I wrote a blog post for the NCTM journal Teaching Children Mathematics. You should head over there to read it.

Here are downloadable images to go along with it, which you are welcome to use in your home or classroom.

I wrote a blog post for the NCTM journal Teaching Children Mathematics. You should head over there to read it.

Here are downloadable images to go along with it, which you are welcome to use in your home or classroom.

I’ve been working on some presentations, and I’d like to share with you some images I’ve collected and made along the way, without further commentary. Enjoy.

I am delighted to announce that *Which One Doesn’t Belong? A Better Shapes Book* is in print and shipping from Stenhouse Publishing this week.

There is a student/home edition, and a set that includes a teacher guide.

I’ll be at Math On-A-Stick at the Minnesota State Fair August 25 through Labor Day. Stop by for a selfie and to get your copy signed!

(Note: The books are *not* for sale at the fair—nothing is for sale at Math On-A-Stick.)

The last time I wrote about this, Math On-A-Stick wasn’t a sure thing.

Now it is.

Details are on my Math On-A-Stick page, so click on through for all the latest updates there.

We need volunteers, so please help spread the word online and in person.

I made a shapes book recently. The response has been a ton of fun. I have heard from parents of preschoolers, from primary grades teachers, upper elementary teachers and middle school teachers. All have reported having interesting and sometimes surprising conversations with their children and students.

I have heard from high school teachers, including a class studying set theory.

But I feel as though I am missing out on the fun. I want in.

If you teach kindergarten, first or second grade in the Twin Cities (MN) area, and you would be willing to have a visitor come talk geometry for a half hour in the coming months, shoot me a note, please. If you know such a teacher send them this post, please.

We’ll work out the details and I’ll see you in class!

Easter Sunday saw St Paul, Minnesota waking up to weather perfection. Sunshine, low seventies (Fahrenheit), cloudless sky. Truly amazing.

There was a loon on Lake Phalen!

This was the sort of April weather that brings Minnesotans out of their homes to rediscover their neighbors.

—

So it is with Griffin, Tabitha and me on this warm spring morning. We are enjoying the warm sunshine on our front steps when L (five year old girl), O (3 year old boy) and their mom come biking, biking and strolling (respectively) down the sidewalk.

L is on a neighborhood mission delivering handmade Easter greeting cards.

It turns out that she has also pocketed some goodies from her own Easter basket. While we chat, she pulls out a bag of Cadbury mini eggs. In case you are unfamiliar, these are the size of pebbles. They are chocolate inside with a crunchy candy shell. Like an oversized egg-shaped M&M. Each little bag contains about a dozen.

*So. Much. Candy.
This is likely a small fraction of the candy L has consumed by the time she stops to chat.*

Anyway, mom notices the bag as soon as it emerges from L’s pocket. (Side note—mom is *across the street! *Holy SuperMom powers!) She warns L not to eat any more of these; arguing that L has had enough candy for one morning.

L(5 years old): Please?

Mom:If you give everybody one, you can have one.

L proceeds to cheerfully open the package, hand one to Tabitha (who eagerly and gratefully receives it), one to Griffin and one to me.

I begin to think about what question to ask to get some math talk going.

But L is ahead of me.

After enjoying both her egg and a long thoughtful pause, she pokes her finger back into the bag. She begins to rummage around and asks:

L: Tabitha, do you want a second one?

Children use math to their advantage.

L knew what mom meant. Mom had compromised on the candy, allowing her **one piece**. L knew that. And she knew that the process was repeatable.

One does not always mean one. One might be taken to mean *each*. “Each time you give everybody one, you can have one.” This is also a reasonable interpretation of mom’s words.

L was rule bending here. But she was also building the precursors of ratios. *For every one you give a friend, you can have one*. This is a ratio. *Giving a friend two and having two* fits this rule just as well as *giving a friend one and having one*. Ratios are one of the more challenging ideas behind multiplication and division relationships, and fractions.

What is maddening for parents is at the same time great thinking practice for children.

This was a brilliant compromise strategy on mom’s part. I doubt that she intended to encourage L to think proportionally, but that doesn’t matter. More likely, she was trying to encourage the admirable social skill of sharing. By including numbers in her compromise, she opened the door for L to think.

