Why do metallic elements have a very small band gap while nonmetallic elements have a large band gap?
The energy of the orbitals may be the first point to explain it at this level. You can use the example of a simple 1-D LCAO to form the bands(check page 723 of Atkins physical chemistry 8th edition). For instance, the energy difference between the bands formed by s orbitals and p orbitals will be small or large depending on the atom.