1 Iron (steel is Iron + Coal)
2 Silver
3 Gold (Jewellery? Rings and Pendants as "smithing" can mean more than just weapon smithing, as in Goldsmith)
4 Mithril
5 Glass (Ebony and Glass both come from the now erupted Red Mt. and mined in destroyed Vvardenfell so their existence as a gatherable raw material is suspect)
6 Ebony (Possibly can be ritually enchanted with Deadra essence to become Deadric)
7 Adamantium
8 Tin
9 Copper (Tin + Copper = Bronze)
10 Stalhrim
11 Coal
12 Zinc (Copper + Zin = Brass)
13 Dwarf / Dwemer (it is made from its own rare material [ http://www.uesp.net/wiki/Morrowind:Item_Materials_and_Styles#Materials_and_Styles ] and some Skyrim cities are built on Dwemer ruines.
Can't think of how Amber or Madness would fit.
So, that is my (present) final guess of the 13!
Source: http://www.computerandvideogames.com/304571/skyrim-gameplay-details-slip-out/