I will distribute a piece of paper to each of you. Hand down the pieces of paper (In a line composed of two people in each row.). Pass them to the students back. Do you have a piece of paper? OK. Write down your name on the paper. Then take the paper attached to the double-edged tape. Then you can paste the paper on your left chest. Are you done? All right. Let's do the Introducing Game.

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Is my explanation grammatical?
Would you let me know more useful expression?

I'd delete the second sentence. The first and third sentences give all the needed instructions.

Use "double-sided" instead of "double-edged" tape.

Instead of "paste," the word "attach" is better.

"Let's play..." -- not "Let's do..."

Everything else looks good.

=)

Based on the text you provided, your explanation appears to be grammatically correct. However, there are a few minor suggestions to make it clearer and more concise:

1. Instead of saying "Hand down the pieces of paper (In a line composed of two people in each row.)", you can say "Pass the pieces of paper down the line, with two people in each row."
2. Instead of saying "Pass them to the students back", you can say "Pass them back to the students."
3. Instead of asking "Do you have a piece of paper? OK", you can simply say "Now, everyone should have a piece of paper."
4. Instead of saying "Are you done? All right.", you can say "Once you have written your name and attached the paper with double-edged tape, let me know you're finished."

Additionally, here are a few more useful expressions related to giving instructions and explanations:

1. Firstly/First of all/To begin with: Use these phrases to introduce the first step or action.
2. Next/Then/After that: Use these words to transition between steps.
3. Finally/Lastly: Use these phrases to introduce the last step or action.
4. Make sure/Ensure: Use these words to stress the importance of a specific instruction.
5. Attach/Secure/Fix: Use these words instead of "paste" to give clearer instructions on how to attach something.

By incorporating these suggestions and expressions, you can make your explanation clearer and more effective.