The 5-Minute Math Vocabulary Routine: Examples Before Definitions

I’ll be honest: I don’t really like vocabulary.

It’s not exactly exciting, and I think vocabulary can sometimes be overemphasized in math classrooms. But vocabulary is important. Students need a common language to communicate, explain their thinking, and make sense of mathematics.

So instead of making vocabulary a list of words and definitions to memorize, I like to give students a reason to think about the word first.

Here’s my favorite 5-minute routine for introducing math vocabulary.

Don’t Start With the Definition

A typical vocabulary introduction looks something like this:

Term → Definition → Example

There’s nothing wrong with that. But I think we can create a little more curiosity by flipping the order.

Instead, try:

Examples + Non-Example → Student Thinking → Definition

This simple change gives students a chance to figure out what a mathematical term might mean before we give them the official definition.

It’s a small routine, but it’s one way I’ve found to keep students thinking—even when the topic is something as dry as vocabulary. It also fits nicely with the ideas in our Unlocking Curiosity workshop.

Start with examples and a non-example—not the definition.

The 5-Minute Math Vocabulary Routine

1. Show, Don’t Define

Project the vocabulary term along with several examples and a non-example.

Hide the definition.

Don't tell students what the word means yet. Just give them something to look at.

2. Notice & Wonder

Ask students:

What do you notice? What makes the examples different from the non-example?

Give students a moment to think silently, then have them discuss their ideas with a partner using a Think-Pair-Share routine.

3. Describe It

Ask students to try to describe what they think the term means in their own words.

Discuss their ideas as a class. You don't necessarily need a perfectly worded definition at this point. The goal is to get students thinking about the characteristics that make something an example of the term.

4. Reveal the Definition

Now reveal the mathematical definition.

At this point, the definition isn't just another sentence for students to memorize. They have already developed some intuition for what the word means.

If there's a vocabulary video available, this is also a great time to watch it and reinforce the idea.

That’s it. Five minutes.

The routine is quick enough to use regularly without turning vocabulary into an entire lesson.

The 5-minute math vocabulary routine: show, notice and wonder, describe, then reveal the definition

Why I Like This Routine

I love this approach because it gives students something to figure out.

Instead of saying, “Here's the definition. Memorize it,” we're asking students to look for patterns, make observations, test their ideas, and then formalize their thinking.

It’s very similar to the philosophy behind three-act math: give students an opportunity to think before giving them the answer.

And this isn't just useful for students who already know a lot of math. It can be especially helpful for English language learners, too. Students get to experience the mathematical idea through examples and non-examples before they have to attach new language to it.

A Math Vocabulary Reference for Your Classroom

One thing my students used to tell me—especially in Geometry—was that they wished they had all of their vocabulary terms in one place. When we were working with proofs, they wanted an easy way to review the theorems and definitions they had learned.

That’s one reason we created the When Math Happens math vocabulary glossary.

Find the math vocabulary you need by grade, unit, or search.

The glossary is continually growing and includes terms organized by grade level and unit, along with a search feature so you can quickly find what you need.

Individual vocabulary pages include carefully selected examples and non-examples, designed to help students understand the term and confront common misconceptions. Many terms also include a short video and a printable PDF.

So you don't have to create all of these examples yourself.

Whether you use the full glossary or simply borrow the examples-before-definitions routine for your own vocabulary, I hope it gives you another way to make math vocabulary a little more interesting—and a lot more meaningful.

And if there’s a math term you think we should add to the glossary, let us know!