今日レッスンの予定はありますか？もしあるなら教えてって英語でなんて言うの？

Accommodate means to fit you into his schedule if he is able.

Open a lesson means you want a lesson with that teacher today.

1. "If you are available for lessons today, could I possibly reserve a slot? " Using the word "if" shows uncertainty and does not seem demanding or impolite. It shows that you intend to ask politely and you are aware that the teacher may be busy. "Possibly"in this case, serves a similar purpose as the word "please." It is very polite! 2. "If you are available today, I am hoping to reserve a lesson with you. Please let me know, thanks!" "I am hoping" suggests that you intend to reserve a lesson, but you are aware that the teacher may be busy, similar to the first answer! "Let me know" is a casual, but also polite way of showing that you look forward to a reply. I hope this helps!!

"Are you available for a lesson today?" asks them if they have time for a lesson. It is not rude. "accommodate me" means to make space for me.

Unbooked slots = lessons that have not yet been reserved, available for booking. Fully booked = All spaces have been taken, no slots available. Open slots = unreserved lessons, open lesson slots that have not been reserved.

>Hi Teacher, do you have any open slots today? I would like to book one. ..................................... Other ways of asking: a.Hi teacher, are you working today? I would like to book a lesson. b.Hi Teacher, do you have any available slots that I can book? ..................*********.................

Both expressions are polite and simple. The second question is more specific and will allow you to know the exact time of an available slot that your teacher has.

Is it possible=可能性がありますか.

There is nothing wrong to ask the question the way you did it. Although I wrote two more examples for you, keep it in mind they are the same version but a bit more polite.