# Tessalation: A great new book

Tessalation is a terrific new picture book by Emily Grosvenor. The story involves a little girl whose mother needs a bit of peace and quiet, so sends her outside to play. While outside, Tessa (get it?) notices shapes fitting together without gaps everywhere she looks.

I helped sponsor Tessalation on Kickstarter this spring, and our hard copies arrived last week. Naturally Tabitha (9 years old) and I read it together right away.

Here are some of the things Tabitha, Griffin (11 years old) and I noticed and discussed while reading it, and afterwards:

• The turtles are delightful.
• While they are somewhat different turtles from the ones we’ve played with around the house for the last year, they have an important characteristic in common—two noses and two tails come together in both tessellations.
• There are tessellating leaves that look an awful lot like some shapes I’ve made and we’ve played with a number of times. We saw kites and hexagons and triangles in the leaves just as we have in the pink quadrilaterals below.
• We wondered whether this object counts as a tessellation. (It’s not from the book, but Tessa set a great example for us to notice and ask about tessellations in our world.)

All in all, Tessalation is perfectly aligned with the Talking Math with Your Kids spirit. It creates a richly structured and playful space for parents and children to notice things and to converse. The language is fun. The images are beautiful. Tabitha and I highly recommend it.

Quick notes: Tessalation will be a component of August’s Summer of Math box. It’s not too late to sign up! Also, we’ll soon have a Tessalation/Tiling Turtles combo pack available. You can order the book right now from Waldorf Books, and e-books from Amazon.

# Talking Shapes with Kids

I have been spending time talking with kindergarteners, first and second graders in schools about my shapes book (coming from Stenhouse, Spring 2016). Many more school visits are ahead of me. I have written up some reflections for a more teacher-ish audience than this blog attracts. If you’re interested in the ways young children talk about shapes, and in what I hear in their ideas, hop on over to the sister-blog Overthinking My Teaching for the details.

You may be delighted to learn how much math there is in the simple collection of shapes below.

# Building a better shapes book [Which One Doesn’t Belong?]

IMPORTANT NOTE: The moment alluded to below has arrived! Which One Doesn’t Belong? is now available from Stenhouse as a student book (awesome for home reading, too!) and a teacher guide.

As a result, I have removed all links to the version I was previously distributing free.

There are many shapes books available for reading with children. Most of them are very bad. I have complained about this for years. Now I have done something about it. Most shapes books—whether board books for babies and toddlers, or more sophisticated books for school-aged children—are full of misinformation and missed opportunities. As an example, there is nearly always one page for squares and a separate one for rectangles. There is almost never a square on the rectangles page. That’s a missed opportunity. Often, the text says that a rectangle has two short sides and two long sides. That’s misinformation. A square is a special rectangle, just as a child is a special person. After years of contemplation, I had a kernel of an idea the other night. The kids are back in school before I am, so I had some flex time available. One thing led to another and voilá. A better shapes book. (Links removed—see above note.)

## How to use this book

On every page are four shapes. The question is the same throughout the book—which one doesn’t belong? For example, which shape doesn’t belong in this set? If you are thinking, “It depends on how you look at it,” then you’ve got the idea.

• The bottom left shape doesn’t belong because it’s not shaded in.
• The top left shape doesn’t belong because it only has three sides, while the others have four.
• The top right doesn’t belong because it is the only square.
• The bottom right doesn’t belong because it’s the only one resting on a side.

Maybe you have different reasons for some of these. That’s great! The only measure of being right is whether your reason is true. With an infant, you can use this book like any other shapes book. Look at each page together. Point at each shape and talk about it as you snuggle. With a young child, ask which one doesn’t belong and why. Most pages in the book have at least one shape that a young child can identify as not belonging. Join the conversation by pointing out a different shape that doesn’t belong for some other reason. With an older child, challenge yourselves to find a reason for each of the 44 shapes in the book. There is no answer key. This is intentional–to encourage further discussion, and to encourage you to return to the book to try again. I have tested the file out on the Kindle app on my iPad, and it looks good. I made one printed copy and prefer it to the e-version because I can leave it out for browsing and we can touch the shapes without accidentally turning the page.

## The legal details

I owe thanks to Terry Wyberg at the University of Minnesota, who regularly plays the “Which one doesn’t belong?” game with numbers in professional development sessions; to Megan Franke at the University of California, Los Angeles, who adapted the old Sesame Street game “One of these things is not like the others?” and to my online colleagues including but limited to Justin Lanier, Megan Schmidt, Dave Peterson, Matt Enlow and Andy Rundquist.

The following Which One Doesn’t Belong? prompts are yours to use in your classroom or home. If you’d like to share them more widely, please link people here. Thanks.

# Fun with tiles

It is no secret that one of my proudest achievements is creating a lovely space on Twitter where people share stories of children’s math talk. Come read along on the #tmwyk hashtag.

