[Mati]

Soon we are going to be doing projects in my chemistry class and one of my ideas was to do a synthesis and extraction of citric acid and test it's purity by either spectroscopy or titration.

However looking through the internet for a simple method to synthesise citric acid I did not find any, this will be since citric acid is rarely produced chemically and more often by growing fungus and fermenting it.

So have I just not looked hard enough? or is there no simple way using high school equipment to produce it?

[AWK]

You are right - there is no simple method of citric acid synthesis. But you can isolate this acid from lemon juice.
From 3 fruits you can obtain about 5 g of acid. And during the isolation of this acid, you should use some chemical reactions.