After many years of charging per lesson, this year I switched to a “semester” payment plan and I love it. I divide the school year into three semesters (Sept-Dec., Jan-March, and April-June). I send out a schedule of the weeks I will be teaching, times that by my lesson fee, and divide by the number of months in the semester. The student pays the resultant sum at the first lesson of each month. If they miss, it’s up to me whether I will schedule a make up based on their reason for missing. Make ups have to be done within two months. I do not send out any invoices and do everything through email.
Although this sounds incredibly complicated on paper, it works beautfiully and I am fairly compensated for time I have set aside for a student. I have had many fewer cancellations this year, which is obviously good for the student as well.
Summer months I charge per lesson due to vacations and my own out-of-town schedule.