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ICT teacher > 9 mathematicians

February 9, 2011

I’m going to ask you to ignore the awful pseudo context here and bear with this interesting problem from the Nrich  website (which you really need to go and visit if you’ve not done so recently). [Original problem here.]

 

Birthday_puzzle

Chris Pearce is a maths advisor and showed this problem to seven heads of maths, me and an ICT specialist (Elly) that teaches maths. Whilst I initially was desperately resisting the urge to use algebra and find another creative way of looking at the problem, I eventually gave in and looked at what someone else was doing. This was along the lines of

 

a + 15 = (a – 15)2

 

With the formal expanding, rearranging, factorising and eliminating the less sensible solution. I believe that this was pretty much what all the mathematicians were doing.

 

Now, Elly on the other hand tried to reason it through with examples – making conjectures about odd numbers working. Thinking out loud through what she was thinking. Revising conjectures. Considering square numbers and the difference between them and their root. [the difference between 16 and 4 is 12 so 6 should work.] Then expanding and revising her explanations when questioned. After brief discussions and making those inspired leaps, we got to triangle numbers.

 

A brilliant bit of mathematical thinking that highlights the advantage of not being trained into a particular way of solving problems.

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