Hi, I’ve received great help on this forum so I’m here with a question for my brother this time. He’s looking for a productive way to fill his summer that focuses on his desired college major: mathematics. He already tutors, so there’s that. Our family is in the economic range where we can’t afford the expensive pre-college programs but we likely wouldn’t get FA for it either. So that’s not likely happening. Someone once suggested he “just go do research with a professor”. Oh, ok. That’s sounds simple. ? Seriously?
I hope to be a vet some day and that offers a LOT of opportunities for great summer activities. However, math is a little more difficult. Hard to find fun or interesting ways to show that you’re focusing on your interest. Any suggestions? (Fun activities or serious ones…we will take any suggestions) FYI, if it matters, my bro is incredibly smart and hardworking and super sweet, so I want to help him out as much as possible. Thanks for your help. 
I wouldn’t assume he won’t get FA, many summer camps give generous aid to families with middle-class income. It doesn’t hurt to inquire. Of course there are also completely free camps like RSI, but they’re very hard to get into. Here’s a good list: https://artofproblemsolving.com/wiki/index.php/Mathematics_summer_program#Math_programs_for_high_school_students
Otherwise it depends on where you live. Our local state university has academic summer camps for kids where high school students can be counselors. Tutoring programs like Kumon hire high school students too. If he has enough tutoring already, he can take summer classes online or in your local community college. Or, you know, just read math books.
Look at your local Colleges and see what they had. My DD attended:
http://archive.dimacs.rutgers.edu/ysp/
Some have scholarships.
He doesn’t have to do something mathy for the summer…colleges want to see you do something productive. Work, Babysit, Attend a camp, Volunteer are all productive things.
I would not say to “just read math books” as something to go on a resume. It is good to do if you like it, but do something productive.