小學英文之preposition

I put some oil with ginger ____ the wok.

I would choose to use preposition "in" as my answer in the above sentence.

Sometime it is the verb that determines the proper choice of preposition to indicate the direction or position of the movement (that the verb acts on its direct object). The object of preposition also plays a major role to limit the choice of the appropriate preposition in respect of position in particular.

First, let's look at the preposition "to", "into" and "in" within the context of movement.
(1) "to" - indicates movement with the aim of a specific destination; (it gives a sense of direction as well)
(2) "into" - refers to movement from the outside to the inside of a three dimensional space;
(3) "in" - expresses movement towards the inside of a container, place or area;
Triggered by some verbs which express actions, "in" has the same meaning as "into".

Next, let's examine the verb "put".
put something + adverbial/prepositional phrase
= to move something to/into a particular place or position (Longman/Oxford)

(1) I put some oil with ginger to the wok.
It tells us that the wok was the destination of "some oil with ginger" in the action of "put", but it doesn't tell the position. So, it could be on the rim of wok or the handle of wok.

(2) I put some oil with ginger into the wok.
It tells us that the object was moved from outside to the inside of the wok. With the action of "put", "into" is sort of redundant in terms of direction.
e.g. We often say "I put the fish in the fridge" instead of "I put the fish into the fridge".

(3) I put some oil with ginger in the wok.
Same as the meaning of (2), it indicates the object was moved towards the inside of the wok. (and ends up in the inside of the wok)

Conclusion: All the three prepositions are correct grammatically.
Semantically, "in" should be the best choice, "into" the second and "to" the last.