One of my favorite pastimes is talking about math with kids. I love following the Talking Math with Your Kids hashtag on Twitter (#tmwyk) and I love sharing my own snippets whenever my kids and I have an interesting conversation.

Recently, my wife and I have been preparing our house and lives so that we can start talking math with our third child (starting on or about February 20th!). As a result, I have basically stopped using Twitter until I make it through the initial maelstrom of parenting a newborn. I still have great chats with my kids, though, so I decided to write them down and collect them into a single post. Here goes!

For context, My son J is 5 years old and my daughter H just turned 3. In these talks, I mostly spend my time just asking "why?" over and over, which is the easiest way I've found to learn as much as possible about how my kids are thinking.

## Bathtime

J: Is Aunt Lil 29?

Me: Yeah, she is. Why?

J: Because Grandmama told me that when you were 5 Aunt Lil was 2 and there's two years between you and now you're 32 and so she is 29. It's the same thing between you but not the same numbers.

## In the car

J: Daddy, what's the biggest number?

Me: Well...

H: 64?

J: No

H: 65?

J: No

H: 66?

J: No, everyone knows 100 and all those are less!

## In the car, several days later

J: What's the biggest number that has a name that you know?

Me: I think a googol.

J: What is it?

Me: You know how ten looks like a 1 and then a 0, and a thousand looks like a 1 and then two 0's? Well a googol looks like a 1 and then a hundred 0s

J: That's big.

Me: But you can always make a bigger number by adding 1. So if you take a googol and add one then you have a googol and one, then a googol and two, and so on.

J: But how do you know it's a real number?

Me: If you add a real number to another real number, the answer is always a real number. So you can always make bigger numbers.

Joel: Like five zero five?

Me: That would make 505.

Here I think Joel and I were not describing the same version of adding. I was describing the mathematical operation, but I think he was talking about saying number words and seeing if they make a real number. Sometimes this works, as in twenty-thousand, and sometimes it doesn't exactly work, as in thirty-four-zero-five-hundred. I am not sure exactly what he meant by five-zero-five, because 505 is only one of the possible options. I hope he asks me about this stuff again!

## Jumping on the couch

H: 82, 83, 84, 25, 26, 27, 28, 29, 30, 21, 22, 23, two mississippi, five mississippi, Daddy, I'm doing math!

## At the breakfast table

*J, H, and I spin a fidget spinner and set it on the table.*

Me: It takes a long time to stop. How long do you think it will take?

J: Your height. And now it's right here (points to my chest).

*pause*

J: Now it's here (points to my chin)

*J continues to point higher and higher as the spinner slows to a stop*

## At the breakfast table, again

J: What has more space inside, a pentagon or an octagon?

Me: Well, which has more, a triangle or a square?

J: A square?

Me: Why?

J: The sides are straight up and not slanted.

Me: How about a square or a circle?

J: A circle.

Me: Why?

J: Because it's round? Oh wait, a square!

Me; Why?

J: Because if you put a circle in a square the corners still have spaces.

Me: What if you put a square in a circle?

J: The square would shrink.

Me: So which would be more?

J: The circle

Me: So how do we answer this question, J?

J: ...

I love this question as well, and I hope he comes back to it! I've learned that sometimes it's best to leave my kids a little unsettled, rather than provide a definitive answer. It keeps them chewing on that same idea. There are so many ways to define the parameters of this question, so we'll see where he takes it. Or maybe he won't! That's fine, on to some other idea.