Not every maths activity needs to be a full lesson or an elaborate project.
Sometimes it’s the tiny demonstrations — the quick, memorable moments — that make a huge difference for students.
Good teachers build a repertoire over time: small, powerful ways to represent ideas. They know half a dozen different ways to show that fractions are equivalent, that negative numbers make sense, or that a straight line has a constant gradient.
These aren’t flashy or time-consuming, but they’re the glue that helps ideas stick.
Take, for instance, one of the simplest geometry demonstrations there is: showing that the angles in a triangle add to 180 degrees.
Rather than simply telling students, “there are 180° in every triangle,” try this quick demonstration:
Have them draw any triangle.
Tear their triangle into three pieces, leaving the corners intact.
Every time, those three angles form a straight line.
That’s it — a 60-second activity, but one that turns a rule to remember into a relationship students can see.
It’s simple, quick, and memorable — but you might wonder: why does it work so effectively?
This tiny demonstration does more than confirm a fact — it builds understanding.
When students physically manipulate the pieces of their triangle, they’re not just seeing a property of angles; they’re connecting ideas:
A straight line is 180°
All triangles share that total
Angles adding to 180° aren’t arbitrary — they form a visible, geometric relationship
It’s a perfect example of moving from rote knowledge (“I can say it”) to relational knowledge (“I know why it’s true”).
These small, hands-on demonstrations are powerful because they engage what researchers call multiple representations — visual, physical, and verbal. Students see it, handle it, and talk about it. That combination strengthens understanding far more than hearing an explanation alone. It only takes a minute, but gives students a mental model to anchor later, more abstract ideas.
Knowing when and how to use these demonstrations is part of what’s often called mathematical pedagogical content knowledge (PCK) — the teacher’s understanding of how particular concepts are best represented, explained, and connected for learners.
It’s what allows a teacher to move beyond “telling” to showing, and to anticipate where students might need something concrete before the abstraction can make sense.
Building this repertoire doesn’t require special equipment — just curiosity, creativity, and a willingness to look for those small, powerful ways to make the maths visible.