Oxidation numbers in the Period 3 oxides and chlorides

The bookkeeping number

An oxidation number is the charge an atom would have if every shared pair of electrons in its bonds belonged to the more electronegative atom.

You do not have to draw those bonds for Period 3 oxides and chlorides. There is a shortcut: the oxidation number of the Period 3 element is decided by how many outer-shell electrons it has put towards bonding with oxygen or chlorine.

Oxygen is more electronegative than every Period 3 element, and chlorine is more electronegative than every Period 3 element that forms a chloride here (argon forms neither oxide nor chloride). So the shared electrons are counted as belonging to oxygen or chlorine.

Outer electrons tell you the number

Across Period 3 the outer shell fills up: Na has 1 outer electron, Mg 2, Al 3, Si 4, P 5, S 6, Cl 7. That count is the maximum positive oxidation number each element can show.

element	outer electrons	oxide	oxidation number in that oxide	chloride	oxidation number in that chloride
Na	1	$\text{Na}_2\text{O}$	+1	$\text{NaCl}$	+1
Mg	2	$\text{MgO}$	+2	$\text{MgCl}_2$	+2
Al	3	$\text{Al}_2\text{O}_3$	+3	$\text{AlCl}_3$	+3
Si	4	$\text{SiO}_2$	+4	$\text{SiCl}_4$	+4
P	5	$\text{P}_4\text{O}_{10}$	+5	$\text{PCl}_5$	+5
S	6	$\text{SO}_2$ and $\text{SO}_3$	+4 in $\text{SO}_2$ , +6 in $\text{SO}_3$	—	—

Two things to notice.

Silicon is not on the syllabus list for learning outcome 2, but it slots into the pattern at +4. Sulfur does not get a chloride in the list.
Sulfur breaks the simple "one compound, one number" look because it forms two oxides. Its +4 in $\text{SO}_2$ is not its maximum; +6 in $\text{SO}_3$ is, and that matches its 6 outer electrons.