Developing number sense through hands-on learning
In episode two of the AAMT x We Support Hands-On Learning video series, Allan Dougan and Professor Catherine Attard turn their attention to one of the most versatile tools in a maths classroom: the number line.
If you’ve ever seen a number line stuck to a classroom wall and wondered how much work it’s actually doing – this one’s for you.
Why do number lines matter?
Number lines are about so much more than knowing where a number sits. As Allan explains, they help children understand the relationships between numbers, their order, their size, their distance from one another. “It’s more than just recognising and seeing a number on a flash card,” he says. “It’s about the relationship that exists between them.”
That sense of magnitude and spatial understanding is what makes number lines such a powerful bridge. It connects early counting to addition and subtraction, and eventually to more complex concepts like fractions, decimals and even negative numbers. Children who can visualise a number line are building the foundations of strong mental computation.
Understanding magnitude on a number line
One of the most important things about number lines, is that numbers sit on the line. But that’s obvious, right? Not quite.
It’s a genuinely common misconception, and it makes sense when you think about where children first encounter numbered sequences in board games, where numbers sit inside squares. Allan flags this early, because getting it right matters. The spaces between the marks aren’t empty; they represent distance, magnitude, and all the numbers in between. Understanding that is what gives a number line its meaning.
How students think about number lines
The number line Allan and Catherine demonstrate with is a closed, labelled one, with every number from 0 to 30 clearly marked. But flip it over, and you have a blank, open number line. And that’s where the real flexibility begins.
An open number line doesn’t have to start at zero, doesn’t have to deal in whole numbers, and can represent fractions, decimals, or percentages just as easily. But most importantly, it’s a window into student thinking. When you ask a child to place numbers on a blank number line, you get a genuine sense of what they understand about numbers.
It’s also worth remembering that “number lines don’t just exist on the horizontal, think about them vertically. That’s important in terms of contextualising with a thermometer.” Bringing that connection into the classroom helps children see that mathematical tools exist in the real world, not just on the whiteboard.
Teacher takeaway: Ideas for your classroom
The through-line in everything Allan and Catherine discuss is this: maths should be engaging, especially for young learners. If computation becomes ‘boring’, children switch off, so finding ways to make number lines active and fun is just as important as understanding how they work.
A few ideas to take into your classroom:
- Dice games – roll the dice, choose an operation, and move along the number line accordingly. Operation dice (marked with +, −, etc.) make this even more dynamic. It keeps things playful and keeps children engaged.
- Take it outside – chalk a number line in the playground and get children on their feet. Movement-based maths is a great way to keep energy and engagement high.
- Bean bags on a floor number line – a physical, full-body version of the same concept that promotes active engagement with number relationships.
And a few things to hold onto as you bring number lines into your classroom:
- Use both closed (labelled) and open (blank) number lines. They serve different purposes
- Don’t always start at zero. Vary the range to suit what you’re exploring
- Use number lines to expose student thinking, not just practise computation
- Think beyond the horizontal. Vertical number lines are number lines too
Number lines used well help children understand that mathematics is connected, spatial, logical, and meaningful. They’re one of the most powerful bridges between counting, operations, and proportional reasoning.