Griffin turned 9 the other day. His birthday dinner request was lobster. We live in Minnesota, where lobsters are not native. They do not come cheap.

Tabitha, who is 6, announced in advance that she would not be having any lobster. My mother joined us for dinner. A grand time was had. Children held live lobsters. There were also clams, oysters and some of the season’s first corn on the cob. Having an August birthday must be great.

That night, the children were overstimulated and exhausted. This may not be the best time for math talk. But I could not resist the opportunity.

Tabitha and I were on her bed in the final stages of bedtime.

Me: Tabitha, how many lobsters were there today?

Tabitha: (6 years old) Two.

Me: You saw that I cut them in half, right?

T: Yes.

Me: How many half lobsters were there?

T: NO! I am not talking about that now!

Me: Oh come on; I promise it won’t be a big talk. How many half lobsters were there?

T: Four.

Of course I knew she knew this, and that my question wasn’t challenging for her. But I was desperate to know how she knew. Could she see them in her mind? Did she remember that everyone at the table, except her, had their own lobster with no leftovers? Had she counted them at dinner time? Did she know to double the number of lobsters (this seemed unlikely—she’s only six)?

I had to know.

Me: OK. Just one more question, I promise.

T: NO!

Me: Seriously. Just one last question, which is: How do you know?

T: I am not…

Me: Come on. You’re right and I just want to know how you thought about it.

T: 2 plus 2 is 4.

Me: Oh. Good.

I pause to ponder my next move.

Me: So I am just going to say something. You don’t have to respond.

T: Grrr….

Me: I think you were thinking that the first “2” was for the two halves of the first lobster, and that the second “2” was for the two halves of the second lobster. So 2+2 adds the parts of the two lobsters together. Is that right?

T: Yeah.

So What Do We Learn?

First of all, we learn that it is dangerous (but still possible) to talk math with overtired children.

Secondly, we learn that 2+2 is a strange math fact. Here’s why. Imagine there had been three lobsters. If my guess about Tabitha’s thinking was right, she would think 2+2+2 is 6. (Well, more likely in stages…2+2 is 4, then 4+2 is 6.)

But because I stated the meaning of her numbers I do not know that for sure. Maybe the first two was really for the 2 left-hand sides of the lobsters, while the second 2 was for the right-hand sides. In that case, she would answer the question about three lobsters with 3+3 (3 left-hand sides plus 3 right-hand sides). There is no way to know based only on the conversation we had.

But there was no way I was going to drag more out of her at the time. I’ll ask her sometime.

Finally, we have another demonstration of changing what we’re counting. In the Things that Come in Pairs conversation, we were grouping eyes and counting the number of pairs. In this conversation we are cutting lobsters in half and cutting the halves. Opposite process, same underlying idea.

Starting the Conversation

There are lots of opportunities to count both things and halves (or thirds, or fourths, or whatever). You do not need to buy lobsters. Pizzas, cookies, sandwiches and cakes are examples of things children experience in both their whole form and cut up.

Start with things that are either right in front of kids, or that have recently been. And start with the actual numbers. Then move to the what-if scenarios. Starting with things children have actually touched or seen makes things concrete and easier for many children to think about.

You can also talk about things you are about to cut. “You see these three grilled-cheese sandwiches? I am about to cut them in half. How many half sandwiches will we have after I do?”

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