Today I was lucky to be able to work with some delightful year 12 students who were visiting. They were part of a series of days for individuals who want to have a look round various departments. They had a talk about the admissions procedure and the STEP exams, some workshops and a fascinating lecture from Professor John Barrow about how to mathematically decide how spiky something is which covered a variety of things including how fractal analysis can be used to authenticate art.

I was running a workshop and I wanted to focus on generalising. We started by looking at the following expression:

I like this as an example for generalising as there is an underlying structure which lends itself to the question: 'When else could I have stopped the series and the answer been an integer?'

The problem is The Root of the Problem from NRICH.

I also shared one of my favourite 'magic' tricks:

Take any prime number greater than 3.

Square it, then take away one.

The result is divisible by 24.

I saw some fabulous reasoning happening and was delighted that one student came up with an algebraic proof using the fact that all primes can be written as 6n±1.

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