Wednesday, 17 September 2014

Prime Factors! (or good maths teaching isn't rocket science)

Not really the place for this but I came home buzzing from today's Y5/6 maths and just needed to write about it. [maybe this means a sideline in maths education posts here!]
We were working on the first unit of Y5/6 maths in our new curriculum which begins the term by exploring factors, multiples, prime numbers, square numbers, etc. and goes on to use this to develop mental multiplication and division skills and then adding and subtracting fractions.

The children had done a lot of exploration of factors and prime numbers and had been working on breaking numbers down into their prime factors.  We introduced this through investigation:

Which of the following numbers will have the greatest number of prime factors? 32, 24, 195.

Of course all but 3 children went for 195 and they then went away and broke them down to find, to their surprise...

Anyway, I had hoped to end the lesson with an investigation in prime factorisation to show that each number can be decomposed into a unique set of prime factors and that each set of prime factors makes a unique number.  However, due to a slightly longer assembly, a technical problem with the online register and the fact that the new cloakrooms are still being built, I was running a bit later than planned.

So, I decided to set the investigation as something for them to think about between this lesson and the next:

I challenge you to find me two different numbers with an identical set of prime factors.  The first child to bring me an answer, before 3 o'clock, will win this box of Roses.

A simple enough question to pose.  No hours of preparation and making of resources (indeed the box of chocolates were stolen from a colleagues cupboard - well, I knew I wasn't going to have to give a prize away didn't I!).  But the response was great.

I first realised quite how into it the children were when I was in the middle of receiving feedback (it was an observed lesson) and 8 children burst into the classroom shouting, "We've got it, Mr Little! We've Got it!".  Of course they hadn't, given there are not two numbers which share the same set of prime factors, and it continued into lunchtime.

Before long, other adults, including the librarian, headteacher and a number of TAs had been enlisted by different groups of children to help them find the answer.  One enterprising group of children convinced a TA to google it on their phone and found out it was impossible (but agreed to keep their silence), while another worked this out and managed to explain to me, "but if you have a 7 in the prime factors and change that for a 7, it is still a 7 so the number cannot be different unless the prime factors are  different" - not bad for a child who scraped a 4C last year and has a sharp, inquisitive mind but is simply lacking in confidence!

At the end of the day, I gathered a group of very excited children just after the end of school at 3pm to admit what most of them had by this point realised - that the question was impossible as no two numbers share the same prime factorisation.  However, their investigation had certainly raised the profile of maths in the school, with many of the younger children following the race with interest during lunchtime, asking me constantly whether anyone had solved it yet.  And in terms of achieving the learning objective, I guarantee that not one of those children will ever forget that each number has a unique prime factorisation.

Anyway, it led me to reflect on the fact that good maths teaching really isn't rocket science, and it doesn't involve hours of making complex resources or endless worksheets.  It certainly doesn't involve a plethora of different learning objectives for children of different 'ability', along with work differentiated to the nth degree.

Sometimes a bit of well-targeted questioning is all you need.

[Needless to say, after all their hard work, I had to share out the box of chocolates.  I wonder if I can replace it before my colleague notices...]

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