Which One Doesn’t Belong?

Welcome! Let me introduce myself. I’m Christopher Danielson, author of Which One Doesn’t Belong? I write, I teach math, I parent. I write about the math teaching part of parenting. By day I work at Desmos, designing curriculum and supporting classroom teachers using technology. (Big shout out to Desmos for many things, not least of these the zoomable heart for Which One Doesn’t Belong?) In case you’re new to Which One Doesn’t Belong? I’ll tell you the important bit up front. Depending on how youRead more


Gourds are Mother Nature’s Attribute Blocks. Warty or not. Pear-shaped, long, or compact. With stems or without. Multi-colored or solid. So many attributes available in so many combinations. Gourds are a natural setting for Which One Doesn’t Belong? Go swing a deal with a farmer at your local market, bring a couple dozen to school, and have your students build their own Which Gourd Doesn’t Belong? sets. Take pictures. Send them to me. On Twitter: @Trianglemancsd or #wodb. By email: talkingmathwithkids@gmail.comRead more

Geometric tiles

I have been playing around with some new tiles, which I’m calling 21st Century Pattern Blocks—an update of the original Pattern Blocks that are so well known and beloved in American classrooms. Whether the originals or the updated versions, Pattern Blocks are great tools for composing and decomposing shapes. So this morning I was thinking about composing equilateral triangles and hexagons. Some surprising combinations began to jump out at me. For example, the dented grey quadrilaterals in the triangle atRead more


I’ve talked about this set with many people, and it nearly always brings up a wonderful mix of functionality and mathematics. The top left isn’t a battery; the bottom right isn’t a cylinder. When people wonder whether there is math in everyday life, or whether mathematicians just say that to make themselves feel important, I like to point to this kind of conversation. “Is a cylinder” is a property of three of things in precisely the same way as “Is a battery”.Read more

A handmade set

One of my favorite mathematical minds (nickname: the Vegan Math Pup, daughter of the Vegan Math Beagle) was inspired to make her own Which One Doesn’t Belong? set. As a teacher, I am most rewarded when I see evidence that I have helped to shape the way students see the world. This is much more rewarding to me than mastery of procedures, or recall of facts. New lenses on the world tend to stay with us longer, and have more subtle but deeper andRead more

Which One Doesn’t Belong? in the produce aisle

A few years back, I worked with TED-Ed to make a video about units. That video combined with Which One Doesn’t Belong? led to this set. What’s the connection? The apple in the lower right is the only one that is just one thing, not a group of things. A bunch of bananas. A bunch of grapes. Even the bok choy is made of a bunch of leaves. But the apple is just one. Each of the others has a reason notRead more

A contribution from a friend

My friend and online colleague Andrew Stadel had a wonderful time reading the first version of Which One Doesn’t Belong? with his then-four-year-old son. They had such a good time that they were inspired to make their own set. They sketched a set on their iPad and sent it to me. I turned it into this version that matched the look of the other graphics in that early version of the book. When I shared the new copy, Andrew and his sonRead more


This is where math meets biology. I don’t know very much about leaves, but I feel quite certain that the things I notice about these leaves probably matter to biologists. I feel comfortable talking about how the one in the lower right is made up of a bunch of little leaves, even though I don’t know for sure what word biologists use for that. Similarly, the rounded tips of the leaf in the upper left probably have a term toRead more


This was one of my first Which One Doesn’t Belong? sets. Having had the basic kernel of the idea, I asked people on Twitter to imagine a shape, and then tell me four characteristics of the shape. Someone told me they were imagining a shape that… had ten sides, was pointy, was convex, and was red Each of the shapes in this set has three of those four properties, so each doesn’t belong because of the property it is missing. Maybe youRead more

Which One Doesn’t Belong? at breakfast

This set required some serious leg work. The cup in the upper right was borrowed from a neighbor (thanks Facebook for facilitating!) and the square bagel at lower left required a special trip to Cosi. The original inspiration for this set comes from a field of math called topology. Topologists study the shape of things, but not their size. To a topologist, a cube and a sphere are the same because each is a surface without edges or holes. A standard exampleRead more