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Secondary Maths Help: The Central Importance of the Number-line

Updated: Jul 24, 2022

This blog was written by one of our specialist tutors, Toby Stone, who teaches Maths and Computer Science.

Learners often describe their experience of learning maths as being lost at sea. They talk about a panicked feeling of sinking, of being unable to grasp anything- any flotsam- to stop them drowning in a sea of numbers.

secondary maths leaves you feeling at sea
Does secondary maths leave you feeling at sea?

As a child, I never liked the sea. My dad had a small boat in Christchurch harbour and would sail us out through ‘the Run’ into the English Channel below the Needles, and along to Brownsea Island.

Beautiful places I didn’t see because I would be wedged below deck in the cabin, refusing to move, with my stomach feeling like it was doing all the moving for me. But I gained a healthy respect for well-built boats. They kept me out of the sea.

The importance in secondary maths of a strong, central plank

One of the first and most important parts of boat building is the laying of the central plank, known as the garboard or master plank. Badly lay the garboard and the hull will distort. But if that master plank is placed with care and precision- all the other planking will run smooth and hydrodynamic.

It’s the same with mathematics. That central plank is the number-line. A deep and meaningful understanding of the number-line means all the rest of it ‘just fits’.

We teach secondary maths with a principle of giving students a deep understanding of basics.

I teach my students to understand the number-line, to see the relationships between its points like those between the grains of the perfectly selected spar of wood. To understand that two and ten are connected, not just by eight, by five, by twenty, and by two tenths but also that any fraction with ten (or a hundred, or a thousand) as a denominator is a description of place value, which connects it right back to the number-line.

Comprehend this line and the rest of maths connects up in a way that is waterproof, that stops you sinking. This is why times-table knowledge is useful: it is a rehearsal of the relationships between numbers on a number-line.

Once you have that precisely laid central plank, then you can place another number-line at right angles from the first. At this point you have a graph, two-dimensional space and an understanding of the x and y axes. Another number-line at another right-angle gives you three-dimensional space. Then bend that number-line further round than the natural curve of a hull, bend it into a circle and you have circle geometry, the number-lines of arcs and angles. From angles: trigonometry.

A good grasp of secondary maths will help your child to set sail for a great future.

From that first, central plank, you build up, number-line after number-line, until you have a vessel capable of carrying your child across the mathematical sea.

Maths can take them to far shores- to future careers we parents can’t yet imagine – but they need the boat to carry them there.

With the right boat they can write whatever story of their lives they wish to.

It all starts with one line.


For more information about how we can help your child to achieve their full potential in secondary maths, contact us today.

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