# 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?

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.

## Postscript

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.

# Waffles [Product review]

From time to time, we will be reviewing products here at Talking Math with Your Kids. Sometimes they will be products that are intended to foster mathematics learning, but not always.

Today, we consider one that is not.

We recently bought Kellogg’s Eggo Homestyle Minis waffles.

Tabitha is obsessed with waffles. We typically get the store brand, which as far as I can tell are mathematically uninteresting. But every so often Eggos go on sale, and then it’s game on!

Consider the Minis.

The minis come in sets of 4.

Here is the kind of fun we can have (and, I assure you, that we have had) with this:

• Say, “I’m making frozen waffles this morning. How many do you want?” Leave the unit deliberately unspoken. Child says “one” and is served one mini waffle. Discuss.
• Do the same thing again the next morning.
• Hold up a set of four waffles and ask a young child (say, 2 to 4 years old) how many you have (answer is likely “four”). Then point out to the child that it says there are “10” in the box. Dump them all out and discuss. Key question: What are there ten of?
• Ask a somewhat older child (say 7 to 9) “If there are 10 sets of 4 waffles in the box, how many waffles are there?” Follow up with “How do you know that’s right?”

Finally, this: In addition to (1) waffles, and (2) sets of waffles, there is a third unit to count in that box: servings.

It turns out that 1 serving is 3 sets of 4 waffles. How awesome is this?

You can ask an older child to predict what the number of “Servings per Container” will be on the Nutrition Facts label. I would have gotten it wrong. I would have applied too much mathematics to the problem and said $3\frac{1}{3}$. You can see the “correct” answer below.

You didn’t think I had something to say about the waffles as food, did you? I’m sure they are everything one would expect of Eggo waffles. You probably already know whether you consider that a good thing. Tabitha likes them.

P.S. My own father turns 70 today. He certainly supported my own mathematical development growing up. Thanks, Dad! And Happy Birthday.