It started with my younger son Duane asking silly questions, as 5-year-olds like to do. The question which started Maggie Math was “What is Maggie plus Maggie?” (Maggie is his younger cousin.)
In the course of playing along with this question (and other similar ones), my older son Henry (who’s 10) invented “Maggie Math” when he realized it was a fun way to explain binary arithmetic to his younger brother.
This is how Maggie Math works:
What’s Maggie + Maggie? Well, there’s only one Maggie, and since we can’t have two, Maggie + Maggie = Duane.
What’s Duane + Maggie? Since Duane and Maggie are different people, there’s no problem. Duane + Maggie is just equal to Duane and Maggie.
What’s Duane and Maggie + Maggie? Well, you can’t have two Maggies, and we know that Maggie + Maggie = Duane. So that gives us Duane + Duane. But we can’t have two Duanes, so that’s Mason (a family friend).
What’s Mason + Maggie? Mason and Maggie.
What’s Mason and Maggie + Maggie? Mason and Duane.
What’s Mason and Duane + Maggie? Mason and Duane and Maggie.
What’s Mason and Duane and Maggie + Maggie? Well, you can’t have two Maggies, and Maggie + Maggie = Duane. So that gives us Mason and Duane + Duane. But we can’t have two Duanes, and we know that Duane + Duane = Mason. So that gives us Mason + Mason. But we can’t have two Masons, because there’s only one Mason. So that gives us … Henry.
I didn’t even realize that Henry knew binary arithmetic before I heard him explaining Maggie Math. I had mentioned it before, but it didn’t really seem to ‘click’ at the time. Now he’s steeped in binary arithmetic. Duane can go thru the first steps of counting in Maggie Math, but then Henry tries to tell him about how it’s all really binary arithmetic and Duane gets all confused. I will advise Henry to be more patient with his pedagogy.
I guess every family develops their own stories and inside jokes. It seems that in this family we invent new forms of mathematics.
A Bewildering Array 
> It seems that in this family we invent new forms of mathematics.
There is nothing new about this. (I’m kidding. Just being a jerk.) That sounds a lot of fun! I think Maggie Math is more interesting than Binary Arithmetic. Unfortunately, it could be difficult to scale, which is a benefit of the already well-established and scaled binary has over Maggie Math…
But it demonstrates a useful concept without bogging someone down with something they might not care about.
I didn’t go thru the whole litany: Henry + Henry = Jed (Mason’s older brother), Jed + Jed = Mommy, and Mommy + Mommy = Daddy. That’s as far as anyone has cared to count in Maggie Math so far, and that’s probably enough: I think that once you’ve gotten that far, you get the idea and are ready for real binary arithmetic.