Which One Doesn't Belong?

Ages: 3 and up
Cost: ~$17 (Buy on Amazon)
Math Ideas: Attributes, Classification, Geometry
Questions to Ask
    Which one doesn't belong?
    Can you think of a reason this shape doesn't belong?
    Can you think of a second reason?

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This week's "game" is actually a book by one of my favorite authors and math thinkers, Christopher Danielson. Christopher is the creator of the Talking Math with Your Kids website, where he has collected all sorts of great resources and conversation prompts for you and your kids. Many of my ideas about mathematical talk come from Christopher, so if you like what you read here, be sure to check out his site.

Not only that, Christopher has a side business making beautiful mathematical toys for kids. I own a copy of just about every set of blocks that he has made, and I can't recommend them highly enough. 


How to Play

Lots of kids' books ask you to find the turtle or apple or dump truck that doesn't belong. Oh, all the cats are wearing red sweaters except this one that is wearing blue! Yaaaawn....


But Which One Doesn't Belong is different. Each page contains four distinct shapes and the question "Which one doesn't belong?" The beauty of this book is that any one of the four shapes could be considered the one that doesn't belong. For example, the top left shape is the only triangle, while the bottom left shape is the only one that isn't colored in. The bottom right shape is the only one resting on its side, rather than on a point. Can you think of a reason why the last shape doesn't belong?

Instead of reading through the whole book, you might only go through a couple of pages with your kids. You could spend ten minutes on a single page, brainstorming multiple reasons why each shape doesn't belong. This book is also a great one to pull out when multiple kids of different ages want a bedtime book. Your 5 year old might notice different things than your 8 or 11 year old, but they'll all be able to debate, discuss, and play around with the same four shapes.

Where's the Math?

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Which One Doesn't Belong is all about classification, which is the mathematical skill of placing different objects into groups based on their attributes. Mathematicians classify shapes, numbers, functions, sequences, and all sorts of other objects and ideas. 

When 5 and 6 year olds are asked to explain why a shape doesn't belong, they get a chance to sharpen their language about the attributes of each shape. Think about it this way: what is it, exactly, about an square that makes it a square? If you stretch it, tilt it, squeeze it, reflect it, is that shape still a square? Is the shape in the bottom left of the picture a square, a diamond, or both? If you ask your kids, you might be surprised at the level of disagreement you get. 

Taking the time to define exactly which categories a shape belongs in can lead to wonderful, branching conversations about the fundamentals of geometry. Your kids might even surprise you with the ways that they see shapes.


Occasionally I run a free math event at the local library for kids ages 4-7. When I showed this picture to my group, one girl said "The bottom right shape doesn't belong because it doesn't have any corners."

I asked her "Can you say more about that?"

She said "The other shapes have corners, but this one's corners are covered up by the circles."

This led to a great conversation about what does and does not count as a corner. In my opinion the bottom right shape has eight corners, but most of the kids disagreed. So we opened up the discussion: How many corners does the heart have? What about the bowl-of-rice-looking thing? And by the way, what should we call that shape? What other categories does it belong to?

In chats like this, every answer prompts another question, which lead to the best mathematical conversations you can have with your kids: the ones that don't end with an answer, but with a new idea to chew on.

Questions to Ask


Ok, so the questions in this book are always the same: Which one doesn't belong? Why? Can you think of a reason why a different shape doesn't belong here?

I'm more interested in talking about when to ask these questions. And the answer is, whenever you can! 

You don't need this book to play this game. In fact, you might even enjoy the process of coming up with your own Which One Doesn't Belong puzzles with stuff from around the house! 


As you can see, lots of people have already made their own puzzles with household objects. If you need some inspiration, check out this website, which collects puzzles made from dice and donuts just as often as numbers and graphs. 

Yes, talking about donuts is mathematical, as long as you focus on its attributes! For me, the top left one doesn't belong because it's the only thing that tastes bad (I don't like chocolate glaze). But that's just my answer. Now it's your turn: Which one doesn't belong?

Buy Which One Doesn't Belong on Amazon