As I have mentioned before, anytime your child wants to open a negotiation, there is an opportunity for math talk. Sometimes we parents need to give a flat out yes or no. But when negotiations are feasible, we can get our children thinking.

March Mathness continues as I guest post on the Tiggly blog. This week: Operation Conversations. Click on through and enjoy!

This is just a quick note to let everyone know that *Talking Math with Your Kids *is guest-posting on Tiggly’s blog throughout the month of March.

It’s March Mathness.

You celebrate that, right?

There have been two posts so far:

While you’re there, browse around a bit. The folks at Tiggly are super smart, sincere and hard working. They have lots of good resources.

This is just a quick note to let you know that Talking Math with Your Kids now has a Facebook page. It will be a place for links and resources as I come across them, and typically before they get worked into posts here on the blog. It can also be a place for quick, informal discussion different from blog comments.

You are invited to join the fun over there! Just click on through.

*What’s Gnu? A Facebook page! That’s what’s gnu!
*

While we’re discussing social media, you can find me on Twitter, too. We like to use the hashtag #tmwyk over there.

I was talking with Griffin one day when he was in third grade.

Me:Do you know what is?

Griffin(8 years old): 6

Me:How do you know that’s right?

G: 2 times 6 is 12.

Me:What about ?

G: 13

Me:How do you know that?

G: There were 26 kids in Ms. Starr’s class [in first grade], so it was her magic number. We had 13 pairs of kids.

Me:What about ?

G: Well, 15 plus 15 is 30…so…19

My notes on the conversation at this point only have *(back and forth)*, which indicates that there was probably some follow-up discussion in which we located and fixed his error. The details are lost to history.

Our conversation continued.

Me:So is 6 because is 12. What is ?

G: [long pause; much longer than for any of the first three tasks] 12.

Me:How do you know this?

G: Because if you gave 1 person 12 things, they would have all 12.

Me:What is ?

G: [pause, but not as long as for 12÷1] Two.

Me:How do you know that?

G: Half of 12 is 6, and is 2, so it’s 2.

Me:OK. You know what a half dollar is, right?

G: Yeah. 50 cents.

Me:How many half dollars are in a dollar?

G: Two.

Me:How many half dollars are in 12 dollars?

G: [long thoughtful pause] Twenty-four.

Me:How do you know that?

G: I can’t say.

Me:One more. How many quarters are in 12 dollars?

G: Oh no! [pause] Forty-eight. Because a quarter is half of a half and so there are twice as many of them as half dollars. 2 times 24=48.

Mathematical ideas have multiple interpretations which people encounter as they live their lives. As we learn more mathematics, we become better at connecting these different ways of thinking about ideas.

In this conversation, Griffin relies on three ways of thinking about division:

- A division fact is a different way of saying a multiplication fact. ( is 6 because is 12).
- Division tells how many groups of a particular size we can make (Ms. Starr’s class has 13 pairs of students).
- Division tells us how many will be in each group if we make groups that are the same size. (When he was working on , Griffin put 15 in each group to start off with.)

We were just talking for fun, not homework or the state test. So I wasn’t worried about his connecting those ways of thinking. I was just curious how he would apply them to some more challenging tasks, such as dividing by 1 or by a fraction.

I was surprised by how difficult was for Griffin. Not because it is an easy problem, but because he could have applied his *how many of this are in that?* idea, or his *multiplication facts* idea. But he did neither and reinterpreted the task as *twelve divided by half-of-twelve*.

I was also surprised at the length of the pause he took for . It makes sense in retrospect. After all, are you really *making groups* if it’s just one group? I imagine he had to think that through, rather than the number relationships involved.

When the opportunity presents itself—when you and your child are not under homework stress, not rushing to get out the door or find the dog’s leash; when you happen to be talking about number anyway—ask follow up questions. Even a simple set of division problems got a lot of good thinking out of Griffin. Problems involving 1, 0 and are especially challenging.

Vary the size of the numbers.

Don’t worry about whether the answers are right or wrong.

Keep asking *How do you know?* and listening to your child’s answer.

Offer a few ideas of your own.

Quit before anybody gets frustrated or bored.