Maths might be your strongest point as you have some hard evidence to back it up.
'Walking distance' - worth a mention, but unexceptional because of course everyone who lives within walking distance will be making exactly the same point.
'Thrives' is quite a strong word. Is it just a feeling that the environment would suit him? Or is there actually evidence that he hasn't thrived in a school with a very different sort of environment? (No need to answer that here - just alerting you to the fact that an appeal panel might probe to see how much substance there is to any points being put forward.)
'Likeminded children' usually comes across as a weakish argument. (Not necessarily saying don't use it, but keep it minimal - unless
there's more substance to it, e.g. he's been teased or bullied for 'wanting to learn'.)
I'm afraid I can't tell if anything is missing, because it depends entirely on your own circumstances.
However, it might help (if true) to mention that this
was the school your child really
wanted to go to, and how heartbroken he was not to have achieved his goal. Of course, it invites the question - why does he
want to go to this particular school?