How does the number of valency electrons help to explain why aluminium is a metal and iodine and bromine are non-metals?

Simple rule of thumb: elements with 1, 2, or 3 valence electrons are metals; elements with 6, 7, or 8 valence electrons are non-metals. Elements with 4 or 5 electrons can go either way; they tend to be non-metals at low Z with increasing metallic character as Z increases (so carbon is pretty definitely a non-metal, while bismuth is pretty metallic, and even astatine ... which has 7 electrons ... exhibits some metallic properties, though it's difficult to say for sure because all known isotopes of astatine are highly radioactive; its most stable isotope has a half-life of only 8.1 hours ... for comparison consider probably the most well-known radioactive element, uranium, whose most stable isotope has a half-life of over four billion years).