My teacher said that on the periodic table there is a "nose" formed by Al, Zn, Ag, and Cd. She said that they are all fixed charged (+3, +2, +1, and +2 respectively), and said that if I write them in ionic equations, I just say Silver Nitrate instead of Silver (I) Nitrate. She also said to put all Al as +3 charge in all cases, etc. But I did some research and found out that you do say Silver (I) Nitrate (actually both are fine, but my teacher specifically said never put the (I) in such cases). So is my teacher wrong? And are there cases where the charges of the elements are not what my teacher says?
All of these elements can form compounds in other oxidation states. Aluminium forms some compounds in the +1 state (e.g. see the section in https://en.wikipedia.org/wiki/Aluminium_iodide), as does Zinc (see the section in https://en.wikipedia.org/wiki/Compounds_of_zinc) and Cadmium (e.g. https://en.wikipedia.org/wiki/Cadmium(I)_tetrachloroaluminate). But Silver is the element that shows this most often in the list given - for instance it forms fluorides in the +1, +2 and +3 oxidation states (https://en.wikipedia.org/wiki/Silver_fluoride). As such I wouldn't say including the oxidation states in the formula is wrong, but on the other hand if you omit it everybody who knows there is an ambiguity will understand what is implied.