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Underground numbers

Plunging temperatures, and why number lines should be vertical.

I recently saw a poll on Twitter in which the public (but I think mainly primary school teachers) were asked:

Which number is bigger:

  (a) 5

  (b) minus 100 

The large majority voted that 5 is the bigger number.  

The popular view is that numbers become bigger as they get more positive, or, if you like to think of numbers being on a horizontal number line, numbers get bigger as you move to the right.

But once negative numbers are introduced, the language of 'bigger' meaning 'more positive' becomes unhelpful, not least because it bears little relation to real life.   If you have an overdraft of £100 (a balance of minus £100 in other words) that's clearly a bigger overdraft than one of £10.  'Bigness' in this case is about how far a number is from zero.  And sometimes bigness is not an appropriate description at all.

Last night the temperature in some parts of England plunged to minus 13C.  That's the lowest temperature we've had in the country this year.  Not the smallest.  And when you travel in a lift, Floor 8 is higher than Floor 7, and Floor -1 is higher than Floor -2.

I'd be happy if the number lines that are introduced to children in primary school were vertical rather than horizontal, so that counting became more like going up and down in a lift.  It would be so much more natural. We already use the language of counting 'up' and counting 'down'.

With a vertical number line, negative numbers would become 'Underground' numbers.  That's the language I use informally with my children at home  So I was delighted this morning when my eight year old excitedly called out: "Dad - it's Underground 2 outside!"


* Or something similar.  I'd be grateful if somebody could point me to the original poll.