Irina,
As you say, the students already know each other, so it’s a case of the students getting to know you and you getting to know them. I suggest you don’t spend a long time on this activity because pupils of that age in secondary schools are not used to this type of activity. If I’m wrong and they do this type of thing in your school, then by all means, extend the activity.
You could ask the students to interview you. Give them time to prepare their questions in pairs or in groups before they ask you. This will make the speaking stage go more smoothly and will give you the chance to assess their level.
I don’t know what level your students are at; if they are at a high level, they should be able to produce questions without too much help from you. If they are at a low level, you can give them prompts to help them write their questions. The following can be used:
Name?
Where from?
Favourite film?
Hobbies?
Favourite TV programme?
Family?
When students have all the answers, ask them to write a short paragraph outlining what they know about you. Go around, monitor and help where necessary. This will also help you to get an idea of their level.
Best wishes,
Lucy
See also TEFL.net's
Idea Thinktank and in particular:
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15 variations on Find Someone Who and mingling games-
Warmer Ideas