Memorizing polyatomic ions? Using Periodic Table
Number of oxygens:

If your anion is in:


the 2nd period;
the VIIth main group/the 17th group/a halogen; or
is silicon:


then the -ate anion will have three oxygens.

All other -ate elemental anions will have four oxygens.

(Take note of ‘aluminate’ which I haven’t physically seen in that form yet but your teacher seems to insist be $\ce{AlO2-}$; disregarding this general trend.)

From the -ate anion, remove one oxygen to arrive at the -ite, remove two for hypo-ite. Add one for per-ate.

Charge:

Start at an anion with the most oxygens. (Note: Usually this is the -ate but because the halogens and permanganate are special they have the per-ate anion which is more oxygen-rich and important here.) Assume the maximum possible oxidation state for the non-oxygen atom. Assume $-\mathrm{II}$ oxidation state for every oxygen. Add up and take the negative value to arrive at the charge.

A hydrogen- will add $\ce{H}$ and lower the charge by one.

A thio- means one oxygen is replaced by sulphur.

A di- means take two of the (hydrogenated) anion and subtract water. Pyro means the same thing.

Memorise all the remaining! That is most importantly:


Chromite. Similar to aluminate I’  not sure if I ever saw it out in the real world.
Cyanide/cyanate. Thiocyanate is just like thiosulphate.
Oxalate, acetate and tartrate. Organic ions that will never fit into this scheme nicely.
Peroxide and superoxide. But those are -ides anyway.
Permanganate; which is almost like a perhalogenate. Luckily, molybdate and chromate fall into a category described above.


Periodic Table