Where is the verb in a "What about...?" clause

As a teacher of ESL to children, I teach the importance of finding/adding both the subject and verb, in their native language, before translating to English. I've come across a grammar construct which I don't fully understand myself, so teaching it to others is even more problematic.

Given the following constructs:

A: "I'd like some coffee. What about you?"

or

A: "Michael is ill."

B: "What about the doctor?"

how would one explain the subject and verb in the "What about...?" clause? Is it even a clause or rather a phrase?

Solution 1:

English, as other languages, does not always require a subject and a verb in a sentence. Just because English requires a subject and a verb in a sentence more often than some other language doesn't mean English requires them all the time. So it's inherently wrong to assume and even teach that any English sentence, no matter how idiomatic, should be able to be rephrased to have both a subject and a verb.

The answer to your question, therefore, should be this:

Stop looking for a verb in the "What about...?" construction and simply accept and teach the fact that English can have a construction without a verb or a subject or both.