Haskell Harr book One. Easy-peasy. and Harr gets them going through the rudiments as well. Translates easily to other drumset-books all that require reading. The kid is ready for jr. high and high school band as well. Yes reading is very important. He'll thank you later. Math skills aren't required in my opinion. An innate grasp of rhythms could be important because as you play through the simple and gradually-more-difficult stuff, the student will need to hear the teacher's competent playing of the material and try to copy what he/she hears, if there's any initial difficulty.
Frankly--knowing what I know now garnered from my experience with lessons beginning at around age 10 or so--I would totally regret it if my teacher hadn't started out with reading in HH book 1 and moved forward with other books such as the Chapin book, The drummer's Cookbook, the Latham book, etc.. I would've experienced NONE of my band days in Jr. High, Highschool, and College.
Furthermore when I hear and read interviews of drummers such as Steve Gadd, I only regret I didn't start drum lessons earlier. One can only imagine. The sky's the limit, so why limit your student early on???? They're going to limit themselves, probably, later. No, teaching reading is essential. I took some piano prior to starting on drums, and feel that helped when learning but even the lack of any previous formal music notation reading is a terribly poor excuse not to learn reading drum music, and a person could transition to melodic instrument music notation from learning (at first snare) drum music in the beginning.
I have fond memories of my earlier drum teacher writing beats for drumset in my little half-sized spiral-bound staff paper notebook. I still remember him (and later myself) putting drum beats in that notebook. You can put markings for open-hihat, syncopation, and other drum/rhythm concepts in there much more easily than by relying solely on memory(which is important as well, this isn't an either-or situation) when utilizing drum/music notation.
This opens up a huge world. I want to also point out that if your goal with a 7-year-old isn't to help the youngin' to SURPASS one's own drumming abilities, you're doing him/her a terrible dis-service.
Edited by Pounder, 16 March 2017 - 08:46 AM.