Question

how to predict the placement of an unknown element based on physical and chemical properties on the periodic table?

Answer 1

You check how many valance electrons there are or check if it is nonmetal or metal...based on its properties..

Answer 2

on the physical part by its atomic weight. on the chemical part by its reactivity to other elements (normally no reaction within the same group)

Answer 3

Weight per mole (atomic weight), whether it's a metal or non metal (which end it's on), and valence electrons (atomic number).

Answer 4

all of the suggestions above really depend on knowing what the element is, which defeats the purpose. The elements on the periodic table are arranged so that similar-behaving elements are in the same vertical column, and the properties that they share vary repeatably as you move down the columns.
If the unknown substance is a shiny solid, odds are it's a metal.
If the unknown substance fizzes, pops, or explodes in water, odds are it comes from column 1 or 2.
If it's a non-reactive gas, it's a noble gas (column 18)
If it's a crumbly, dull, brittle solid, it's a non-metal
The real usefulness of the periodic table is in its predictive abilities, not just the list of information that may be contained in each square.