Some modeling problems are so polished, so complete, so ready to go… they’re kind of boring.

Yes, some structure is helpful. Some students need more scaffolding. But there’s something about the real-world problems that don’t arrive neatly packaged (the ones that are half-formed or even slightly annoying) that tend to stick with us longer.

We’re talking about the problems that bug you.

You know the ones…

• Why do elevators always seem to stop at every floor when you’re in a rush?
• Why does the grocery store only ever open two lanes, no matter how long the line is?
• Why do traffic jams happen even when there’s no accident or construction?
• Why is your coffee cold in seven minutes, but your soup is lava for an hour?

They’re not “big” problems. They’re not going to change the world. But they get under your skin just enough to make you want to figure them out.

And that is exactly the energy we want in a modeling problem.

It Starts with an Observation and a Hunch

These annoying little questions are modeling gold because they do something that too many classroom problems don’t: they provoke. They invite questions. They get personal.

There’s no clear starting point, no obvious equation to apply, which means students have to do the hard and wonderful work of defining the problem themselves. They need to get comfortable with ambiguity, which is a hallmark of a strong mathematical modeling mindset.

Take the elevator example. How do you model elevator behavior? That depends. Are you optimizing for speed? Efficiency? Least amount of awkward silence? There’s no one “right” version.

This is where students start to move from “what’s the formula?” to “what’s actually happening here?” That shift to open-ended thinking is what builds real critical thinking in math.

The Itch Is the Point

A good modeling problem should plant a tiny, annoying (or intriguing!) seed of curiosity that a student can’t shake.

That kind of cognitive itch is what drives the best group modeling experiences, too. When each team member brings a different idea of what’s bugging them, what matters, and how to define success, it’s messy. It can be frustrating. But that’s what makes it real. It involves a strong desire to understand.

Even the idea of “uncomputable” problems (like the mesmerizing Busy Beaver problem) lives in this space. Once you see it, you can’t stop thinking about it. You want to know how it works, even if you know you might never fully solve it.

Bugged = Engaged

If there’s one thing we’ve learned about curiosity in math modeling, it’s that it doesn’t always come from relevance or “real-world” tie-ins. Sometimes it comes from friction. From frustration. 

From a little voice in your head that goes: Wait a minute. That can’t be right.

So if you’re looking for a way to get students truly invested in math modeling, don’t just hand them a problem that’s tidy and teachable. Give them one that bugs them.

Let them chase the question. Let them disagree on what matters. Let them build models that don’t quite work, and then revise them again. Because that itch is the beginning of real thinking.