Martial Arts has been about money since the '70's here in the states.  Before Jhoon Rhee had his own children saying "Nobody bothers me!" I had never seen any M.A. "advertiszed" on TV. 

Now, what you are doing is being a good human being that just happens to be a Martial Artist.  If your Master is allowing you to do carry on w/ this student then be thankful you have that.  Try talking to the 11 year old's mother to see if there is something she might be able to do for the school.  Can she donate time for promotions?  Like being a greater at the door or something?  Can she provide refreshments?  Make flyers?  Anything that she can do to help out the school and the Master.  This may ease things w/ your instructor. 

Not everyone can afford to pay for their kids to attend a decent TKD Dojang.  But, I wish more schools would look at what people "can" do other then paying.  Trust me, if a kid has a Dad that can do Air conditioning work, maybe he can service the schools system if he can't pay.  If a kid's parents are into construction, maybe get them to fix things around the Dojang for a reduced rate or in exchange for training.  I can't tell you how I often I have seen this sort "swap of services" done in building trades and it benefits both parties.  Paying students will come when word spreads about the commitment to the community the school shows.

Also, as B-H has said, some community groups maybe able to help w/ donations to the school.  You may have to do some leg work but a good place to start would be w/ your local Americans w. Disabilities office.  If you work to help out your Master and your school as well as the child you will win all the way around and so will everyone else.  Heck, get in touch w/ the local paper and see if they will do a write up on the school and it's charity to this 11 year old.  Maybe B_H can give you more advice on how to go about that as well... 

Good luck

There are plenty of scholarship programs out there and other sources of funding programs that can help cover the cost, google them and hopefully one will work for the young lady.

You are right in my mind to step out and offer help but if you are not the school owner or have the owner's permisson to do that type of thing then you shouldn't be doing it. I'm sure that there are plenty of instructors that if they had all the wealth in the world would gladly teach for free but in the world that we live in it doesn't work. Bills need to be paid, food needs to be on the table.

I always laugh when people tell me the purpose of newspaper (to tell the news, to be the governmental watch dog, the fifth estate among others) but the honest reason for a newspaper is to make money.  My job is protected by the bill of rights (freedom of the press) but there are federal and state guidelines on what defines a newspaper to protect the cost of printing.  Most journalism students are shocked to hear that, but when I was a business major that is the first thing that we are told, everything business wise is done for money.

Yes every instructor that I know personally, instructs because they wish to spread their knowledge, but many of them do it as their profession so they have to make ends meet hence charging for class so  most insturctors require I know are equal across the board because they don't want to be seen so showing favoritism because in the US at least it is a sue happy world. 

I feel that you are doing the right thing.  You're trying to guide a young person down the right path.  Remember the tenets:  Courtesy, Integrity, Perserverance, Self Control, & Indomitable Spirit!

You are one heck of a person!! Do what your years of training tells you to do. Follow the tenets in whatever way you feel is right.