Maths Brain

Doing theory with a 16-yr-old girl (the same one mentioned here).  She hasn't done much for a while, so we backed up a bit to grade 5.  We got to a question which asked for the C# major scale, with the key signature.  Then things got interesting.

Me: Read the question.  We need the key signature of C# major. 
Girl: So, C sharp, right?
Me: Yep.  [pause] What sharps are you going to need?
Girl: ... C... sharp...
Me [thinking this could take a while]: Okay, think back years and years, to when you did grade 1 theory...
Girl: I'll try...
Me: ...and you did C major scale first. 
Girl: Uh huh.
Me: Why did they make you do C major first?
Girl: Um... because it's only one octave? [nope] because it's only got one sharp?
Me: Does is really?
Girl: Oh - does it have 2 sharps?
Me: Ah, no.  [skip a few similar, incorrect, statements] C major has no sharps or flats.  It's all natural.
Girl [light bulb, I thought]: Ohhh...
Me: So, switch on your maths brain -
Girl [eyebrow raised]: But I don't have a maths brain, haven't you realised that yet?
Me: Oh yeah... If C major was all natural, you have to make every note sharper.  C sharp, and D sharp, and E sharp [etc]
Girl: No wonder they didn't make us do that in grade 1 - that's scary even now!