## Thursday, 19 February 2015

### A further thought on composite numbers definition

Going back to the erroneous 'definition' of composite numbers in the Year 5 Programme of Study for the Mathematics National Curriculum for England ... where we read that pupils should learn about 'composite (non-prime) numbers'.

In my previous post I pointed out that you cannot use 'non-prime' as a synonym for 'composite' because the integer 1 is neither prime nor composite.

On reflection, I realised that the error here is much more substantial than this. The concept of 'prime' applies only to positive integers. So, a prime number can be defined as an integer with precisely two factors (which will be 1 and itself).

This means that 'non-prime numbers' would include all numbers that are not positive integers. So, the identification of composite numbers with non-prime numbers would imply that numbers such as –3, 2.4, ⅚ and √2, for example, are all composite!

Of course, they are not! 'Composite' is also a concept that applies only to positive integers – those integers with two or more factors greater than 1.

That was a sloppy bit of work by whoever wrote that programme of study.

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Any reader looking for professional help in the area of primary mathematics education might like to take a look at the recently-launched website of my colleague, Ralph Manning: www.manningeducation.co.uk