I think there are a lot of your classmates whose name you don't know. You met many of them for the first time in this semester. So I want you to do the Introducing Game. I'll distribute a piece of paper to each of you. There is a piece of double-side tape on the back of the paper. You should write down your name on the paper. You should make your name big so that your friend can see with ease. Make sure your name is big. After that take off the paper attached to the double-side tape. Then you should paste the paper, the name tag on your left chest. After that, I will call your numbers. Number 1,2, and 3. You three come up here and the student in the middle should introduce your friends on both sides. Introduce your friends looking at the name tags. OK. Good job. Go back to your seats.

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Are the expressions above all correct?

I think there are many of your classmates whose names you don't know. You met many of them for the first time in this semester. So I want you to play the Introducing Game. I'll distribute a piece of paper to each of you. There is a piece of double-sided tape on the back of the paper. You should write down your name on the paper. You should make your name big so that your friends can see it with ease. Make sure your name is big.<~~Delete this sentence; you've already said this. After that<~~comma take the double-sided tape off the paper, and paste the paper as a name tag on your left chest. After that, I will call your numbers. Number 1,2, and 3. You three come up here and the student in the middle introduces your friends on both sides. Introduce your friends looking at the name tags. OK. Good job. Go back to your seats.

It's still a bit awkward in a couple of places.

Two instances of "After that" very close together...

The parts about the double-sided tape is confusing. Do you want them to keep the tape on there in order to make the name tag stick to their clothing? If so, then that part needs rephrasing.

The expressions in the given text are mostly correct. However, there are a few minor improvements that can be made for clarity:

1. Instead of saying "I'll distribute a piece of paper to each of you," it would be clearer to say "I will pass out a piece of paper to each of you."

2. Instead of saying "You should write down your name on the paper," it would be more precise to say "Please write your name on the paper."

3. Instead of saying "Make sure your name is big," it would be better to say "Please write your name in large letters."

4. Instead of saying "After that take off the paper attached to the double-side tape," it would be clearer to say "Then remove the paper from the double-sided tape."

5. Instead of saying "You should paste the paper, the name tag on your left chest," it would be more specific to say "Please affix the name tag to the left side of your chest."

Other than these minor tweaks, the expressions in the given text are correct.