting as recently as the previous week.

She went for the generic Cocoa Puffs.

I steered her towards the real deal. If you’re only gonna eat ’em once a year, you might as well have the sugar-addled bird bouncing off the box in front of you, right?

A sugar-addled bird

One morning shortly afterwards, we had this conversation:

Tabitha: Do I have Cocoa Puffs or Cocoa Puff in my hand?

Me: Well, you have four Cocoa Puffs.

T: [with only one in her hand now] Do I have Cocoa Puffs or Cocoa Puff?

Me: You have Cocoa Puff.

T: [huge smile] Right!

Me: [with empty hand displayed] Do I have Cocoa Puffs or Cocoa Puff in my hand?

T: [silent but smirking]

Me: Well…Is it Cocoa Puff or Cocoa Puffs?

T: [continued silence]

Me: I have zero…

T: [bigger smile]

Me: …Cocoa…

T: Puffs!

Me: Yeah. Isn’t that weird? If you have one, it’s Puff; if you have none it’s Puffs.

T: I knew that.

Me: Of course you did.

T: No! I knew that; I was showing you that [you had zero] by not saying anything-zero words!

So what do we learn?

Children listen carefully to language patterns. They do not learn a native language like a second language in school. The rules are not carefully explained to them one at a time.

Instead they listen, speak, get corrected, and try again. All of this can be tremendously fun for child and parent alike.

It is an odd quirk of English that zero is plural, grammatically speaking. We talk about having one child, but zero children. More commonly, we use no instead of zero, as in My neighbors have no children. The grammar is the same either way; saying My neighbors have no child sounds funny to our ears.

Starting the conversation

In discussing place value, zero is sometimes called a place holder. To understand that, children need to understand zero as a number. They need to understand that zero can legitimately answer the question, How many are there?

We talk a lot about zero in our house. You can too. Ask your children, “Would you rather have one cookie, two cookies or zero cookies?” Ask who has more of something, even when one of the people has none.

The Mad Hatter in Alice in Wonderland gives an example of this. The March Hare offers Alice “some more tea”. When Alice says she can’t possibly have more, since she hasn’t had any yet, the March Hare replies, “It’s very easy to take more than nothing.”

Another silly language game we play in our house is this. If you look in the pantry and see that there are three cookies left, you can report this in the following two ways: (1) “I checked the cookies; there are three left,” and (2) “There are three cookies.” If, however, there are no cookies in the pantry, these two ways of reporting the sad fact become: (1) “I checked the cookies; there are none left,” and (2) “There are none cookies.” We like to treat none as a number. There is no good reason for this; it is for personal amusement purposes only.


Tabitha again chose Cocoa Puffs on this, the week of her eleventh birthday. She is enjoying them, but she has also stated the obvious—they look like rabbit poop.

A tale of two conversations

Here are two conversations about hot chocolate.

The first one didn’t happen. The second one did. Read them both, then I’ll tell you about their meaning.

Both conversations begin on a cold November night in Minnesota. Unseasonably cold. Fourteen degrees, to be precise (–10 Celsius).

A cup of hot chocolate

Zero marshmallows for me on this cold night.

Tabitha (7 years old), Griffin (10 years old) and I get in the car to head for Tabitha’s basketball practice.

What might have been

Me: Wow! It is cold!

Tabitha (7 years old): You know what you do when it’s cold? You make hot chocolate.

Me: Ooooo! Good idea! We can do that when we get back home after practice.

T: Does it count as dessert?

Me: If you have marshmallows in it, it does.

T: I won’t have any marshmallows, then. So I can have some Jell-O.

Griffin agrees that this is the way to go, and the conversation moves on to other things.

What actually happened

Me: Wow! It is cold!

Tabitha (7 years old): You know what you do when it’s cold? You make hot chocolate.

Me: Ooooo! Good idea! We can do that when we get back home after practice.

T: Does it count as dessert?

Me: If you have two marshmallows in it, it does.

T: I’ll have zero marshmallows in mine, then, so I can have some Jell-O.

Griffin (10 years old): I’ll have one marshmallow, and a small serving of Jell-O. Wait, no! I know! I’ll cut a marshmallow in half!

I presume that this is in order to maximize his allowable Jell-O serving, while still retaining some marshmallow in his hot chocolate. It’s a scheme nearly as complicated as credit default swaps.

So what do we learn?

One small difference changed the course of the conversation—my use of a number word. I could have said, “It counts as dessert if you have marshmallows in it.” But I did say, “It counts as dessert if you have two marshmallows in it.”

Using numbers—two marshmallows instead of just marshmallows—invited the children to talk about numbers. It invited them to use numbers to maximize their benefit. It invited them to think about numbers.

This invitation is important.

A few years back, researchers paid careful attention to the ways preschool teachers talked with their students. Those teachers who used more number words and concepts as they talked with children stimulated greater growth in math than those who used less math talk.

This was not a study about math instruction; it was a study about the math language that these teachers used when they weren’t teaching math. “Yes, you three may help me.” versus “Yes, you may help me.” is the sort of difference that matters.

Using number words and math concepts in everyday speech invites children to notice and to think about number. That’s what Talking Math with Your Kids is all about.

Link to full study ($)

Ten hundred Doras

There was a while when Tabitha (five and six years old at the time) would try to get away without wearing underpants when she dressed herself. Those days are pretty much over, but I still like to make sure she has done the complete job, so I ask her from time to time.

Tabitha (7 years old): I’m dressed!

Me: Are you wearing underpants?

T: Yup—Dora the Explorer.

ten hundred dora


Don’t worry. The child is not wearing these in the picture.

