Answer:
Yes
Explanation
You may not trust a 11 year with a phone, but many parents give 11 year old's their own phone. I feel like you should trust them, and they would be responsible enough. I am a 11 year old myself and got my first phone when I was 10. If you don't fully trust them with that privilege buy them a phone that cant have games and can only call and text emergency numbers and your phone number.