According to the Maths-Whizz Teachers’ Resource dictionary, a number line is: “a line that shows numbers ordered by magnitude from left to right, or bottom to top.” Pretty simple? Yes, and then again, no.
The number line can be a powerful beast, employed in addition and subtraction, and frequently in concepts of place value. The number line describes the world in the way instantly familiar to most of us, with smaller items on the left (if horizontal) or towards the bottom (vertical).
We could investigate the many ways culture and psychology define our experience of numbers, and why so many (but not all) of us perceive numbers increasing in those two directions, but that would be beyond the scope of this blog – even if the God of Whizz might enjoy the intellectual excursion…
Number lines in addition and subtraction
Instead, we can have a quick look at how to add and subtract using the number line. The line is a great way to visualise the ‘journey’ up and down through the numbers. Just like a ruler, the line can be any length, at any level of detail. Keep zooming in, and the increments on our number line show smaller and smaller amounts.
Number lines can be to scale (like a ruler) or not to scale, like a simple ordered list. In the example maths addition lesson above, we show how you can add a number with Tens and Units digits to a number with Hundreds by counting along the number line, starting with the larger number.
You need to understand the values of digits; for example, 63 is made up of six tens and three units (or 60 + 3). You also need to know that adding numbers means moving to the right along the number line, and subtracting means moving to the left. We make a large rightward ‘hop’ to add six tens and a smaller ‘hop’ to add three units.
For those of us who think in visual terms, it can be very helpful to think of addition and subtraction as movement along the number line. More complex examples show the benefits of this approach. Say we have to answer this question:
800 + 300 – 150 + 220 – 400 = ?
We can imagine starting on the line at 800. We jump forward 300, and we jump backward 150, and so on. If we plot our frog-like adventures we find we’ve gone backwards 550 and forwards 520. This puts us 30 behind where we started. 30 less than 800 is… 770!
Of course, this is a slow and round-about method when your mental maths improves, but visualisation of the process can help enormously. You can do all the forward jumps in one go, and then to all the backward jumps in one go; the answer is the same.
At Maths-Whizz we know that anything that helps reveal the underlying maths is good – because once you can get a mental grasp of the ideas, the numbers suddenly seem to make sense…
This only scratches the surface, of course, so do share any ideas you have about working with number lines on the Whizz Forum.
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