Oh the wide array of students one music educator will encounter in their teaching career, especially if it's not in the school system setting.
I have experience in the public school setting as a music teacher, as well as an independent music teacher in a music education centre, also on my own. It all depends on the individual as to preference. As an independent music teacher, I set myself up for a wider range of learners in terms of age.
My experience includes teaching youngsters as early as 3.5 years old: at this age they are JUST starting to learn about a few colours they've seen around home, numbers 1, 2, 3, and lessons primarily consists of call-and-response with clapping, connecting sounds with pictures, and pointing. Usually, you don't get many words from them, but if they respond, it'll be with pointing to the answer ...and the answer will be in pictures. :) I find that you can get a good amount done in 10-15 minutes, with a huge focus on rhythm, singing songs for pitch, and more feeling music by dancing showing tempo.
From 4-6, depending on the learner, these kidlings are more developed to understand numbers, basic word connections, and are able to begin Faber's First Piano Adventures with supplemental boardwork and music theory hidden within games. :)
Ages 7-9, usually I begin these students with Faber's Piano Adventures, or if they are gifted, Fletcher's Piano Lessons Have Begun to start note-reading right away.
Students ages 10 and up, depending on learning style and goals, I usually drift towards Faber's Piano Adventures for the Older Beginner. Some students who come to learn with me from a prior teacher, they have Alfred's Beginner Piano Lessons book, which most do not like. I find it moves very fast into playing chords with their LH, and since the LH is the least developed for most people, it's a frustrating path. Faber allows the older student to learn notes, rhythm, and simple known tunes (albiet, not all are the most pleasant to study, so we skip those!) in a slower manner, creating a greater feeling of success. After 'graduating' from this book (with supplemental work in theory booklets), the student then chooses their path they would like to pursue in piano: classical, blues, composition, pop, etc. At this point they should be decent note-readers being able to figure out notes and connect them to the keyboard.
Teens and Youngs Adults, I find have a wonderful self-driven attitude towards music. Usually since it is their own decision to pursue lessons. Practice is usually more consistent, and they uphold their responsibility to putting in the time to learn and practice each week.
Adults have a schedule to adhere to with their everyday lives, so practice may come and go. But adult learners are also very self-driven as they are the ones who actively choose to pursue lessons. They have a more focused learning objective in terms of piano style, and which pieces they would like to accomplish.
Whatever age group you teach, I find it's important that you yourself, as the music educator, enjoys what you're doing! If you're not, you need to change something you're doing, or not doing. Create an environment (as much as you can anyway) that you like going to, being in for long hours, and come up with activities that you and your students can have fun doing together! :)
One artist/teacher once said to me, "if you're not having fun doing it, you're doing it wrong". And if ever I encounter that I'm not happy, I remind myself to take a step back to think of what I can do to change it, from my part.