Children should be taught to their ability levels rather than their class year.
My son is also in Y1 and obviously a bright thing. My - also small - school (15 per year, mixed class), have been exposing him to Y2 work all school year as he's in a mixed Y1/2 class.
However, they recently called a mtg with me to discuss what they're doing with him as they've found he has finished KS1 and is 'somewhere in KS2 but we don't know where because if he hasn't been taught the skills he can't do the work'. So they're currently giving him 1 2 1 for 20 mins a day, when the class activities aren't appropriate, and leading him into KS2 work so they can find his level and tailor his needs accordingly.
They are committed to getting his needs addressed, and have basically admitted that running his education plan according to his peers is stopping his needs being met.
I'm in no way saying this to crow about my own son - I'm trying to say in a similar situation my school have pro-actively and at great cost to themselves resource wise, identified a need and done something about it.
Your school's suggestion about doing sideways Y1 activities is laughable - if your child is way ahead of Y1, then doing the basic Y1 work will bore him silly, never mind giving him more of the same! Long term this may well lead to him becoming maths-phobic and actually stopping learning.
What my sons teacher has done though, is give him some early KS2 level-type work which is 'off curriculum' - sudoku, logic problems, shape work which is outside the norm - THAT in my view is 'sideways stretching' - work at the RIGHT level which doesn't race them on and on through KS2 so he spends the last 2 years twiddling his thumbs.
I guess my very long winded post is saying - you are currently being fobbed off because, in my opininon, the teacher can't be bothered to differentiate or think outside the box. Your son has the right for his education to meet his needs as much as any other child. If she ain't offering to do it, you need to fight for it.