“Which One Doesn’t Belong? Playing with Shapes” by math teacher Christopher Danielson is an amazing picture book sure to make those who read it feel great about their math abilities. It’s a no-brainer, because in this wonderful and creative book of math problems, there are no wrong answers!

Many adults grew up playing the game “What doesn’t belong?” There would be a goose, a blue bird, an eagle, and a horse. Obviously, the horse didn’t belong because all the others were birds, or could fly, or had wings. There was one right answer and that was that. I remember doing that with my children and thinking, “There could be other right answers so long as the child can explain why their “wrong” answer is right.” Well, now there is a book that does just that — there are NO wrong answers, so long as the readers can explain why they made their choices.

Each set of problems asks the reader to pick which figure doesn’t belong. For the first set, the author explains why the reader might have picked one shape over another. “Did you choose the shape in the lower left? If you did, maybe it’s because this shape isn’t colored in.” And on another page, “Or maybe you said that this shape doesn’t belong because it has three sides, and the others have four.” And then, at the end, “The important thing is to have a reason why.”

The rest of the set of problems do not have explanations. The reader or readers get to do the explaining themselves. At the end of the small book, there’s a letter from the author. He tells readers not to worry about being “right.” He explains that “the properties are more important than the words you use to describe them.” So words like “smooshed” and “stretched” work just fine!

Math today is all about helping students learn their strengths in math. It’s not about the students who can compute the fastest, indicating, of course, that they are the best at math. In fact, some students who can’t memorize their math facts might still be wonderful mathematicians. They might be able to figure out creative ways to problem solve and love working on complex problems. It’s all about thinking great math thoughts, and there are many ways that can happen.

The third graders I teach who read this book had many positive comments to share. “I like that there are many different ways to solve it.” Another student thought that “… it’s difficult and it makes you think.” One astute student commented, “It’s a new idea. Lots of books have the same idea, but here all responses are right. I haven’t seen one like this.” High praise indeed from a student who reads four to five books a night! They all loved that there are no wrong answers.

This is an important addition to the home library where parents can start math conversations with kids of all ages. In fact, a great activity would be to think of how many different ways each shape may differ from all the others. “The square is different because…” it’s a different color, it’s a different size, it had 90 degree angles, it has equal length sides, it looks like a table, or whatever clever reason the readers might come up with. When kids are playing games that involve mathematical thinking, everyone’s a winner. And that’s not to say that this wouldn’t be a great addition to classroom libraries as well.

This little gem encourages creative math thinking — out-of-the-box thinking — and that’s a marvelous thing.

Please note: This review is based on the final, hardcover book provided by the publisher, Charlesbridge, for review purposes.