Question Did you play VS Were you playing

Hello, native English speakers, I need your help.

What's the difference in meaning between (a) and (b)?
A native speaker says "They are both the same in meaning",
but is that true?
(a) Did you play tennis at that time?
(b) Were you playing tennis at that time?

How about this? Does it sound right?
(c) Were you playing tennis this morning?

I would be careful with "asking native speakers" Hirashin. Depending on who you ask they might not be someone who has considered the possible differences in meaning, not think it important enough, not have time to give a detailed answer, not be a teacher etc etc. so a lot of people might say a lot of your options are equal in meaning, especially as there is often a small difference.
Probably more than any other contrast, the past tense and past progressive depend so much on context that you can't say one is wrong without context, of which "at that time" is insufficent. They differ in meaning, but could all be acceptable.

The simple answer that will probably be right in nearly all cases is b. c is also correct English. When focusing on a point of time during a contiunous activity, use the past continuous for the continuous activity.

I was having a bath when the earthquake started.

That's the basic pattern you should be teaching your students.

I know what you're thinking Lothor, but "at that time" could also refer to a certain period of time, not only an instant in time. "Did you play tennis?" could be referring to a particular period in your life, e.g if you were having a chat about your school days with someone you might say, "Did you play tennis at that time?"

I think another problem with the sentences is that "at that time" is hardly ever used in English for this purpose. When you're having a conversation about a topic it's obvious what the time period is, you don't need to say "at that time", and I think it confuses the matter in sentences like these.

Hi Michael,

I agree with both your points. Hirashin was mainly asking which of two tenses was better, and I gave what I thought was the most helpful answer for a high school English teacher teaching what students need to know for multiple-choice exam questions and, who knows, even future use of functional English!