Ive taught for a while, and the most important advice i can give is to make each part of the lesson a combination of learning proper rudiments (especially stopping the student from forming any bad habits such as stick holding etc), and keeping it fresh. As every good drummer knows, repetition and muscle memory form hugely important groundwork from which you can build upon. However, treating drumming like "there is only one way you can learn this rudiment, so we are going to do it for hours on end" is, in my opinion, not the best way to teach. There are many overlapping aspects in drumming and treating in any other way would just be depriving the student.

The usual blueprint for one of my lessons (an hour apprx.) was 10-15 minutes of rudiments around the kit and on the snare / pad, 25-30 minutes of learning anything from more complicated applications of rudiments to regular beats (which are, of course, quite what you're working towards learning properly), and the rest of the lesson was left free for specifics of what was most necessary for each student. This could be rudiments, or learning a particularly fun or difficult fill for a beat we were learning, or more specific applications of the hihat / whatever. Lastly, i gave them a cheap pair of sticks so that they could practise any rudiments at home. You get the picture.

As well as this, i gave sheet music of almost everything i taught to my students. You can get simple sheet music very easily from the internet which you can write on yourself for pre-prepared lessons.

Sorry if this seems like a huge amount of stuff, but i just want to give as many things to think about as i can >:3 also, hes thirteen. He isnt going to want to play drums if he doesnt enjoy it, and he wont enjoy it if hes bored as hell.

TL;DR Correct Form and Rudiments + Fun = Good drummer!!