That’s where I came across this tutorial-in-photos.

I decided to make myself some. I modified the design a bit (but the food coloring is a genius idea! I used that for sure.)

Then I left them out on Sunday morning and waited for a child to happen along.

Sure enough, Tabitha began making things.

I ate breakfast in the other room.

Ten minutes later, she came in carrying two tiles, put together so that the blue triangles made a square.

Tabitha (7 years old): A square is just a diamond, but I don’t think all diamonds are squares.

Me: Can you draw me a diamond that isn’t a square?

T: The skinny ones wouldn’t be squares.

Me: Yeah. I think I get it. Draw me one, though.

She proceeded to do so. It took a couple of tries.

I lost the paper, but the result looked something like this.

Then, a few moments later she asked a new question.

T: Aren’t all 4-sided things squares?

Me: The doorway isn’t. One of those tiles has four sides but isn’t a square.

I  quickly draw a parallelogram in my notebook.

Me: This isn’t

I drew another 4-sided shape.

Me: This isn’t either.

T: That has 3 corners, not 4. So it can’t be a square.

Me: Show me the three corners.

She counted the three corners that point out from the center of the shape, missing the one that points back inward. She paused.

T: Oh…four.

## So What Do We Learn?

Opportunity to think about math is important. Something as simple as leaving an interesting math object out for children to play with can lead to fun math talk.

Tabitha was working on the definitions of square and diamond in this conversation, and she was paying attention to the properties of shapes. This is important work for elementary children. When children are very young—before about first grade—they are learning to identify shapes based on appearances. As they move further into elementary school, they need to start paying attention to properties—the number of sides, the number of vertices (“corners”), etc.

## Starting the conversation

Make some of these tiles. The materials cost me less than $20 (mostly for the wood—I probably could have gotten it a lot cheaper), and the dying and painting took about an hour on a Saturday evening. Then leave them out. Or leave out a bunch of squares, triangles and rectangles you cut out of construction paper (you can do this for under$3 and less than 10 minutes of cutting).

Then let the children play and be ready to talk.

# Spirals

A few weeks back, this short cryptic video came to my attention thanks to the magic of Twitter.

Thanks to kids connect (@KinderFynes on Twitter)

For more than a year now, I have been posting links and other short bits on Twitter using the #tmwyk hashtag. In the last few months, it has gained momentum. A day rarely goes by without someone posting something interesting or delightful or surprising there.

But back to the video.

We get a very brief glimpse of a classroom of Kindergarteners on a walk. At the moment the video captures, they are trying to decide whether the object on the wall is, or is not, a spiral.

That image in the video was not a spiral because “Spirals are connected”.

So I drew this.

Griffin’s reply: That’s three things connected, not one thing.

So I drew this (sort of).

The part I actually drew was two disconnected spirals. He drew the short line segments on the ends.

Griffin: If you close them off like this, it’s an outline of a spiral.

Next I drew this.

I was wondering whether spirals needed to be roughly circular.

Griffin: In this one, you are looking at a spiral from its edge.

Finally, this one.

I cannot recall his response. We were on the porch on a warm lazy sunny spring morning at the end of a long long winter. We may have gotten distracted.

## So what do we learn

This is how I teach critical thinking. Not just at home, but in my work, too. Get the child to make a claim and to give a reason supporting it. Cook up a problematic example and ask for a new claim. Repeat. Quit before angering child.

WARNING: It is my experience with my own children—as well as with my students of all ages—that they learn these lessons well. This means that over time they begin to argue back intelligently, and that they begin to pick apart my own claims and arguments.

# [Product Review] Tupperware Shape-O Toy

You know this thing.

This thing has been around for many, many years. You may not know that it is officially the “Tupperware Shape-O Toy” but if grew up in or near the United States anytime since about 1960, you have encountered this toy. It is the rare math-y toy that is actually awesome in the ways it was intended to be.

(See discussion of the Multiplication Machine on this blog for an example of a math-y toy that is awesome in unintended ways. See your local Target for a wide selection of math-y toys that are not awesome in any way at all.)

We had some fun on Twitter last fall when a math teacher and father, Dan Anderson, invited speculation about which shapes would be easiest and most difficult for his $1 \frac{1}{2}$ year-old to put in the holes.

[Fun fact about Dan Anderson—if you heard last year about how Double Stuf Oreos are not actually doubly stuffed, it was his classroom that got the media ball rolling.] Anyway, here is his ranking—following his son Calvin’s lead:

And here is an amusing video of a cute kid playing with one. The parental participation in the play may be a bit heavy-handed but the spirit is right—encouraging and playful.

Notice that the triangle is harder for him to fit in than the square, and that it’s tough for him to distinguish the hexagon from the pentagon.

Tons of fun to be had with this classic!