One of my favorite things about teaching middle school math is when students’ curiosity drives the lesson. It doesn’t always happen on its own; sometimes I need to create the conditions for wonder to bubble up. Over the years, I’ve leaned on two approaches that consistently spark inquiry: Which One Doesn’t Belong? and Show Me Your Math.
Which One Doesn’t Belong?
Inspired by Christopher Danielson’s books, this routine invites students to look at four numbers, shapes, or images and decide which one doesn’t belong. The beauty of this activity is that there isn’t just one right answer.
In the image below, students might say that D doesn't belong because it's the only circle, while C doesn't belong because it's the only blue shape, and A doesn't belong because it's the only shape broken into thirds.
Once students can find reasons why one item doesn't belong, you can challenge them to find a reason why each of the items doesn't belong.
What I love about this is how it shifts the classroom dynamic. Suddenly, math isn’t about memorizing rules, it’s about noticing, reasoning, and defending your thinking. I’ve seen students who usually stay quiet light up when they spot a pattern no one else has mentioned.
Show Me Your Math
Another routine that’s had a huge impact in my classroom is Show Me Your Math, which originated with Indigenous educators in Atlantic Canada. The idea is simple but powerful: students are asked to find and share examples of math in their own lives, communities, and interests.
When we did this in class, students came back with examples ranging from video game stats to baking recipes to the geometry of hockey shots to patterns in beadwork. It wasn’t just about showing that math is everywhere, but about students claiming ownership of the math around them. The inquiry flowed naturally: Why does this pattern repeat? How do the ratios work in this recipe? Why do these stats matter in the game?
Other Inquiry Routines Worth Trying
If you’re looking for more ways to bring curiosity into your classroom, here are a few that have worked for me (or colleagues I admire):
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Notice & Wonder: Present a graph, picture, or math problem and ask students only two questions: What do you notice? and What do you wonder? This simple frame slows down thinking and gives all students an entry point.
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Number Talks: Pose a single problem (like 18 × 5) and invite students to share different strategies. The conversation becomes about the thinking, not just the answer, and students often surprise each other with creative methods.
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Estimation 180 (by Andrew Stadel): Show students a photo (for example, a giant jar of gummy bears) and have them estimate quantities, justifying their reasoning. This builds number sense and shows that estimates can be both mathematical and fun.
Each of these routines has one thing in common: they invite students to think, to share, and to see math as more than a set of procedures.
Why It Matters
For me, these routines are reminders that inquiry doesn’t always mean a big project or a complex investigation. Sometimes, it’s as simple as opening the door for multiple perspectives or giving students a chance to connect math to their own worlds.
It can feel risky at times. What if students go in a direction I hadn’t planned? How do I make sure that students are still learning the curriculum? But those moments usually end up being the richest. They remind me that when students are invited to notice, wonder, and connect, they often push the learning further than I could have scripted.
Have you tried any of these math routines? Which works well for you? Let me know in the comments below.
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