Me: Nice. How do you feel about your Dora the Explorer underpants?

T: I don’t really like Dora that much, but I have a thousand of them.

Me: That’s a lot.

T: I counted them once.

Me: All one thousand?

T: No. I don’t really have a thousand. I don’t even know how to count to a thousand. Just to ten hundred.

I pause for a moment. Does she mean one-hundred-ten? Can’t be. She must know that one-hundred-eleven comes next.

Me: Ten hundred. You mean like after nine hundred is ten hundred?

T: Yeah. That’s as high as I know how to count. I don’t even know how many a thousand is.

Me: A thousand is ten hundred.

T: Oh. Cool.

A few minutes later, I get an idea. I wonder how she would write ten hundred. She needs to get out the door for school so I make it quick. I ask her to read some numbers out loud as I write them.

  • 900
  • 832
  • 110
  • 1000.

For that last one, she says one thousand.

I ask how she would write ten hundred.

She writes, “1000”.

ten hundred

T: It’s the same.

Me: Because I just told you that. Right. How would you have written ten hundred before I told you it was the same as one thousand?

She shrugs her shoulders. Drat. Moment lost. We talk about hundreds for a moment. One hundred, two hundred, etc. up to ten hundred.

Then I have one more.

Me: OK. Last one, then off to school. How would you read this one?

I write 10,000.

She looks for a moment. And thinks.

T: Ten….

More thinking.

T: Ten thousand?

High five!

I zip up her sweatshirt and send her out the door to catch her bus.

So What Do We Learn?

A recent research article argued that children learn a lot about place value through everyday conversation, and that kindergarteners know a lot more about the structure of the number system than parents and kindergarten teachers (on average) think they do.

Here you can see that knowledge in action. Tabitha knows that 1000 is a big and important number. She knows the pattern that allows you to keep counting by hundreds. She has not put these two pieces together. A short conversation helped her put those two pieces together, and then to extend the pattern.

Starting the conversation

This didn’t start out as a math talk. It began as a clothing inspection. But the opportunity presented itself. Listen for those times your children use numbers, and ask follow up questions about them. You won’t get this much learning out of every such conversation, but if even 10% of those opportunities turn into a little bit of learning, the interest compounds.

I promise you that.

Counting by fives

The time I spend doing the dishes is frequently productive. Tabitha (6 years old) or Griffin (9 years old) will often linger nearby playing and talking. Sometimes they talk to me. Sometimes they talk about math, as on a recent evening.

Tabitha (6 years old): 5, 10, 15, 20, 25, 30…

She continues until 170, at which point she becomes bored.

T: Dad! I can count by hundreds. Want to hear?

Me: Yes. Yes I do.

T: One hundred, two hundred, …

She continues to nine hundred, when she pauses. I wait a few beats to see what will happen. When nothing does, I ask.

Me: What comes next?

T: Ten hundred.


T: Hey Dad, when do you get to one thousand?

Me: Awesome. Ten hundred is one thousand. That’s the word for ten hundreds.

T: What comes next?

Me: One thousand one hundred.

T: One thousand two hundred, one thousand three hundred,…

She continues. She reaches one thousand nine hundred.

Long pause.

T: Two thousand. [She smiles broadly.]

Later that evening, she is doing her weekly homework, which involves counting by fives. It is not clear from the directions whether she is to start over for each kind of five, or whether she is to continue counting all the way down the page.

Tabitha decides to continue the counting, and this seems the more appropriate challenge for her.

She gets to 95.

T: How do you write one hundred?

Me: A one and two zeroes.

T: How do you write one hundred five?

Me: You tell me. You try, and I’ll tell you whether it’s right.

T: One-zero-five.

Me: How did you know that?

T: Replace the zero with a five. How do you write one hundred ten?

Me: What do you think?

T: One-one-zero.

So What Do We Learn?

The first activity was about number language. Tabitha was following the patterns in number language and puzzling over the places where the patterns break down. One hundred, two hundred, three hundred…how does one thousand pop out of this sequence?

The second activity was about writing numbers (or numeration). Tabitha had no trouble counting through one hundred five, but she wasn’t sure how to write it.

A common error is to write this: 1005. The thinking goes like this: One hundred is 100, so I’ll write that, then put a 5 at the end.

Starting the conversation

Any time a child asks if you want to hear her count, the correct answer is yes. Then listen. Listen for the challenging bits (the teens are difficult, as is anything following a ‘9’—such as 19 to 20, or 49 to 50). Be ready to help if they get stuck but also to let them think it through and try for themselves. Then talk about how they knew to do what they did. Talk about their thinking.

Learning to count

I am fascinated by watching children learn to count. There are many surprising twists and turns kids take along the way.

Even more surprising, perhaps, is that what seem like crazy mistakes to us adults are completely sensible attempts at getting it right for kids.

For example…

  • In English, the pattern that occurs in the teens is complicated. “Thirteen” doesn’t sound very much like what it is: three plus ten, while “Fourteen” does.
  • Likewise, the names for the “decades”: “Twenty” means two tens and “Thirty” means three tens.
  • But once you get to twenty-one, the pattern is regular until twenty-nine.
  • We start counting at 1 (not 0), but we don’t start the decades at 21 or 31, so kids following the 1, 2, 3 pattern will often skip 20 and 30.

If you put all of this together, you might expect a typical young child who is counting “as high as I can” to:

  1. Have trouble in the teens
  2. Skip 20 in favor of 21
  3. Have more success in the twenties than in the teens, and
  4. End the count at or about twenty-nine (since the word thirty is not very predictable from the previous language patterns).

Here goes…